Working…
This commit is contained in:
Stefan Kebekus
+18
-13
@@ -49,13 +49,13 @@ example (x y : ℚ) (h : x = y) : x + 1 = y + 1 := by
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Definition 2.1.1 des Skripts:
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> *Definition (Gruppe).* Eine Gruppe ist eine nicht-leere Menge `G`
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> mit einer Abbildung `m : G ⨯ G → G`, sodass folgende Eigenschaften
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> gelten. _Assoziativität:_ … _Neutrales Element:_ Es gibt genau ein
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> Element `e` aus `G`, sodass für alle `a` aus `G` gilt:
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> `m(e,a) = m(a,e) = a`. _Inverse Elemente:_ Für alle `a` aus `G`
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> gibt es genau ein Element `b` aus `G`, sodass `m(a,b) = m(b,a) = e`
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> ist.
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> *Definition (Gruppe).* Eine Gruppe ist eine nicht-leere Menge $`G`
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mit einer Abbildung $`m : G \times G \to G`, sodass folgende
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Eigenschaften gelten. _Assoziativität:_ … _Neutrales Element:_ Es
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gibt genau ein Element $`e` aus $`G`, sodass für alle $`a` aus $`G`
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gilt: $`m(e,a) = m(a,e) = a`. _Inverse Elemente:_ Für alle $`a`
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aus $`G` gibt es genau ein Element $`b` aus $`G`, sodass
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$`m(a,b) = m(b,a) = e` ist.
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In Mathlib ist eine Gruppe eine Typklasse `Group G`. Die Verknüpfung
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schreibt sich `a * b`, das neutrale Element `1`, das Inverse `a⁻¹`;
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@@ -68,9 +68,10 @@ Widerspruch — die Eindeutigkeit folgt aus den übrigen Axiomen. Genau
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das beweisen wir jetzt, mit dem Standardargument aus der linearen
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Algebra:
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> Es sei `e` ein weiteres Element, das von links neutral wirkt. Weil
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> `1` neutral ist, gilt `e·1 = e`. Weil `e` neutral wirkt, gilt
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> `e·1 = 1`. Zusammen folgt `e = e·1 = 1`.
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> Es sei $`e` ein weiteres Element, das von links neutral wirkt.
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Weil $`1` neutral ist, gilt $`e \cdot 1 = e`. Weil $`e` neutral
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wirkt, gilt $`e \cdot 1 = 1`. Zusammen folgt
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$`e = e \cdot 1 = 1`.
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Der Lean-Beweis benutzt die Taktik `calc`, die eine Kette von
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Gleichungen Schritt für Schritt abarbeitet — das Lean-Gegenstück zur
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@@ -87,9 +88,13 @@ theorem neutral_eindeutig {G : Type*} [Group G] (e : G)
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# Übungsaufgabe
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Zeigen Sie ebenso die Eindeutigkeit des Inversen: Wenn `a·b = 1` ist,
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dann ist `b` bereits _das_ Inverse `a⁻¹`. Das Standardargument:
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`b = 1·b = (a⁻¹·a)·b = a⁻¹·(a·b) = a⁻¹·1 = a⁻¹`. Öffnen Sie
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Zeigen Sie ebenso die Eindeutigkeit des Inversen: Wenn
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$`a \cdot b = 1` ist, dann ist $`b` bereits _das_ Inverse $`a^{-1}`.
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Das Standardargument:
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$$`b = 1 \cdot b = (a^{-1} \cdot a) \cdot b = a^{-1} \cdot (a \cdot b) = a^{-1} \cdot 1 = a^{-1}`
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Öffnen Sie
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`AlgebraInLean/Basics.lean` und ersetzen Sie das `sorry` durch einen
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Beweis — `calc` und die Lemmata `one_mul`, `inv_mul_cancel`,
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`mul_assoc`, `mul_one` genügen.
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+49
-43
@@ -29,26 +29,27 @@ ersten Mal selbst etwas in Lean _definieren_: eine Gruppenwirkung.
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# Das zentrale Schlüssellemma
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> *Lemma 18.1.1 (Zentrales Schlüssellemma).* Es sei `m ∈ ℕ` und es sei `p`
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> eine Primzahl. Weiter sei `G` eine Gruppe der Ordnung `p^m`, die auf
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> einer endlichen Menge `M` operiert. Weiter sei
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> `M₀ = { m ∈ M : ∀ g ∈ G: g·m = m }` die Menge der Fixpunkte. Dann
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> ist `|M| ≡ |M₀| (mod p)`.
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> *Lemma 18.1.1 (Zentrales Schlüssellemma).* Es sei
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$`m \in \mathbb{N}` und es sei $`p` eine Primzahl. Weiter sei $`G`
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eine Gruppe der Ordnung $`p^m`, die auf einer endlichen Menge $`M`
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operiert. Weiter sei
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$`M_0 = \{ m \in M : g \cdot m = m \ \forall g \in G \}` die Menge
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der Fixpunkte. Dann ist $`|M| \equiv |M_0| \pmod{p}`.
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Wie sagt Mathlib das alles?
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* „eine Gruppe der Ordnung `p^m`“: Dafür hat Mathlib ein Prädikat
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`IsPGroup p G` („die Ordnung jedes Elements ist eine p-Potenz“ — für
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endliche Gruppen ist das äquivalent, nach dem Satz von Cauchy
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unten!). Das Lemma `IsPGroup.of_card` übersetzt unsere
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Voraussetzung `Nat.card G = p ^ m` dorthin.
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* „eine Gruppe der Ordnung $`p^m`“: Dafür hat Mathlib ein Prädikat
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`IsPGroup p G` („die Ordnung jedes Elements ist eine
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$`p`-Potenz“ — für endliche Gruppen ist das äquivalent, nach dem
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Satz von Cauchy unten!). Das Lemma `IsPGroup.of_card` übersetzt
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unsere Voraussetzung `Nat.card G = p ^ m` dorthin.
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* „die auf einer endlichen Menge `M` operiert“: Eine Wirkung von `G`
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auf `M` ist eine Typklasse, `[MulAction G M]`; die Endlichkeit von
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`M` ist die Typklasse `[Finite M]`.
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* Die Fixpunktmenge heißt `MulAction.fixedPoints G M`, und die
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Kongruenz `|M| ≡ |M₀| (mod p)` schreibt sich
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Kongruenz $`|M| \equiv |M_0| \pmod{p}` schreibt sich
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`Nat.card M ≡ Nat.card (fixedPoints G M) [MOD p]`.
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Der Beweis im Skript zerlegt `M` in Bahnen und zitiert die
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@@ -75,8 +76,9 @@ gleich auf.)
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# Der Satz von Cauchy
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> *Satz 18.1.2 (Satz von Cauchy).* Wenn die Ordnung einer endlichen Gruppe
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> durch `p` teilbar ist, dann existiert ein Element von Ordnung `p`.
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> *Satz 18.1.2 (Satz von Cauchy).* Wenn die Ordnung einer endlichen
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Gruppe durch $`p` teilbar ist, dann existiert ein Element von
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Ordnung $`p`.
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Wir folgen dem Beweis des Skripts Satz für Satz. Der Beweis
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konstruiert eine raffinierte Hilfsmenge mit einer raffinierten
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@@ -86,22 +88,23 @@ Arbeit: Wir bauen erst die Menge und die Wirkung.
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## Die Menge M
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„Betrachte die Menge
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`M = { (a₁, …, a_p) ∈ G ⨯ ⋯ ⨯ G : a₁·a₂ ⋯ a_p = e }`.“
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$`M = \bigl\{ (a_1, \dots, a_p) \in G \times \dots \times G : a_1 \cdot a_2 \cdots a_p = e \bigr\}`.“
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Mathlib kennt diese Menge. Ein p-Tupel von Gruppenelementen ist ein
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`List.Vector G p` — eine Liste der Länge `p` —, und `M` ist die Menge
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`Equiv.Perm.vectorsProdEqOne G p` aller Vektoren, deren Einträge sich
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zu 1 multiplizieren.
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Mathlib kennt diese Menge. Ein $`p`-Tupel von Gruppenelementen ist
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ein `List.Vector G p` — eine Liste der Länge $`p` —, und $`M` ist die
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Menge `Equiv.Perm.vectorsProdEqOne G p` aller Vektoren, deren
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Einträge sich zu 1 multiplizieren.
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„Gegeben ein Tupel `(a₁, …, a_p) ∈ M`, dann stellen wir erst einmal
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fest, dass der letzte Eintrag des Tupels durch die ersten Einträge
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eindeutig bestimmt ist, `a_p = (a₁ ⋯ a_{p-1})⁻¹`. Wir erhalten die
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folgende Gleichung: `|M| = |G^{p-1}| = |G|^{p-1}`.“
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„Gegeben ein Tupel $`(a_1, \dots, a_p) \in M`, dann stellen wir erst
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einmal fest, dass der letzte Eintrag des Tupels durch die ersten
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Einträge eindeutig bestimmt ist,
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$`a_p = (a_1 \cdots a_{p-1})^{-1}`. Wir erhalten die folgende
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Gleichung: $`|M| = |G^{p-1}| = |G|^{p-1}`.“
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Auch das steht schon in Mathlib: Die Bijektion
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`(a₁, …, a_{p-1}) ↦ (a₁, …, a_{p-1}, (a₁ ⋯ a_{p-1})⁻¹)` heißt
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`VectorsProdEqOne.vectorEquiv`, und die resultierende Zählformel ist
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`VectorsProdEqOne.card`:
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$`(a_1, \dots, a_{p-1}) \mapsto (a_1, \dots, a_{p-1}, (a_1 \cdots a_{p-1})^{-1})`
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heißt `VectorsProdEqOne.vectorEquiv`, und die resultierende
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Zählformel ist `VectorsProdEqOne.card`:
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```
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VectorsProdEqOne.card (G : Type) [Group G] (n : ℕ) [Fintype G] :
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@@ -112,22 +115,25 @@ VectorsProdEqOne.card (G : Type) [Group G] (n : ℕ) [Fintype G] :
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„Als Nächstes brauchen wir eine schicke Gruppenwirkung, denn wir
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wollen das zentrale Schlüssellemma anwenden. Dazu lassen wir die
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zyklische Gruppe `ℤ/(p)` auf `M` durch zyklisches Vertauschen wirken.“
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zyklische Gruppe $`\mathbb{Z}/(p)` auf $`M` durch zyklisches
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Vertauschen wirken.“
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Der zyklische Shift eines Vektors `v ∈ vectorsProdEqOne G p` um `k`
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Stellen ist `VectorsProdEqOne.rotate v k`. Die Fußnote des Skripts —
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der Shift bildet `M` auf sich ab, „weil in jeder Gruppe aus `a·b = e`
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auch `b·a = e` gilt“ — ist das Mathlib-Lemma
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Der zyklische Shift eines Vektors `v ∈ vectorsProdEqOne G p` um
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$`k` Stellen ist `VectorsProdEqOne.rotate v k`. Die Fußnote des
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Skripts — der Shift bildet $`M` auf sich ab, „weil in jeder Gruppe
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aus $`a \cdot b = e` auch $`b \cdot a = e` gilt“ — ist das
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Mathlib-Lemma
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`List.prod_rotate_eq_one_of_prod_eq_one`, das schon in der Definition
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von `rotate` steckt.
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Damit `ℤ/(p)` _als Gruppe_ wirkt, müssen wir die Wirkungsaxiome
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nachprüfen: Der Shift um 0 tut nichts, und der Shift um `j + k` ist
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der Shift um `k` gefolgt vom Shift um `j`. Mathlib stellt
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`rotate_zero`, `rotate_rotate` und `rotate_length` bereit (der Shift
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um die volle Länge `p` tut nichts); daraus leiten wir zuerst ab, dass
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der Shift nur von der Verschiebung _modulo p_ abhängt — genau deshalb
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wirkt `ℤ/(p)` und nicht bloß `ℕ`.
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Damit $`\mathbb{Z}/(p)` _als Gruppe_ wirkt, müssen wir die
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Wirkungsaxiome nachprüfen: Der Shift um 0 tut nichts, und der Shift
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um $`j + k` ist der Shift um $`k` gefolgt vom Shift um $`j`. Mathlib
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stellt `rotate_zero`, `rotate_rotate` und `rotate_length` bereit (der
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Shift um die volle Länge $`p` tut nichts); daraus leiten wir zuerst
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ab, dass der Shift nur von der Verschiebung _modulo p_ abhängt —
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genau deshalb wirkt $`\mathbb{Z}/(p)` und nicht bloß
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$`\mathbb{N}`.
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```lean
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theorem rotate_mul {G : Type*} [Group G] {p : ℕ}
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@@ -151,7 +157,7 @@ theorem rotate_mod {G : Type*} [Group G] {p : ℕ}
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Nun können wir die Wirkung definieren. Zwei technische Anmerkungen.
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Mathlibs `MulAction` erwartet eine multiplikativ geschriebene Gruppe;
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`ℤ/(p)` = `ZMod p` ist aber additiv geschrieben. Der Wrapper
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$`\mathbb{Z}/(p)` = `ZMod p` ist aber additiv geschrieben. Der Wrapper
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`Multiplicative` wechselt die Notation (dank
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`open Multiplicative` oben schreiben sich seine Übergänge kurz
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`toAdd` und `ofAdd`). Die Voraussetzung `[NeZero p]` schließt
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@@ -176,13 +182,13 @@ instance rotateAction {G : Type*} [Group G] {p : ℕ}
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## Die Fixpunkte
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„Die Fixpunktmenge dieser Wirkung ist
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`M₀ = { (a, …, a) ∈ G^p : a^p = e }`.“
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$`M_0 = \{ (a, \dots, a) \in G^p : a^p = e \}`.“
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Mit anderen Worten: Ein Tupel ist genau dann ein Fixpunkt, wenn es
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konstant ist, seine Liste also für ein `a` die Liste
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`List.replicate p a` — das ist `(a, …, a)` — ist. (Die Bedingung
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`a^p = e` gilt dann automatisch, weil sich die Einträge eines Tupels
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in `M` zu `e` multiplizieren.) Der Schlüsselschritt ist das Lemma
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konstant ist, seine Liste also für ein $`a` die Liste
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`List.replicate p a` — das ist $`(a, \dots, a)` — ist. (Die
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Bedingung $`a^p = e` gilt dann automatisch, weil sich die Einträge
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eines Tupels in $`M` zu $`e` multiplizieren.) Der Schlüsselschritt ist das Lemma
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`List.rotate_one_eq_self_iff_eq_replicate`: Eine Liste, die der
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zyklische Shift um _eine_ Stelle nicht ändert, ist konstant.
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+30
-26
@@ -27,34 +27,37 @@ und Körpererweiterungen als Vektorräume.
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# Das Mathlib-Wörterbuch
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* Eine Körpererweiterung `L/K` ist in Mathlib eine
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`Algebra K L`-Instanz zwischen zwei Körpern — `L` wird damit
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insbesondere ein K-Vektorraum, genau wie im Skript.
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* Eine Körpererweiterung $`L/K` ist in Mathlib eine
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`Algebra K L`-Instanz zwischen zwei Körpern — $`L` wird damit
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insbesondere ein $`K`-Vektorraum, genau wie im Skript.
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* Eine Kette `K ⊆ L ⊆ M` besteht aus drei Algebra-Instanzen und der
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Verträglichkeitsbedingung `IsScalarTower K L M` („erst nach `L`,
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dann nach `M` einbetten ist dasselbe wie direkt nach `M`“).
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* Eine Kette $`K \subseteq L \subseteq M` besteht aus drei
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Algebra-Instanzen und der Verträglichkeitsbedingung
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`IsScalarTower K L M` („erst nach $`L`, dann nach $`M` einbetten
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ist dasselbe wie direkt nach $`M`“).
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* Der Grad `[L:K]` heißt `Module.finrank K L`. Achtung, hier weicht
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die Konvention vom Skript ab: `finrank` hat Werte in `ℕ`, und
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unendlichdimensionale Erweiterungen bekommen den Wert 0 — wo das
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Skript in seiner Fußnote mit `∞` rechnet, rechnet Mathlib mit 0.
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„`[L:K]` ist endlich“ ist die Typklasse `FiniteDimensional K L`.
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* Der Grad $`[L:K]` heißt `Module.finrank K L`. Achtung, hier weicht
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die Konvention vom Skript ab: `finrank` hat Werte in $`\mathbb{N}`,
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und unendlichdimensionale Erweiterungen bekommen den Wert 0 — wo
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das Skript in seiner Fußnote mit $`\infty` rechnet, rechnet Mathlib
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mit 0. „$`[L:K]` ist endlich“ ist die Typklasse
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`FiniteDimensional K L`.
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# Die Gradformel
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Satz 3.6.1 des Skripts, mit Beweis:
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> *Satz 3.6.1 (Gradformel).* Es sei `K ⊆ L ⊆ M` eine Kette von
|
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> Körpererweiterungen. Dann gilt die Gleichung
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> `[M:K] = [M:L]·[L:K]`.
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>
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> *Satz 3.6.1 (Gradformel).* Es sei $`K \subseteq L \subseteq M` eine
|
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Kette von Körpererweiterungen. Dann gilt die Gleichung
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$`[M:K] = [M:L] \cdot [L:K]`.
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> _Beweis._ Wir kümmern uns zuerst um die unendlichen Fälle. … Es
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> seien jetzt also `a := [L:K]` und `b := [M:L]` beide endlich. Wähle
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> Basen `ℓ₁, …, ℓ_a` von `L` als K-Vektorraum und `m₁, …, m_b` von `M`
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> als L-Vektorraum. Ich behaupte, dass die `a·b` Produkte `(ℓᵢ·mⱼ)`
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> eine Basis von `M` als K-Vektorraum bilden; damit ist dann sofort
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> `[M:K] = a·b` gezeigt.
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seien jetzt also $`a := [L:K]` und $`b := [M:L]` beide endlich.
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Wähle Basen $`\ell_1, \dots, \ell_a` von $`L` als
|
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$`K`-Vektorraum und $`m_1, \dots, m_b` von $`M` als
|
||||
$`L`-Vektorraum. Ich behaupte, dass die $`a \cdot b` Produkte
|
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$`(\ell_i \cdot m_j)` eine Basis von $`M` als $`K`-Vektorraum
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bilden; damit ist dann sofort $`[M:K] = a \cdot b` gezeigt.
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Die unendlichen Fälle entfallen in unserer Fassung, weil wir
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Endlichkeit voraussetzen; in Mathlibs 0-Konvention gilt die Formel
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@@ -63,8 +66,9 @@ sogar uneingeschränkt (`Module.finrank_mul_finrank`).
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Die Behauptung — mit den beiden Beweisschritten „Die Produkte bilden
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ein Erzeugendensystem“ und „Die Produkte sind linear unabhängig“ —
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ist in Mathlib die Konstruktion `Basis.smulTower`: Aus einer Basis
|
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`ℓ` von `L/K` und einer Basis `m` von `M/L` baut sie die Basis
|
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`(ℓᵢ • mⱼ)` von `M/K` (das Lemma `Basis.smulTower_apply` bestätigt,
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$`\ell` von $`L/K` und einer Basis $`m` von $`M/L` baut sie die
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Basis $`(\ell_i \cdot m_j)` von $`M/K` (das Lemma
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`Basis.smulTower_apply` bestätigt,
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dass die Basiselemente wirklich die Produkte sind). Der Rest ist
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Abzählen der Indexmenge.
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@@ -101,12 +105,12 @@ Skript.
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|
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Das erste Korollar des Skripts zur Gradformel:
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|
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> Es sei `K ⊆ L ⊆ M` eine Kette von Körpererweiterungen. Wenn
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> `[M:K]` endlich ist, dann ist `[L:K]` endlich, und sogar ein Teiler
|
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> von `[M:K]`.
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> Es sei $`K \subseteq L \subseteq M` eine Kette von
|
||||
Körpererweiterungen. Wenn $`[M:K]` endlich ist, dann ist
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||||
$`[L:K]` endlich, und sogar ein Teiler von $`[M:K]`.
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|
||||
Der erste Teil ist `Module.Finite.left` (und `Module.Finite.right`
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liefert die Endlichkeit von `[M:L]`) — beide müssen mit `have := …`
|
||||
liefert die Endlichkeit von $`[M:L]`) — beide müssen mit `have := …`
|
||||
in den Kontext geholt werden, damit die Instanzsuche sie sieht. Der
|
||||
Teiler-Teil ist die Übung: Öffnen Sie `AlgebraInLean/Degrees.lean`
|
||||
und ersetzen Sie das `sorry` durch einen Beweis mit `gradformel`.
|
||||
|
||||
+23
-19
@@ -22,13 +22,13 @@ file := "frobenius"
|
||||
|
||||
Dieses Kapitel übersetzt den Satz über den Frobenius-Endomorphismus
|
||||
aus Kapitel 14 des Skripts Satz für Satz nach Lean — den „Traum jedes
|
||||
Studienanfängers“: `(a+b)^p = a^p + b^p`.
|
||||
Studienanfängers“: $`(a+b)^p = a^p + b^p`.
|
||||
|
||||
# Das Mathlib-Wörterbuch
|
||||
|
||||
* „`R` hat Charakteristik `p`“ ist die Typklasse `CharP R p`. Das
|
||||
entscheidende Lemma ist `CharP.cast_eq_zero`: Das Bild von `p` in
|
||||
`R` ist Null.
|
||||
* „$`R` hat Charakteristik $`p`“ ist die Typklasse `CharP R p`.
|
||||
Das entscheidende Lemma ist `CharP.cast_eq_zero`: Das Bild von
|
||||
$`p` in $`R` ist Null.
|
||||
|
||||
* Binomialkoeffizienten heißen `Nat.choose`; die binomische Formel
|
||||
ist `add_pow`, eine Summe über `Finset.range`. Endliche Summen und
|
||||
@@ -38,19 +38,22 @@ Studienanfängers“: `(a+b)^p = a^p + b^p`.
|
||||
|
||||
Satz und Definition 14.2.2 des Skripts:
|
||||
|
||||
> *Satz und Definition 14.2.2 (Frobenius-Endomorphismus).* Es sei `p` eine
|
||||
> Primzahl und es sei `R` ein kommutativer Ring mit Eins der
|
||||
> Charakteristik `p`. Dann ist die Abbildung `F : R → R`, `a ↦ a^p`
|
||||
> ein Ringmorphismus.
|
||||
>
|
||||
> _Beweis._ Die Verträglichkeit mit der Multiplikation ist klar, weil
|
||||
> `R` kommutativ ist: `(a·b)^p = a^p·b^p`. Ebenso ist `F(1) = 1`.
|
||||
> Interessant ist nur die Verträglichkeit mit der Addition. … Die
|
||||
> binomische Formel gilt in jedem kommutativen Ring …. Für alle
|
||||
> Indizes `0 < k < p` ist der Binomialkoeffizient ein Vielfaches von
|
||||
> `p` …. Weil `R` die Charakteristik `p` hat, ist `p = 0` in `R`,
|
||||
> und alle diese Summanden verschwinden. Übrig bleiben nur die
|
||||
> Summanden für `k = 0` und `k = p`.
|
||||
> *Satz und Definition 14.2.2 (Frobenius-Endomorphismus).* Es sei
|
||||
$`p` eine Primzahl und es sei $`R` ein kommutativer Ring mit Eins
|
||||
der Charakteristik $`p`. Dann ist die Abbildung
|
||||
$`F : R \to R`, $`a \mapsto a^p` ein Ringmorphismus.
|
||||
|
||||
> _Beweis._ Die Verträglichkeit mit der Multiplikation ist klar,
|
||||
weil $`R` kommutativ ist: $`(a \cdot b)^p = a^p \cdot b^p`.
|
||||
Ebenso ist $`F(1) = 1`. Interessant ist nur die Verträglichkeit
|
||||
mit der Addition. … Die binomische Formel gilt in jedem
|
||||
kommutativen Ring, also ist
|
||||
$`(a+b)^p = \sum_{k=0}^{p} \binom{p}{k} \cdot a^k \cdot b^{p-k}`.
|
||||
Für alle Indizes $`0 < k < p` ist der Binomialkoeffizient
|
||||
$`\binom{p}{k}` ein Vielfaches von $`p` …. Weil $`R` die
|
||||
Charakteristik $`p` hat, ist $`p = 0` in $`R`, und alle diese
|
||||
Summanden verschwinden. Übrig bleiben nur die Summanden für
|
||||
$`k = 0` und $`k = p`.
|
||||
|
||||
```lean
|
||||
theorem frobenius_mul {R : Type*} [CommRing R] (p : ℕ)
|
||||
@@ -115,8 +118,9 @@ Elementen. In Mathlib heißt er `GaloisField p n`.
|
||||
|
||||
# Übungsaufgabe
|
||||
|
||||
Der Frobenius des Körpers `𝔽_p` ist die Identität: Für jedes
|
||||
`a ∈ 𝔽_p` ist `a^p = a`. Das ist ein alter Bekannter — der kleine
|
||||
Der Frobenius des Körpers $`\mathbb{F}_p` ist die Identität: Für
|
||||
jedes $`a \in \mathbb{F}_p` ist $`a^p = a`. Das ist ein alter
|
||||
Bekannter — der kleine
|
||||
Satz von Fermat aus unserem dritten Kapitel! In Mathlib heißt er
|
||||
`ZMod.pow_card`. Öffnen Sie `AlgebraInLean/Frobenius.lean` und
|
||||
ersetzen Sie das `sorry` durch einen Beweis.
|
||||
|
||||
+22
-15
@@ -28,11 +28,11 @@ ist und es auch hier bleibt.
|
||||
|
||||
# Das Mathlib-Wörterbuch
|
||||
|
||||
* Die Galoisgruppe einer Körpererweiterung `L/K` ist der Typ
|
||||
* Die Galoisgruppe einer Körpererweiterung $`L/K` ist der Typ
|
||||
`L ≃ₐ[K] L` der K-Algebren-Automorphismen; Mathlib stellt dafür
|
||||
sogar die Notation `Gal(L/K)` bereit.
|
||||
|
||||
* „`L/K` ist galoissch“ ist die Typklasse `IsGalois K L` — definiert
|
||||
* „$`L/K` ist galoissch“ ist die Typklasse `IsGalois K L` — definiert
|
||||
als „separabel und normal“, genau wie im Skript.
|
||||
|
||||
* Ein Zwischenkörper ist ein Term `Z : IntermediateField K L`; der
|
||||
@@ -43,10 +43,12 @@ ist und es auch hier bleibt.
|
||||
|
||||
Satz und Definition 16.1.1 des Skripts:
|
||||
|
||||
> *Satz und Definition 16.1.1 (Invariante Elemente, Fixkörper).* Sei `L` ein
|
||||
> Körper und `G` eine Menge von Automorphismen `L → L`. Dann ist die
|
||||
> Menge `Fix G = { a ∈ L : σ(a) = a für alle σ ∈ G }` ein Unterkörper
|
||||
> von `L`. … Der Beweis des folgenden Satzes ist eine Hausaufgabe.
|
||||
> *Satz und Definition 16.1.1 (Invariante Elemente, Fixkörper).* Sei
|
||||
$`L` ein Körper und $`G` eine Menge von Automorphismen
|
||||
$`L \to L`. Dann ist die Menge
|
||||
$`\operatorname{Fix} G = \{ a \in L : \sigma(a) = a \ \forall \sigma \in G \}`
|
||||
ein Unterkörper von $`L`. … Der Beweis des folgenden Satzes ist
|
||||
eine Hausaufgabe.
|
||||
|
||||
Wir definieren die Menge in Lean und beweisen exemplarisch die
|
||||
Abgeschlossenheit unter der Multiplikation — der Rest der Hausaufgabe
|
||||
@@ -71,23 +73,28 @@ theorem mul_mem_fix {L : Type*} [Field L]
|
||||
Auch die großen Sätze dieses Teils der Vorlesung stehen in Mathlib;
|
||||
wir zitieren sie mit ihren Namen.
|
||||
|
||||
> *Satz von Emil Artin (Satz 16.1.2).* Es sei `G` eine endliche Untergruppe der
|
||||
> Automorphismengruppe eines Körpers `L` und es sei `K := Fix G`.
|
||||
> Dann ist `L/K` eine Galoiserweiterung mit Galoisgruppe
|
||||
> `Gal(L/K) = G`. Insbesondere ist `[L:K] = |G|`.
|
||||
> *Satz von Emil Artin (Satz 16.1.2).* Es sei $`G` eine endliche
|
||||
Untergruppe der Automorphismengruppe eines Körpers $`L` und es sei
|
||||
$`K := \operatorname{Fix} G`. Dann ist $`L/K` eine
|
||||
Galoiserweiterung mit Galoisgruppe
|
||||
$`\operatorname{Gal}(L/K) = G`. Insbesondere ist
|
||||
$`[L:K] = |G|`.
|
||||
|
||||
Die Gradaussage ist `FixedPoints.finrank_eq_card`; das gebündelte
|
||||
Fixkörper-Objekt heißt dort `FixedPoints.subfield G L`.
|
||||
|
||||
> *Hauptsatz der Galoistheorie (Satz 16.3.2).* Es sei `L/K` eine Galoiserweiterung
|
||||
> mit Galoisgruppe `G`. Dann sind die Abbildungen `Z ↦ Gal(L/Z)` und
|
||||
> `H ↦ Fix H` zueinander inverse, inklusionsumkehrende Bijektionen
|
||||
> zwischen Zwischenkörpern und Untergruppen. …
|
||||
> *Hauptsatz der Galoistheorie (Satz 16.3.2).* Es sei $`L/K` eine
|
||||
Galoiserweiterung mit Galoisgruppe $`G`. Dann sind die Abbildungen
|
||||
$`Z \mapsto \operatorname{Gal}(L/Z)` und
|
||||
$`H \mapsto \operatorname{Fix} H` zueinander inverse,
|
||||
inklusionsumkehrende Bijektionen zwischen Zwischenkörpern und
|
||||
Untergruppen. …
|
||||
|
||||
In Mathlib ist das der ordnungsumkehrende Isomorphismus
|
||||
`IsGalois.intermediateFieldEquivSubgroup`; das „ᵒᵈ“ (_order dual_)
|
||||
in seinem Typ ist genau das „inklusionsumkehrend“ des Skripts. Die
|
||||
Gradaussage `|Gal(L/K)| = [L:K]` für Galoiserweiterungen heißt
|
||||
Gradaussage $`|\operatorname{Gal}(L/K)| = [L:K]` für
|
||||
Galoiserweiterungen heißt
|
||||
`IsGalois.card_aut_eq_finrank`:
|
||||
|
||||
```lean
|
||||
|
||||
+16
-14
@@ -31,7 +31,7 @@ Lean.
|
||||
* Ein Ideal in einem kommutativen Ring `R` ist ein Term
|
||||
`I : Ideal R`. Die beiden Bedingungen aus der Ideal-Definition des
|
||||
Skripts heißen `I.add_mem` (für alle `a, b ∈ I` ist `a+b ∈ I`) und
|
||||
`I.mul_mem_left` (für alle `r ∈ R` und `a ∈ I` ist `r·a ∈ I`);
|
||||
`I.mul_mem_left` (für alle $`r \in R` und $`a \in I` ist $`r \cdot a \in I`);
|
||||
außerdem ist `I.zero_mem : 0 ∈ I`.
|
||||
|
||||
* Das von einer Menge `s` erzeugte Ideal ist `Ideal.span s`; ein
|
||||
@@ -46,15 +46,16 @@ Lean.
|
||||
|
||||
Satz 9.3.7 des Skripts, mit Beweis:
|
||||
|
||||
> Es sei `I ⊂ ℤ` ein Ideal und `I ≠ {0}`. Dann gibt es ein
|
||||
> `x ∈ I∖{0}`. Beachte, dass dann auch `−x = (−1)·x` in `I` ist.
|
||||
> Also enthält `I` positive Elemente. Sei `a ∈ I` jetzt das kleinste
|
||||
> positive Element. Wir werden zeigen, dass `I = (a)` ist. Die
|
||||
> Inklusion `(a) ⊆ I` ist klar. Sei `b ∈ I` irgendein positives
|
||||
> Element, dann teilen wir mit Rest: `b = q·a + r` mit `0 ≤ r < a`.
|
||||
> Die Zahl `r` ist jetzt aber in `I`, denn `b` und `q·a` sind in `I`.
|
||||
> Weiter muss wegen der Minimalität von `a` also `r = 0` sein und
|
||||
> somit `b ∈ (a)`.
|
||||
> Es sei $`I \subset \mathbb{Z}` ein Ideal und $`I \neq \{0\}`.
|
||||
Dann gibt es ein $`x \in I \setminus \{0\}`. Beachte, dass dann
|
||||
auch $`-x = (-1) \cdot x` in $`I` ist. Also enthält $`I` positive
|
||||
Elemente. Sei $`a \in I` jetzt das kleinste positive Element. Wir
|
||||
werden zeigen, dass $`I = (a)` ist. Die Inklusion
|
||||
$`(a) \subseteq I` ist klar. Sei $`b \in I` irgendein positives
|
||||
Element, dann teilen wir mit Rest: $`b = q \cdot a + r` mit
|
||||
$`0 \leq r < a`. Die Zahl $`r` ist jetzt aber in $`I`, denn $`b`
|
||||
und $`q \cdot a` sind in $`I`. Weiter muss wegen der Minimalität
|
||||
von $`a` also $`r = 0` sein und somit $`b \in (a)`.
|
||||
|
||||
Zwei Anmerkungen zur Übersetzung. Das „kleinste positive Element“
|
||||
liefert das Wohlordnungsprinzip, in Mathlib
|
||||
@@ -133,10 +134,11 @@ aus diesem Kapitel steht in Mathlib: `Polynomial.isNoetherianRing`.
|
||||
|
||||
Das Beispiel „Triviale Ideale“ des Skripts:
|
||||
|
||||
> Wenn `R` ein Körper und `I ⊂ R` ein Ideal ist und `a ∈ I∖{0}`,
|
||||
> dann ist auch jedes andere Körperelement in `I`. Sei nämlich
|
||||
> irgendein Element `r ∈ R` gegeben. Nach Definition ist
|
||||
> `r = (r·a⁻¹)·a ∈ I`. Also ist `I = R`.
|
||||
> Wenn $`R` ein Körper und $`I \subset R` ein Ideal ist und
|
||||
$`a \in I \setminus \{0\}`, dann ist auch jedes andere
|
||||
Körperelement in $`I`. Sei nämlich irgendein Element $`r \in R`
|
||||
gegeben. Nach Definition ist
|
||||
$`r = (r \cdot a^{-1}) \cdot a \in I`. Also ist $`I = R`.
|
||||
|
||||
Übersetzen Sie dieses Argument: Öffnen Sie
|
||||
`AlgebraInLean/Ideals.lean` und ersetzen Sie das `sorry` durch einen
|
||||
|
||||
+28
-24
@@ -21,16 +21,20 @@ file := "little-fermat"
|
||||
Unser erster Beweis übersetzt Satz 17.5.1 des Skripts. Hier das
|
||||
deutsche Original, Aussage und Beweis:
|
||||
|
||||
> *Satz 17.5.1 (Kleiner Satz von Fermat).* Es sei `p ∈ ℕ` eine Primzahl und es
|
||||
> sei `a ∈ ℤ` irgendeine Zahl. Dann ist `a^p ≡ a (mod p)`.
|
||||
>
|
||||
> _Beweis._ Falls `a` ein Vielfaches von `p` ist, ist die Sache klar.
|
||||
> Ansonsten liefert die Restklasse von `a` ein nicht-verschwindendes
|
||||
> Element `ā ∈ ℤ/(p) = 𝔽_p`, also ein Element der multiplikativen
|
||||
> Gruppe `𝔽_p^*`, welche `p−1` Elemente hat. Nach dem Satz von
|
||||
> Lagrange ist die Ordnung von `ā`, also die Größe der von `ā`
|
||||
> erzeugten Untergruppe, ein Teiler von `|𝔽_p^*| = p−1`. Es gilt also
|
||||
> `ā^(p−1) = 1 ∈ 𝔽_p^*`, oder äquivalent `a^p ≡ a (mod p)`. ∎
|
||||
> *Satz 17.5.1 (Kleiner Satz von Fermat).* Es sei $`p \in \mathbb{N}`
|
||||
eine Primzahl und es sei $`a \in \mathbb{Z}` irgendeine Zahl. Dann
|
||||
ist $`a^p \equiv a \pmod{p}`.
|
||||
|
||||
> _Beweis._ Falls $`a` ein Vielfaches von $`p` ist, ist die Sache
|
||||
klar. Ansonsten liefert die Restklasse von $`a` ein
|
||||
nicht-verschwindendes Element
|
||||
$`\overline{a} \in \mathbb{Z}/(p) = \mathbb{F}_p`, also ein Element
|
||||
der multiplikativen Gruppe $`\mathbb{F}_p^*`, welche $`p-1` Elemente
|
||||
hat. Nach dem Satz von Lagrange ist die Ordnung von
|
||||
$`\overline{a}`, also die Größe der von $`\overline{a}` erzeugten
|
||||
Untergruppe, ein Teiler von $`|\mathbb{F}_p^*| = p-1`. Es gilt also
|
||||
$`\overline{a}^{p-1} = 1 \in \mathbb{F}_p^*`, oder äquivalent
|
||||
$`a^p \equiv a \pmod{p}`. ∎
|
||||
|
||||
Fünf Sätze. Unser Ziel ist ein Lean-Beweis mit genau dieser Struktur —
|
||||
jeder deutsche Satz kehrt als Kommentar über dem Lean-Code wieder, der
|
||||
@@ -41,24 +45,24 @@ ihn umsetzt.
|
||||
Bevor wir den Satz überhaupt formulieren können, müssen wir wissen, wie
|
||||
Mathlib über die beteiligten Objekte spricht.
|
||||
|
||||
* Der Restklassenring `ℤ/(p)` heißt `ZMod p`. Die Restklasse einer
|
||||
ganzen Zahl `a : ℤ` schreibt sich `(a : ZMod p)` — Lean fügt den
|
||||
kanonischen Ringmorphismus `ℤ → ℤ/(p)` automatisch ein (eine
|
||||
_Koerzion_).
|
||||
* Der Restklassenring $`\mathbb{Z}/(p)` heißt `ZMod p`. Die
|
||||
Restklasse einer ganzen Zahl `a : ℤ` schreibt sich `(a : ZMod p)` —
|
||||
Lean fügt den kanonischen Ringmorphismus
|
||||
$`\mathbb{Z} \to \mathbb{Z}/(p)` automatisch ein (eine _Koerzion_).
|
||||
|
||||
* Die Kongruenz `a ≡ b (mod p)` für ganze Zahlen schreibt sich
|
||||
* Die Kongruenz $`a \equiv b \pmod{p}` für ganze Zahlen schreibt sich
|
||||
`a ≡ b [ZMOD p]`.
|
||||
|
||||
* Die multiplikative Gruppe `𝔽_p^*` ist die Gruppe der _Einheiten_ des
|
||||
Rings `ZMod p`, geschrieben `(ZMod p)ˣ`. Eine Einheit
|
||||
`u : (ZMod p)ˣ` kennt ihr Inverses; das zugrundeliegende Ringelement
|
||||
schreibt sich wieder `(u : ZMod p)`.
|
||||
* Die multiplikative Gruppe $`\mathbb{F}_p^*` ist die Gruppe der
|
||||
_Einheiten_ des Rings `ZMod p`, geschrieben `(ZMod p)ˣ`. Eine
|
||||
Einheit `u : (ZMod p)ˣ` kennt ihr Inverses; das zugrundeliegende
|
||||
Ringelement schreibt sich wieder `(u : ZMod p)`.
|
||||
|
||||
* Das Skript sagt „es sei `p` eine Primzahl“. In Lean führen wir die
|
||||
* Das Skript sagt „es sei $`p` eine Primzahl“. In Lean führen wir die
|
||||
Primalität von `p` als Hypothese `hp : p.Prime` mit. Manche
|
||||
Tatsachen — etwa dass `ℤ/(p)` ein Körper ist — findet Leans
|
||||
Automatisierung nur, wenn die Hypothese als _Instanz_ registriert
|
||||
ist; genau das leistet die erste Beweiszeile
|
||||
Tatsachen — etwa dass $`\mathbb{Z}/(p)` ein Körper ist — findet
|
||||
Leans Automatisierung nur, wenn die Hypothese als _Instanz_
|
||||
registriert ist; genau das leistet die erste Beweiszeile
|
||||
`have : Fact p.Prime := ⟨hp⟩`.
|
||||
|
||||
# Der Beweis, Satz für Satz
|
||||
@@ -135,7 +139,7 @@ example (p : ℕ) [Fact p.Prime] (a : ZMod p) : a ^ p = a :=
|
||||
|
||||
Das ist die Bemerkung nach dem Satz im Skript: In Anwendungen
|
||||
verwendet man häufig die äquivalente Formulierung
|
||||
`a^(p−1) ≡ 1 (mod p)` für nicht durch `p` teilbare `a`. Leiten Sie
|
||||
$`a^{p-1} \equiv 1 \pmod{p}` für nicht durch $`p` teilbare $`a`. Leiten Sie
|
||||
sie aus `little_fermat` ab — oder geben Sie einen direkten Beweis nach
|
||||
den Ideen oben. Öffnen Sie `AlgebraInLean/LittleFermat.lean` im
|
||||
Übungs-Repository und ersetzen Sie das `sorry` durch einen Beweis.
|
||||
|
||||
+23
-17
@@ -43,30 +43,34 @@ Polynom-API kennen.
|
||||
|
||||
Satz 7.2.1 des Skripts:
|
||||
|
||||
> *Satz 7.2.1 (Eisenstein-Kriterium).* Es sei `R` ein faktorieller Ring und
|
||||
> es sei `f = a₀ + a₁·x + … + aₙ·xⁿ ∈ R[x]` ein Polynom vom Grad
|
||||
> `n > 0`. Weiter sei `ggT(a₀, …, aₙ) = 1`. Wenn es ein Primelement
|
||||
> `p ∈ R` gibt mit `p|a₀`, `p|a₁`, …, `p|a_{n−1}` und `p² ∤ a₀`, dann
|
||||
> ist `f` irreduzibel in `R[x]`.
|
||||
> *Satz 7.2.1 (Eisenstein-Kriterium).* Es sei $`R` ein faktorieller
|
||||
Ring und es sei
|
||||
$`f = a_0 + a_1 \cdot x + \dots + a_n \cdot x^n \in R[x]` ein
|
||||
Polynom vom Grad $`n > 0`. Weiter sei
|
||||
$`\operatorname{ggT}(a_0, \dots, a_n) = 1`. Wenn es ein
|
||||
Primelement $`p \in R` gibt mit $`p \mid a_0`, $`p \mid a_1`, …,
|
||||
$`p \mid a_{n-1}` und $`p^2 \nmid a_0`, dann ist $`f` irreduzibel
|
||||
in $`R[x]`.
|
||||
|
||||
In Mathlib heißt der Satz
|
||||
`Polynomial.irreducible_of_eisenstein_criterion`. Er ist dort über
|
||||
ein Primideal `P` statt eines Primelements `p` formuliert — für uns
|
||||
ist `P` das Hauptideal `(p)` aus dem letzten Kapitel, und „`p` teilt
|
||||
`aₖ`“ wird zu `f.coeff k ∈ Ideal.span {p}`. Statt „`p ∤ aₙ`“ (was im
|
||||
Skript aus `ggT = 1` folgt) verlangt Mathlib direkt
|
||||
`f.leadingCoeff ∉ P`.
|
||||
ein Primideal `P` statt eines Primelements $`p` formuliert — für uns
|
||||
ist `P` das Hauptideal $`(p)` aus dem letzten Kapitel, und „$`p`
|
||||
teilt $`a_k`“ wird zu `f.coeff k ∈ Ideal.span {p}`. Statt
|
||||
„$`p \nmid a_n`“ (was im Skript aus $`\operatorname{ggT} = 1` folgt)
|
||||
verlangt Mathlib direkt `f.leadingCoeff ∉ P`.
|
||||
|
||||
# Erstes Beispiel: xⁿ − r
|
||||
|
||||
> Das Polynom `xⁿ − r ∈ ℤ[x]` ist irreduzibel, wenn `r` durch eine
|
||||
> Primzahl `p`, aber nicht durch `p²` teilbar ist.
|
||||
> Das Polynom $`x^n - r \in \mathbb{Z}[x]` ist irreduzibel, wenn
|
||||
$`r` durch eine Primzahl $`p`, aber nicht durch $`p^2` teilbar
|
||||
ist.
|
||||
|
||||
Das Skript lässt die Kontrolle der Eisenstein-Bedingungen als
|
||||
Kopfrechnung weg — in Lean führen wir sie aus und lernen dabei die
|
||||
Koeffizienten-API kennen: `coeff_sub`, `coeff_X_pow` und `coeff_C`
|
||||
berechnen die Koeffizienten von `xⁿ − r`, nämlich `aₙ = 1`, `a₀ = −r`
|
||||
und `aₖ = 0` sonst.
|
||||
berechnen die Koeffizienten von $`x^n - r`, nämlich $`a_n = 1`,
|
||||
$`a_0 = -r` und $`a_k = 0` sonst.
|
||||
|
||||
```lean
|
||||
open Polynomial
|
||||
@@ -128,11 +132,13 @@ Körpererweiterungen wieder auf.
|
||||
|
||||
Genau dieses zweite Beispiel ist die Übung:
|
||||
|
||||
> Das Polynom `xⁿ − p ∈ ℤ[x]` ist für jede Primzahl `p` irreduzibel.
|
||||
> Das Polynom $`x^n - p \in \mathbb{Z}[x]` ist für jede Primzahl
|
||||
$`p` irreduzibel.
|
||||
|
||||
Wenden Sie `xn_sub_r_irreduzibel` mit `r = p` an. Zu zeigen bleibt
|
||||
`p² ∤ p`: Aus `p = p²·c` folgt durch Kürzen `1 = p·c` — dann wäre `p`
|
||||
eine Einheit, im Widerspruch zur Primalität. Nützlich sind
|
||||
$`p^2 \nmid p`: Aus $`p = p^2 \cdot c` folgt durch Kürzen
|
||||
$`1 = p \cdot c` — dann wäre $`p` eine Einheit, im Widerspruch zur
|
||||
Primalität. Nützlich sind
|
||||
`mul_left_cancel₀`, `isUnit_of_dvd_one` und `Prime.not_isUnit`.
|
||||
Öffnen Sie `AlgebraInLean/Polynomials.lean` und ersetzen Sie das
|
||||
`sorry` durch einen Beweis.
|
||||
|
||||
+23
-19
@@ -24,8 +24,8 @@ file := "quotients"
|
||||
Dieses Kapitel übersetzt zwei Beweise rund um normale Untergruppen
|
||||
Satz für Satz nach Lean: das Argument aus Erklärvideo 1-1 des
|
||||
Skripts, dass Kerne von Gruppenmorphismen abgeschlossen unter
|
||||
Konjugation sind, und die Beobachtung aus Kapitel 17.3, dass `U·N`
|
||||
für normales `N` wieder eine Untergruppe ist.
|
||||
Konjugation sind, und die Beobachtung aus Kapitel 17.3, dass
|
||||
$`U \cdot N` für normales $`N` wieder eine Untergruppe ist.
|
||||
|
||||
# Das Mathlib-Wörterbuch
|
||||
|
||||
@@ -41,18 +41,19 @@ für normales `N` wieder eine Untergruppe ist.
|
||||
|
||||
* „`N` ist Normalteiler“ ist das Prädikat `N.Normal`; sein Feld
|
||||
`conj_mem` ist wörtlich die Bedingung des Skripts: für alle
|
||||
`n ∈ N` und alle `g` ist `g·n·g⁻¹ ∈ N`.
|
||||
$`n \in N` und alle $`g` ist $`g \cdot n \cdot g^{-1} \in N`.
|
||||
|
||||
# Kerne sind abgeschlossen unter Konjugation
|
||||
|
||||
Aus Erklärvideo 1-1 des Skripts:
|
||||
|
||||
> Die Antwort lautet: Nein! Nicht jede Untergruppe kann Kern eines
|
||||
> Gruppenmorphismus sein. Wenn es nämlich einen Gruppenmorphismus
|
||||
> `φ : G → Q` mit `H = ker(φ)` gibt, dann gilt für alle `h ∈ H` und
|
||||
> alle `g ∈ G` die Gleichung `φ(g·h·g⁻¹) = φ(g)·φ(h)·φ(g)⁻¹ = e`,
|
||||
> wobei `e` das neutrale Element von `Q` bezeichnet. Also ist stets
|
||||
> `g·h·g⁻¹ ∈ H`.
|
||||
Gruppenmorphismus sein. Wenn es nämlich einen Gruppenmorphismus
|
||||
$`\varphi : G \to Q` mit $`H = \ker(\varphi)` gibt, dann gilt für
|
||||
alle $`h \in H` und alle $`g \in G` die Gleichung
|
||||
$`\varphi(g \cdot h \cdot g^{-1}) = \varphi(g) \cdot \varphi(h) \cdot \varphi(g)^{-1} = e`,
|
||||
wobei $`e` das neutrale Element von $`Q` bezeichnet. Also ist
|
||||
stets $`g \cdot h \cdot g^{-1} \in H`.
|
||||
|
||||
```lean
|
||||
theorem kern_konjugation {G Q : Type*} [Group G] [Group Q]
|
||||
@@ -98,17 +99,20 @@ example {G H : Type*} [Group G] [Group H] (N : Subgroup G)
|
||||
|
||||
Beobachtung 17.3.5 des Skripts:
|
||||
|
||||
> Es sei `G` eine Gruppe und es sei `N ⊂ G` eine normale
|
||||
> Untergruppe. Weiter sei `U ⊂ G` irgendeine Untergruppe. Dann ist
|
||||
> `U·N = {u·n : u ∈ U, n ∈ N}` wieder eine Untergruppe. Zum Beweis
|
||||
> müssen wir lediglich zeigen, dass `U·N` abgeschlossen unter der
|
||||
> Gruppenoperation ist. … Wir wissen, dass `N` normal ist. Also
|
||||
> ist `ñ₁ := u₂⁻¹·n₁·u₂ ∈ N` und es gilt `n₁·u₂ = u₂·ñ₁`. Demnach
|
||||
> ist `u₁n₁u₂n₂ = u₁u₂·ñ₁n₂ ∈ U·N`. Fertig ist der Beweis.
|
||||
> Es sei $`G` eine Gruppe und es sei $`N \subset G` eine normale
|
||||
Untergruppe. Weiter sei $`U \subset G` irgendeine Untergruppe.
|
||||
Dann ist $`U \cdot N = \{u \cdot n : u \in U,\ n \in N\}` wieder
|
||||
eine Untergruppe. Zum Beweis müssen wir lediglich zeigen, dass
|
||||
$`U \cdot N` abgeschlossen unter der Gruppenoperation ist. … Wir
|
||||
wissen, dass $`N` normal ist. Also ist
|
||||
$`\widetilde{n_1} := u_2^{-1} \cdot n_1 \cdot u_2 \in N` und es
|
||||
gilt $`n_1 \cdot u_2 = u_2 \cdot \widetilde{n_1}`. Demnach ist
|
||||
$`u_1 n_1 u_2 n_2 = u_1 u_2 \cdot \widetilde{n_1} n_2 \in U \cdot N`.
|
||||
Fertig ist der Beweis.
|
||||
|
||||
Neu ist hier die Taktik `group`: Sie verrechnet Ausdrücke, die
|
||||
allein mit den Gruppenaxiomen ineinander umgeformt werden können.
|
||||
(Das `ñ₁` des Skripts heißt im Code `n₁'`.)
|
||||
(Das $`\widetilde{n_1}` des Skripts heißt im Code `n₁'`.)
|
||||
|
||||
```lean
|
||||
theorem mul_mem_mul {G : Type*} [Group G] (U N : Subgroup G)
|
||||
@@ -136,9 +140,9 @@ theorem mul_mem_mul {G : Type*} [Group G] (U N : Subgroup G)
|
||||
|
||||
Das Skript sagt, es sei „lediglich“ die Abgeschlossenheit unter der
|
||||
Verknüpfung zu zeigen — prüfen Sie den verschwiegenen Teil selbst
|
||||
nach: `U·N` ist auch abgeschlossen unter Inversen. Tipp:
|
||||
`(u·n)⁻¹ = u⁻¹·(u·n⁻¹·u⁻¹)`, und der zweite Faktor liegt nach
|
||||
`conj_mem` in `N`. Öffnen Sie `AlgebraInLean/Quotients.lean` und
|
||||
nach: $`U \cdot N` ist auch abgeschlossen unter Inversen. Tipp:
|
||||
$`(u \cdot n)^{-1} = u^{-1} \cdot (u \cdot n^{-1} \cdot u^{-1})`,
|
||||
und der zweite Faktor liegt nach `conj_mem` in $`N`. Öffnen Sie `AlgebraInLean/Quotients.lean` und
|
||||
ersetzen Sie das `sorry` durch einen Beweis.
|
||||
|
||||
```lean
|
||||
|
||||
+13
-10
@@ -24,8 +24,9 @@ schließt den Kreis zum Anfang des Kurses.
|
||||
|
||||
# Das Mathlib-Wörterbuch
|
||||
|
||||
* Das Legendre-Symbol `(a/p)` heißt `legendreSym p a : ℤ`; es setzt
|
||||
eine `Fact (Nat.Prime p)`-Instanz voraus.
|
||||
* Das Legendre-Symbol $`\left(\tfrac{a}{p}\right)` heißt
|
||||
`legendreSym p a : ℤ`; es setzt eine `Fact (Nat.Prime p)`-Instanz
|
||||
voraus.
|
||||
|
||||
* „`a` ist ein quadratischer Rest modulo `p`“ ist einfach
|
||||
`IsSquare (a : ZMod p)`.
|
||||
@@ -39,14 +40,16 @@ schließt den Kreis zum Anfang des Kurses.
|
||||
|
||||
Satz 24.2.1 des Skripts:
|
||||
|
||||
> *Satz 24.2.1 (Quadratisches Reziprozitätsgesetz).* Es seien `p` und `q`
|
||||
> zwei unterschiedliche, ungerade Primzahlen. Dann gilt die
|
||||
> Gleichung `(p/q)·(q/p) = (−1)^((p−1)/2 · (q−1)/2)`.
|
||||
> *Satz 24.2.1 (Quadratisches Reziprozitätsgesetz).* Es seien $`p`
|
||||
und $`q` zwei unterschiedliche, ungerade Primzahlen. Dann gilt
|
||||
die Gleichung
|
||||
$`\left(\tfrac{p}{q}\right) \cdot \left(\tfrac{q}{p}\right) = (-1)^{\frac{p-1}{2} \cdot \frac{q-1}{2}}`.
|
||||
|
||||
In Mathlib: `legendreSym.quadratic_reciprocity` — dort mit den
|
||||
Exponenten `p / 2` geschrieben, was für ungerade `p` dasselbe ist wie
|
||||
`(p−1)/2`. Dazu die beiden Ergänzungssätze: Der erste —
|
||||
`(−1/p) = 1` genau für `p ≡ 1 (mod 4)` — ist in der
|
||||
Exponenten `p / 2` geschrieben, was für ungerade $`p` dasselbe ist
|
||||
wie $`(p-1)/2`. Dazu die beiden Ergänzungssätze: Der erste —
|
||||
$`\left(\tfrac{-1}{p}\right) = 1` genau für
|
||||
$`p \equiv 1 \pmod{4}` — ist in der
|
||||
Quadrat-Formulierung `ZMod.exists_sq_eq_neg_one_iff`:
|
||||
|
||||
```lean
|
||||
@@ -60,8 +63,8 @@ example (p : ℕ) [Fact p.Prime] (hp : p % 4 ≠ 3) :
|
||||
Aus dem Skript:
|
||||
|
||||
> Ist 7 ein quadratischer Rest modulo 17?
|
||||
> `(7/17) = (17/7)·(−1)^{8·3} = (3/7) = (7/3)·(−1)^{3·1} = −(1/3)
|
||||
> = −1`. Also ist die Antwort: „Nein!“
|
||||
$$`\left(\tfrac{7}{17}\right) = \left(\tfrac{17}{7}\right) \cdot (-1)^{8 \cdot 3} = \left(\tfrac{3}{7}\right) = \left(\tfrac{7}{3}\right) \cdot (-1)^{3 \cdot 1} = -\left(\tfrac{1}{3}\right) = -1.`
|
||||
Also ist die Antwort: „Nein!“
|
||||
|
||||
So rechnet man von Hand — und in der Klausur. In Lean können wir
|
||||
dieselbe Frage der Taktik `decide` übergeben, die das Legendre-Symbol
|
||||
|
||||
@@ -7,6 +7,10 @@ open Verso.Genre.Manual
|
||||
-- The static assets (theme, fonts, KaTeX) follow the setup of
|
||||
-- Peter Pfaffelhuber's course notes, https://github.com/pfaffelh/leancourse.
|
||||
|
||||
-- Kein eigenes KaTeX mehr: Das aktuelle Verso liefert seinen eigenen
|
||||
-- Mathe-Renderer mit (-verso-data/katex/…); eine zweite Kopie würde
|
||||
-- jede Formel doppelt rendern.
|
||||
|
||||
open Verso.Output.Html in
|
||||
def staticCss := {{
|
||||
<link rel="stylesheet" href="/static/colors.css" />
|
||||
@@ -14,45 +18,13 @@ def staticCss := {{
|
||||
<link rel="stylesheet" href="/static/print.css" />
|
||||
<link rel="stylesheet" href="/static/fonts/source-serif/source-serif-text.css" />
|
||||
<link rel="stylesheet" href="/static/fonts/source-code-pro/source-code-pro.css" />
|
||||
<link rel="stylesheet" href="/static/katex/katex.min.css" />
|
||||
}}
|
||||
|
||||
open Verso.Output.Html in
|
||||
def staticJs := {{
|
||||
<script src="/static/katex/katex.min.js"></script>
|
||||
<script src="/static/math.js"></script>
|
||||
<script src="/static/print.js"></script>
|
||||
}}
|
||||
|
||||
def KaTeXLicense : LicenseInfo where
|
||||
identifier := "MIT"
|
||||
dependency := "KaTeX"
|
||||
howUsed := "KaTeX is used to render mathematical notation."
|
||||
link := "https://katex.org/"
|
||||
text := #[(some "The MIT License", text)]
|
||||
where
|
||||
text := r#"
|
||||
Copyright (c) 2013-2020 Khan Academy and other contributors
|
||||
|
||||
Permission is hereby granted, free of charge, to any person obtaining a copy
|
||||
of this software and associated documentation files (the "Software"), to deal
|
||||
in the Software without restriction, including without limitation the rights
|
||||
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||||
copies of the Software, and to permit persons to whom the Software is
|
||||
furnished to do so, subject to the following conditions:
|
||||
|
||||
The above copyright notice and this permission notice shall be included in all
|
||||
copies or substantial portions of the Software.
|
||||
|
||||
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
||||
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
|
||||
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
|
||||
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
|
||||
SOFTWARE.
|
||||
"#
|
||||
|
||||
def main :=
|
||||
manualMain (%doc Book) (config := config)
|
||||
where
|
||||
|
||||
@@ -6,5 +6,4 @@ set -e
|
||||
|
||||
lake build
|
||||
lake exe algebrainlean --output _out
|
||||
mkdir -p public
|
||||
rsync -a --delete _out/html-multi/ public/
|
||||
rsync -arvz --delete _out/html-multi/ kebekus@cplx.vm.uni-freiburg.de:/var/www/storage/algebra-in-lean
|
||||
|
||||
+3
-1
@@ -1 +1,3 @@
|
||||
The directory `katex` contains KaTeX v0.16.11 (MIT license)
|
||||
Theme, Schriften und Druck-Stile nach dem Vorbild von
|
||||
https://github.com/pfaffelh/leancourse.
|
||||
Die Fonts (Source Serif, Source Code Pro) stehen unter der SIL OFL.
|
||||
|
||||
@@ -1,125 +0,0 @@
|
||||
<h1><a href="https://katex.org/">
|
||||
<picture>
|
||||
<source media="(prefers-color-scheme: dark)" srcset="https://katex.org/img/katex-logo.svg">
|
||||
<img alt="KaTeX" width=130 src="https://katex.org/img/katex-logo-black.svg">
|
||||
</picture>
|
||||
</a></h1>
|
||||
|
||||
[](https://www.npmjs.com/package/katex)
|
||||
[](https://github.com/semantic-release/semantic-release)
|
||||
[](https://github.com/KaTeX/KaTeX/actions?query=workflow%3ACI)
|
||||
[](https://codecov.io/gh/KaTeX/KaTeX)
|
||||
[](https://github.com/KaTeX/KaTeX/discussions)
|
||||
[](https://www.jsdelivr.com/package/npm/katex)
|
||||
|
||||
[](https://gitpod.io/#https://github.com/KaTeX/KaTeX)
|
||||
[](https://opencollective.com/katex)
|
||||
|
||||
KaTeX is a fast, easy-to-use JavaScript library for TeX math rendering on the web.
|
||||
|
||||
* **Fast:** KaTeX renders its math synchronously and doesn't need to reflow the page. See how it compares to a competitor in [this speed test](https://www.intmath.com/cg5/katex-mathjax-comparison.php).
|
||||
* **Print quality:** KaTeX's layout is based on Donald Knuth's TeX, the gold standard for math typesetting.
|
||||
* **Self contained:** KaTeX has no dependencies and can easily be bundled with your website resources.
|
||||
* **Server side rendering:** KaTeX produces the same output regardless of browser or environment, so you can pre-render expressions using Node.js and send them as plain HTML.
|
||||
|
||||
KaTeX is compatible with all major browsers, including Chrome, Safari, Firefox, Opera, Edge, and IE 11.
|
||||
|
||||
KaTeX supports much (but not all) of LaTeX and many LaTeX packages. See the [list of supported functions](https://katex.org/docs/supported.html).
|
||||
|
||||
Try out KaTeX [on the demo page](https://katex.org/#demo)!
|
||||
|
||||
## Getting started
|
||||
|
||||
### Starter template
|
||||
|
||||
```html
|
||||
<!DOCTYPE html>
|
||||
<!-- KaTeX requires the use of the HTML5 doctype. Without it, KaTeX may not render properly -->
|
||||
<html>
|
||||
<head>
|
||||
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/katex.min.css" integrity="sha384-nB0miv6/jRmo5UMMR1wu3Gz6NLsoTkbqJghGIsx//Rlm+ZU03BU6SQNC66uf4l5+" crossorigin="anonymous">
|
||||
|
||||
<!-- The loading of KaTeX is deferred to speed up page rendering -->
|
||||
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/katex.min.js" integrity="sha384-7zkQWkzuo3B5mTepMUcHkMB5jZaolc2xDwL6VFqjFALcbeS9Ggm/Yr2r3Dy4lfFg" crossorigin="anonymous"></script>
|
||||
|
||||
<!-- To automatically render math in text elements, include the auto-render extension: -->
|
||||
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/contrib/auto-render.min.js" integrity="sha384-43gviWU0YVjaDtb/GhzOouOXtZMP/7XUzwPTstBeZFe/+rCMvRwr4yROQP43s0Xk" crossorigin="anonymous"
|
||||
onload="renderMathInElement(document.body);"></script>
|
||||
</head>
|
||||
...
|
||||
</html>
|
||||
```
|
||||
|
||||
You can also [download KaTeX](https://github.com/KaTeX/KaTeX/releases) and host it yourself.
|
||||
|
||||
For details on how to configure auto-render extension, refer to [the documentation](https://katex.org/docs/autorender.html).
|
||||
|
||||
### API
|
||||
|
||||
Call `katex.render` to render a TeX expression directly into a DOM element.
|
||||
For example:
|
||||
|
||||
```js
|
||||
katex.render("c = \\pm\\sqrt{a^2 + b^2}", element, {
|
||||
throwOnError: false
|
||||
});
|
||||
```
|
||||
|
||||
Call `katex.renderToString` to generate an HTML string of the rendered math,
|
||||
e.g., for server-side rendering. For example:
|
||||
|
||||
```js
|
||||
var html = katex.renderToString("c = \\pm\\sqrt{a^2 + b^2}", {
|
||||
throwOnError: false
|
||||
});
|
||||
// '<span class="katex">...</span>'
|
||||
```
|
||||
|
||||
Make sure to include the CSS and font files in both cases.
|
||||
If you are doing all rendering on the server, there is no need to include the
|
||||
JavaScript on the client.
|
||||
|
||||
The examples above use the `throwOnError: false` option, which renders invalid
|
||||
inputs as the TeX source code in red (by default), with the error message as
|
||||
hover text. For other available options, see the
|
||||
[API documentation](https://katex.org/docs/api.html),
|
||||
[options documentation](https://katex.org/docs/options.html), and
|
||||
[handling errors documentation](https://katex.org/docs/error.html).
|
||||
|
||||
## Demo and Documentation
|
||||
|
||||
Learn more about using KaTeX [on the website](https://katex.org)!
|
||||
|
||||
## Contributors
|
||||
|
||||
### Code Contributors
|
||||
|
||||
This project exists thanks to all the people who contribute code. If you'd like to help, see [our guide to contributing code](CONTRIBUTING.md).
|
||||
<a href="https://github.com/KaTeX/KaTeX/graphs/contributors"><img src="https://contributors-svg.opencollective.com/katex/contributors.svg?width=890&button=false" alt="Code contributors" /></a>
|
||||
|
||||
### Financial Contributors
|
||||
|
||||
Become a financial contributor and help us sustain our community.
|
||||
|
||||
#### Individuals
|
||||
|
||||
<a href="https://opencollective.com/katex"><img src="https://opencollective.com/katex/individuals.svg?width=890" alt="Contribute on Open Collective"></a>
|
||||
|
||||
#### Organizations
|
||||
|
||||
Support this project with your organization. Your logo will show up here with a link to your website.
|
||||
|
||||
<a href="https://opencollective.com/katex/organization/0/website"><img src="https://opencollective.com/katex/organization/0/avatar.svg" alt="Organization 1"></a>
|
||||
<a href="https://opencollective.com/katex/organization/1/website"><img src="https://opencollective.com/katex/organization/1/avatar.svg" alt="Organization 2"></a>
|
||||
<a href="https://opencollective.com/katex/organization/2/website"><img src="https://opencollective.com/katex/organization/2/avatar.svg" alt="Organization 3"></a>
|
||||
<a href="https://opencollective.com/katex/organization/3/website"><img src="https://opencollective.com/katex/organization/3/avatar.svg" alt="Organization 4"></a>
|
||||
<a href="https://opencollective.com/katex/organization/4/website"><img src="https://opencollective.com/katex/organization/4/avatar.svg" alt="Organization 5"></a>
|
||||
<a href="https://opencollective.com/katex/organization/5/website"><img src="https://opencollective.com/katex/organization/5/avatar.svg" alt="Organization 6"></a>
|
||||
<a href="https://opencollective.com/katex/organization/6/website"><img src="https://opencollective.com/katex/organization/6/avatar.svg" alt="Organization 7"></a>
|
||||
<a href="https://opencollective.com/katex/organization/7/website"><img src="https://opencollective.com/katex/organization/7/avatar.svg" alt="Organization 8"></a>
|
||||
<a href="https://opencollective.com/katex/organization/8/website"><img src="https://opencollective.com/katex/organization/8/avatar.svg" alt="Organization 9"></a>
|
||||
<a href="https://opencollective.com/katex/organization/9/website"><img src="https://opencollective.com/katex/organization/9/avatar.svg" alt="Organization 10"></a>
|
||||
|
||||
## License
|
||||
|
||||
KaTeX is licensed under the [MIT License](https://opensource.org/licenses/MIT).
|
||||
@@ -1,341 +0,0 @@
|
||||
(function webpackUniversalModuleDefinition(root, factory) {
|
||||
if(typeof exports === 'object' && typeof module === 'object')
|
||||
module.exports = factory(require("katex"));
|
||||
else if(typeof define === 'function' && define.amd)
|
||||
define(["katex"], factory);
|
||||
else if(typeof exports === 'object')
|
||||
exports["renderMathInElement"] = factory(require("katex"));
|
||||
else
|
||||
root["renderMathInElement"] = factory(root["katex"]);
|
||||
})((typeof self !== 'undefined' ? self : this), function(__WEBPACK_EXTERNAL_MODULE__771__) {
|
||||
return /******/ (function() { // webpackBootstrap
|
||||
/******/ "use strict";
|
||||
/******/ var __webpack_modules__ = ({
|
||||
|
||||
/***/ 771:
|
||||
/***/ (function(module) {
|
||||
|
||||
module.exports = __WEBPACK_EXTERNAL_MODULE__771__;
|
||||
|
||||
/***/ })
|
||||
|
||||
/******/ });
|
||||
/************************************************************************/
|
||||
/******/ // The module cache
|
||||
/******/ var __webpack_module_cache__ = {};
|
||||
/******/
|
||||
/******/ // The require function
|
||||
/******/ function __webpack_require__(moduleId) {
|
||||
/******/ // Check if module is in cache
|
||||
/******/ var cachedModule = __webpack_module_cache__[moduleId];
|
||||
/******/ if (cachedModule !== undefined) {
|
||||
/******/ return cachedModule.exports;
|
||||
/******/ }
|
||||
/******/ // Create a new module (and put it into the cache)
|
||||
/******/ var module = __webpack_module_cache__[moduleId] = {
|
||||
/******/ // no module.id needed
|
||||
/******/ // no module.loaded needed
|
||||
/******/ exports: {}
|
||||
/******/ };
|
||||
/******/
|
||||
/******/ // Execute the module function
|
||||
/******/ __webpack_modules__[moduleId](module, module.exports, __webpack_require__);
|
||||
/******/
|
||||
/******/ // Return the exports of the module
|
||||
/******/ return module.exports;
|
||||
/******/ }
|
||||
/******/
|
||||
/************************************************************************/
|
||||
/******/ /* webpack/runtime/compat get default export */
|
||||
/******/ !function() {
|
||||
/******/ // getDefaultExport function for compatibility with non-harmony modules
|
||||
/******/ __webpack_require__.n = function(module) {
|
||||
/******/ var getter = module && module.__esModule ?
|
||||
/******/ function() { return module['default']; } :
|
||||
/******/ function() { return module; };
|
||||
/******/ __webpack_require__.d(getter, { a: getter });
|
||||
/******/ return getter;
|
||||
/******/ };
|
||||
/******/ }();
|
||||
/******/
|
||||
/******/ /* webpack/runtime/define property getters */
|
||||
/******/ !function() {
|
||||
/******/ // define getter functions for harmony exports
|
||||
/******/ __webpack_require__.d = function(exports, definition) {
|
||||
/******/ for(var key in definition) {
|
||||
/******/ if(__webpack_require__.o(definition, key) && !__webpack_require__.o(exports, key)) {
|
||||
/******/ Object.defineProperty(exports, key, { enumerable: true, get: definition[key] });
|
||||
/******/ }
|
||||
/******/ }
|
||||
/******/ };
|
||||
/******/ }();
|
||||
/******/
|
||||
/******/ /* webpack/runtime/hasOwnProperty shorthand */
|
||||
/******/ !function() {
|
||||
/******/ __webpack_require__.o = function(obj, prop) { return Object.prototype.hasOwnProperty.call(obj, prop); }
|
||||
/******/ }();
|
||||
/******/
|
||||
/************************************************************************/
|
||||
var __webpack_exports__ = {};
|
||||
// This entry need to be wrapped in an IIFE because it need to be isolated against other modules in the chunk.
|
||||
!function() {
|
||||
|
||||
// EXPORTS
|
||||
__webpack_require__.d(__webpack_exports__, {
|
||||
"default": function() { return /* binding */ auto_render; }
|
||||
});
|
||||
|
||||
// EXTERNAL MODULE: external "katex"
|
||||
var external_katex_ = __webpack_require__(771);
|
||||
var external_katex_default = /*#__PURE__*/__webpack_require__.n(external_katex_);
|
||||
;// CONCATENATED MODULE: ./contrib/auto-render/splitAtDelimiters.js
|
||||
/* eslint no-constant-condition:0 */
|
||||
const findEndOfMath = function (delimiter, text, startIndex) {
|
||||
// Adapted from
|
||||
// https://github.com/Khan/perseus/blob/master/src/perseus-markdown.jsx
|
||||
let index = startIndex;
|
||||
let braceLevel = 0;
|
||||
const delimLength = delimiter.length;
|
||||
|
||||
while (index < text.length) {
|
||||
const character = text[index];
|
||||
|
||||
if (braceLevel <= 0 && text.slice(index, index + delimLength) === delimiter) {
|
||||
return index;
|
||||
} else if (character === "\\") {
|
||||
index++;
|
||||
} else if (character === "{") {
|
||||
braceLevel++;
|
||||
} else if (character === "}") {
|
||||
braceLevel--;
|
||||
}
|
||||
|
||||
index++;
|
||||
}
|
||||
|
||||
return -1;
|
||||
};
|
||||
|
||||
const escapeRegex = function (string) {
|
||||
return string.replace(/[-/\\^$*+?.()|[\]{}]/g, "\\$&");
|
||||
};
|
||||
|
||||
const amsRegex = /^\\begin{/;
|
||||
|
||||
const splitAtDelimiters = function (text, delimiters) {
|
||||
let index;
|
||||
const data = [];
|
||||
const regexLeft = new RegExp("(" + delimiters.map(x => escapeRegex(x.left)).join("|") + ")");
|
||||
|
||||
while (true) {
|
||||
index = text.search(regexLeft);
|
||||
|
||||
if (index === -1) {
|
||||
break;
|
||||
}
|
||||
|
||||
if (index > 0) {
|
||||
data.push({
|
||||
type: "text",
|
||||
data: text.slice(0, index)
|
||||
});
|
||||
text = text.slice(index); // now text starts with delimiter
|
||||
} // ... so this always succeeds:
|
||||
|
||||
|
||||
const i = delimiters.findIndex(delim => text.startsWith(delim.left));
|
||||
index = findEndOfMath(delimiters[i].right, text, delimiters[i].left.length);
|
||||
|
||||
if (index === -1) {
|
||||
break;
|
||||
}
|
||||
|
||||
const rawData = text.slice(0, index + delimiters[i].right.length);
|
||||
const math = amsRegex.test(rawData) ? rawData : text.slice(delimiters[i].left.length, index);
|
||||
data.push({
|
||||
type: "math",
|
||||
data: math,
|
||||
rawData,
|
||||
display: delimiters[i].display
|
||||
});
|
||||
text = text.slice(index + delimiters[i].right.length);
|
||||
}
|
||||
|
||||
if (text !== "") {
|
||||
data.push({
|
||||
type: "text",
|
||||
data: text
|
||||
});
|
||||
}
|
||||
|
||||
return data;
|
||||
};
|
||||
|
||||
/* harmony default export */ var auto_render_splitAtDelimiters = (splitAtDelimiters);
|
||||
;// CONCATENATED MODULE: ./contrib/auto-render/auto-render.js
|
||||
/* eslint no-console:0 */
|
||||
|
||||
|
||||
/* Note: optionsCopy is mutated by this method. If it is ever exposed in the
|
||||
* API, we should copy it before mutating.
|
||||
*/
|
||||
|
||||
const renderMathInText = function (text, optionsCopy) {
|
||||
const data = auto_render_splitAtDelimiters(text, optionsCopy.delimiters);
|
||||
|
||||
if (data.length === 1 && data[0].type === 'text') {
|
||||
// There is no formula in the text.
|
||||
// Let's return null which means there is no need to replace
|
||||
// the current text node with a new one.
|
||||
return null;
|
||||
}
|
||||
|
||||
const fragment = document.createDocumentFragment();
|
||||
|
||||
for (let i = 0; i < data.length; i++) {
|
||||
if (data[i].type === "text") {
|
||||
fragment.appendChild(document.createTextNode(data[i].data));
|
||||
} else {
|
||||
const span = document.createElement("span");
|
||||
let math = data[i].data; // Override any display mode defined in the settings with that
|
||||
// defined by the text itself
|
||||
|
||||
optionsCopy.displayMode = data[i].display;
|
||||
|
||||
try {
|
||||
if (optionsCopy.preProcess) {
|
||||
math = optionsCopy.preProcess(math);
|
||||
}
|
||||
|
||||
external_katex_default().render(math, span, optionsCopy);
|
||||
} catch (e) {
|
||||
if (!(e instanceof (external_katex_default()).ParseError)) {
|
||||
throw e;
|
||||
}
|
||||
|
||||
optionsCopy.errorCallback("KaTeX auto-render: Failed to parse `" + data[i].data + "` with ", e);
|
||||
fragment.appendChild(document.createTextNode(data[i].rawData));
|
||||
continue;
|
||||
}
|
||||
|
||||
fragment.appendChild(span);
|
||||
}
|
||||
}
|
||||
|
||||
return fragment;
|
||||
};
|
||||
|
||||
const renderElem = function (elem, optionsCopy) {
|
||||
for (let i = 0; i < elem.childNodes.length; i++) {
|
||||
const childNode = elem.childNodes[i];
|
||||
|
||||
if (childNode.nodeType === 3) {
|
||||
// Text node
|
||||
// Concatenate all sibling text nodes.
|
||||
// Webkit browsers split very large text nodes into smaller ones,
|
||||
// so the delimiters may be split across different nodes.
|
||||
let textContentConcat = childNode.textContent;
|
||||
let sibling = childNode.nextSibling;
|
||||
let nSiblings = 0;
|
||||
|
||||
while (sibling && sibling.nodeType === Node.TEXT_NODE) {
|
||||
textContentConcat += sibling.textContent;
|
||||
sibling = sibling.nextSibling;
|
||||
nSiblings++;
|
||||
}
|
||||
|
||||
const frag = renderMathInText(textContentConcat, optionsCopy);
|
||||
|
||||
if (frag) {
|
||||
// Remove extra text nodes
|
||||
for (let j = 0; j < nSiblings; j++) {
|
||||
childNode.nextSibling.remove();
|
||||
}
|
||||
|
||||
i += frag.childNodes.length - 1;
|
||||
elem.replaceChild(frag, childNode);
|
||||
} else {
|
||||
// If the concatenated text does not contain math
|
||||
// the siblings will not either
|
||||
i += nSiblings;
|
||||
}
|
||||
} else if (childNode.nodeType === 1) {
|
||||
// Element node
|
||||
const className = ' ' + childNode.className + ' ';
|
||||
const shouldRender = optionsCopy.ignoredTags.indexOf(childNode.nodeName.toLowerCase()) === -1 && optionsCopy.ignoredClasses.every(x => className.indexOf(' ' + x + ' ') === -1);
|
||||
|
||||
if (shouldRender) {
|
||||
renderElem(childNode, optionsCopy);
|
||||
}
|
||||
} // Otherwise, it's something else, and ignore it.
|
||||
|
||||
}
|
||||
};
|
||||
|
||||
const renderMathInElement = function (elem, options) {
|
||||
if (!elem) {
|
||||
throw new Error("No element provided to render");
|
||||
}
|
||||
|
||||
const optionsCopy = {}; // Object.assign(optionsCopy, option)
|
||||
|
||||
for (const option in options) {
|
||||
if (options.hasOwnProperty(option)) {
|
||||
optionsCopy[option] = options[option];
|
||||
}
|
||||
} // default options
|
||||
|
||||
|
||||
optionsCopy.delimiters = optionsCopy.delimiters || [{
|
||||
left: "$$",
|
||||
right: "$$",
|
||||
display: true
|
||||
}, {
|
||||
left: "\\(",
|
||||
right: "\\)",
|
||||
display: false
|
||||
}, // LaTeX uses $…$, but it ruins the display of normal `$` in text:
|
||||
// {left: "$", right: "$", display: false},
|
||||
// $ must come after $$
|
||||
// Render AMS environments even if outside $$…$$ delimiters.
|
||||
{
|
||||
left: "\\begin{equation}",
|
||||
right: "\\end{equation}",
|
||||
display: true
|
||||
}, {
|
||||
left: "\\begin{align}",
|
||||
right: "\\end{align}",
|
||||
display: true
|
||||
}, {
|
||||
left: "\\begin{alignat}",
|
||||
right: "\\end{alignat}",
|
||||
display: true
|
||||
}, {
|
||||
left: "\\begin{gather}",
|
||||
right: "\\end{gather}",
|
||||
display: true
|
||||
}, {
|
||||
left: "\\begin{CD}",
|
||||
right: "\\end{CD}",
|
||||
display: true
|
||||
}, {
|
||||
left: "\\[",
|
||||
right: "\\]",
|
||||
display: true
|
||||
}];
|
||||
optionsCopy.ignoredTags = optionsCopy.ignoredTags || ["script", "noscript", "style", "textarea", "pre", "code", "option"];
|
||||
optionsCopy.ignoredClasses = optionsCopy.ignoredClasses || [];
|
||||
optionsCopy.errorCallback = optionsCopy.errorCallback || console.error; // Enable sharing of global macros defined via `\gdef` between different
|
||||
// math elements within a single call to `renderMathInElement`.
|
||||
|
||||
optionsCopy.macros = optionsCopy.macros || {};
|
||||
renderElem(elem, optionsCopy);
|
||||
};
|
||||
|
||||
/* harmony default export */ var auto_render = (renderMathInElement);
|
||||
}();
|
||||
__webpack_exports__ = __webpack_exports__["default"];
|
||||
/******/ return __webpack_exports__;
|
||||
/******/ })()
|
||||
;
|
||||
});
|
||||
-1
@@ -1 +0,0 @@
|
||||
!function(e,t){"object"==typeof exports&&"object"==typeof module?module.exports=t(require("katex")):"function"==typeof define&&define.amd?define(["katex"],t):"object"==typeof exports?exports.renderMathInElement=t(require("katex")):e.renderMathInElement=t(e.katex)}("undefined"!=typeof self?self:this,(function(e){return function(){"use strict";var t={771:function(t){t.exports=e}},n={};function r(e){var o=n[e];if(void 0!==o)return o.exports;var i=n[e]={exports:{}};return t[e](i,i.exports,r),i.exports}r.n=function(e){var t=e&&e.__esModule?function(){return e.default}:function(){return e};return r.d(t,{a:t}),t},r.d=function(e,t){for(var n in t)r.o(t,n)&&!r.o(e,n)&&Object.defineProperty(e,n,{enumerable:!0,get:t[n]})},r.o=function(e,t){return Object.prototype.hasOwnProperty.call(e,t)};var o={};return function(){r.d(o,{default:function(){return d}});var e=r(771),t=r.n(e);const n=function(e,t,n){let r=n,o=0;const i=e.length;for(;r<t.length;){const n=t[r];if(o<=0&&t.slice(r,r+i)===e)return r;"\\"===n?r++:"{"===n?o++:"}"===n&&o--,r++}return-1},i=/^\\begin{/;var a=function(e,t){let r;const o=[],a=new RegExp("("+t.map((e=>e.left.replace(/[-/\\^$*+?.()|[\]{}]/g,"\\$&"))).join("|")+")");for(;r=e.search(a),-1!==r;){r>0&&(o.push({type:"text",data:e.slice(0,r)}),e=e.slice(r));const a=t.findIndex((t=>e.startsWith(t.left)));if(r=n(t[a].right,e,t[a].left.length),-1===r)break;const l=e.slice(0,r+t[a].right.length),s=i.test(l)?l:e.slice(t[a].left.length,r);o.push({type:"math",data:s,rawData:l,display:t[a].display}),e=e.slice(r+t[a].right.length)}return""!==e&&o.push({type:"text",data:e}),o};const l=function(e,n){const r=a(e,n.delimiters);if(1===r.length&&"text"===r[0].type)return null;const o=document.createDocumentFragment();for(let e=0;e<r.length;e++)if("text"===r[e].type)o.appendChild(document.createTextNode(r[e].data));else{const i=document.createElement("span");let a=r[e].data;n.displayMode=r[e].display;try{n.preProcess&&(a=n.preProcess(a)),t().render(a,i,n)}catch(i){if(!(i instanceof t().ParseError))throw i;n.errorCallback("KaTeX auto-render: Failed to parse `"+r[e].data+"` with ",i),o.appendChild(document.createTextNode(r[e].rawData));continue}o.appendChild(i)}return o},s=function(e,t){for(let n=0;n<e.childNodes.length;n++){const r=e.childNodes[n];if(3===r.nodeType){let o=r.textContent,i=r.nextSibling,a=0;for(;i&&i.nodeType===Node.TEXT_NODE;)o+=i.textContent,i=i.nextSibling,a++;const s=l(o,t);if(s){for(let e=0;e<a;e++)r.nextSibling.remove();n+=s.childNodes.length-1,e.replaceChild(s,r)}else n+=a}else if(1===r.nodeType){const e=" "+r.className+" ";-1===t.ignoredTags.indexOf(r.nodeName.toLowerCase())&&t.ignoredClasses.every((t=>-1===e.indexOf(" "+t+" ")))&&s(r,t)}}};var d=function(e,t){if(!e)throw new Error("No element provided to render");const n={};for(const e in t)t.hasOwnProperty(e)&&(n[e]=t[e]);n.delimiters=n.delimiters||[{left:"$$",right:"$$",display:!0},{left:"\\(",right:"\\)",display:!1},{left:"\\begin{equation}",right:"\\end{equation}",display:!0},{left:"\\begin{align}",right:"\\end{align}",display:!0},{left:"\\begin{alignat}",right:"\\end{alignat}",display:!0},{left:"\\begin{gather}",right:"\\end{gather}",display:!0},{left:"\\begin{CD}",right:"\\end{CD}",display:!0},{left:"\\[",right:"\\]",display:!0}],n.ignoredTags=n.ignoredTags||["script","noscript","style","textarea","pre","code","option"],n.ignoredClasses=n.ignoredClasses||[],n.errorCallback=n.errorCallback||console.error,n.macros=n.macros||{},s(e,n)}}(),o=o.default}()}));
|
||||
@@ -1,244 +0,0 @@
|
||||
import katex from '../katex.mjs';
|
||||
|
||||
/* eslint no-constant-condition:0 */
|
||||
var findEndOfMath = function findEndOfMath(delimiter, text, startIndex) {
|
||||
// Adapted from
|
||||
// https://github.com/Khan/perseus/blob/master/src/perseus-markdown.jsx
|
||||
var index = startIndex;
|
||||
var braceLevel = 0;
|
||||
var delimLength = delimiter.length;
|
||||
|
||||
while (index < text.length) {
|
||||
var character = text[index];
|
||||
|
||||
if (braceLevel <= 0 && text.slice(index, index + delimLength) === delimiter) {
|
||||
return index;
|
||||
} else if (character === "\\") {
|
||||
index++;
|
||||
} else if (character === "{") {
|
||||
braceLevel++;
|
||||
} else if (character === "}") {
|
||||
braceLevel--;
|
||||
}
|
||||
|
||||
index++;
|
||||
}
|
||||
|
||||
return -1;
|
||||
};
|
||||
|
||||
var escapeRegex = function escapeRegex(string) {
|
||||
return string.replace(/[-/\\^$*+?.()|[\]{}]/g, "\\$&");
|
||||
};
|
||||
|
||||
var amsRegex = /^\\begin{/;
|
||||
|
||||
var splitAtDelimiters = function splitAtDelimiters(text, delimiters) {
|
||||
var index;
|
||||
var data = [];
|
||||
var regexLeft = new RegExp("(" + delimiters.map(x => escapeRegex(x.left)).join("|") + ")");
|
||||
|
||||
while (true) {
|
||||
index = text.search(regexLeft);
|
||||
|
||||
if (index === -1) {
|
||||
break;
|
||||
}
|
||||
|
||||
if (index > 0) {
|
||||
data.push({
|
||||
type: "text",
|
||||
data: text.slice(0, index)
|
||||
});
|
||||
text = text.slice(index); // now text starts with delimiter
|
||||
} // ... so this always succeeds:
|
||||
|
||||
|
||||
var i = delimiters.findIndex(delim => text.startsWith(delim.left));
|
||||
index = findEndOfMath(delimiters[i].right, text, delimiters[i].left.length);
|
||||
|
||||
if (index === -1) {
|
||||
break;
|
||||
}
|
||||
|
||||
var rawData = text.slice(0, index + delimiters[i].right.length);
|
||||
var math = amsRegex.test(rawData) ? rawData : text.slice(delimiters[i].left.length, index);
|
||||
data.push({
|
||||
type: "math",
|
||||
data: math,
|
||||
rawData,
|
||||
display: delimiters[i].display
|
||||
});
|
||||
text = text.slice(index + delimiters[i].right.length);
|
||||
}
|
||||
|
||||
if (text !== "") {
|
||||
data.push({
|
||||
type: "text",
|
||||
data: text
|
||||
});
|
||||
}
|
||||
|
||||
return data;
|
||||
};
|
||||
|
||||
/* eslint no-console:0 */
|
||||
/* Note: optionsCopy is mutated by this method. If it is ever exposed in the
|
||||
* API, we should copy it before mutating.
|
||||
*/
|
||||
|
||||
var renderMathInText = function renderMathInText(text, optionsCopy) {
|
||||
var data = splitAtDelimiters(text, optionsCopy.delimiters);
|
||||
|
||||
if (data.length === 1 && data[0].type === 'text') {
|
||||
// There is no formula in the text.
|
||||
// Let's return null which means there is no need to replace
|
||||
// the current text node with a new one.
|
||||
return null;
|
||||
}
|
||||
|
||||
var fragment = document.createDocumentFragment();
|
||||
|
||||
for (var i = 0; i < data.length; i++) {
|
||||
if (data[i].type === "text") {
|
||||
fragment.appendChild(document.createTextNode(data[i].data));
|
||||
} else {
|
||||
var span = document.createElement("span");
|
||||
var math = data[i].data; // Override any display mode defined in the settings with that
|
||||
// defined by the text itself
|
||||
|
||||
optionsCopy.displayMode = data[i].display;
|
||||
|
||||
try {
|
||||
if (optionsCopy.preProcess) {
|
||||
math = optionsCopy.preProcess(math);
|
||||
}
|
||||
|
||||
katex.render(math, span, optionsCopy);
|
||||
} catch (e) {
|
||||
if (!(e instanceof katex.ParseError)) {
|
||||
throw e;
|
||||
}
|
||||
|
||||
optionsCopy.errorCallback("KaTeX auto-render: Failed to parse `" + data[i].data + "` with ", e);
|
||||
fragment.appendChild(document.createTextNode(data[i].rawData));
|
||||
continue;
|
||||
}
|
||||
|
||||
fragment.appendChild(span);
|
||||
}
|
||||
}
|
||||
|
||||
return fragment;
|
||||
};
|
||||
|
||||
var renderElem = function renderElem(elem, optionsCopy) {
|
||||
for (var i = 0; i < elem.childNodes.length; i++) {
|
||||
var childNode = elem.childNodes[i];
|
||||
|
||||
if (childNode.nodeType === 3) {
|
||||
// Text node
|
||||
// Concatenate all sibling text nodes.
|
||||
// Webkit browsers split very large text nodes into smaller ones,
|
||||
// so the delimiters may be split across different nodes.
|
||||
var textContentConcat = childNode.textContent;
|
||||
var sibling = childNode.nextSibling;
|
||||
var nSiblings = 0;
|
||||
|
||||
while (sibling && sibling.nodeType === Node.TEXT_NODE) {
|
||||
textContentConcat += sibling.textContent;
|
||||
sibling = sibling.nextSibling;
|
||||
nSiblings++;
|
||||
}
|
||||
|
||||
var frag = renderMathInText(textContentConcat, optionsCopy);
|
||||
|
||||
if (frag) {
|
||||
// Remove extra text nodes
|
||||
for (var j = 0; j < nSiblings; j++) {
|
||||
childNode.nextSibling.remove();
|
||||
}
|
||||
|
||||
i += frag.childNodes.length - 1;
|
||||
elem.replaceChild(frag, childNode);
|
||||
} else {
|
||||
// If the concatenated text does not contain math
|
||||
// the siblings will not either
|
||||
i += nSiblings;
|
||||
}
|
||||
} else if (childNode.nodeType === 1) {
|
||||
(function () {
|
||||
// Element node
|
||||
var className = ' ' + childNode.className + ' ';
|
||||
var shouldRender = optionsCopy.ignoredTags.indexOf(childNode.nodeName.toLowerCase()) === -1 && optionsCopy.ignoredClasses.every(x => className.indexOf(' ' + x + ' ') === -1);
|
||||
|
||||
if (shouldRender) {
|
||||
renderElem(childNode, optionsCopy);
|
||||
}
|
||||
})();
|
||||
} // Otherwise, it's something else, and ignore it.
|
||||
|
||||
}
|
||||
};
|
||||
|
||||
var renderMathInElement = function renderMathInElement(elem, options) {
|
||||
if (!elem) {
|
||||
throw new Error("No element provided to render");
|
||||
}
|
||||
|
||||
var optionsCopy = {}; // Object.assign(optionsCopy, option)
|
||||
|
||||
for (var option in options) {
|
||||
if (options.hasOwnProperty(option)) {
|
||||
optionsCopy[option] = options[option];
|
||||
}
|
||||
} // default options
|
||||
|
||||
|
||||
optionsCopy.delimiters = optionsCopy.delimiters || [{
|
||||
left: "$$",
|
||||
right: "$$",
|
||||
display: true
|
||||
}, {
|
||||
left: "\\(",
|
||||
right: "\\)",
|
||||
display: false
|
||||
}, // LaTeX uses $…$, but it ruins the display of normal `$` in text:
|
||||
// {left: "$", right: "$", display: false},
|
||||
// $ must come after $$
|
||||
// Render AMS environments even if outside $$…$$ delimiters.
|
||||
{
|
||||
left: "\\begin{equation}",
|
||||
right: "\\end{equation}",
|
||||
display: true
|
||||
}, {
|
||||
left: "\\begin{align}",
|
||||
right: "\\end{align}",
|
||||
display: true
|
||||
}, {
|
||||
left: "\\begin{alignat}",
|
||||
right: "\\end{alignat}",
|
||||
display: true
|
||||
}, {
|
||||
left: "\\begin{gather}",
|
||||
right: "\\end{gather}",
|
||||
display: true
|
||||
}, {
|
||||
left: "\\begin{CD}",
|
||||
right: "\\end{CD}",
|
||||
display: true
|
||||
}, {
|
||||
left: "\\[",
|
||||
right: "\\]",
|
||||
display: true
|
||||
}];
|
||||
optionsCopy.ignoredTags = optionsCopy.ignoredTags || ["script", "noscript", "style", "textarea", "pre", "code", "option"];
|
||||
optionsCopy.ignoredClasses = optionsCopy.ignoredClasses || [];
|
||||
optionsCopy.errorCallback = optionsCopy.errorCallback || console.error; // Enable sharing of global macros defined via `\gdef` between different
|
||||
// math elements within a single call to `renderMathInElement`.
|
||||
|
||||
optionsCopy.macros = optionsCopy.macros || {};
|
||||
renderElem(elem, optionsCopy);
|
||||
};
|
||||
|
||||
export { renderMathInElement as default };
|
||||
@@ -1,127 +0,0 @@
|
||||
(function webpackUniversalModuleDefinition(root, factory) {
|
||||
if(typeof exports === 'object' && typeof module === 'object')
|
||||
module.exports = factory();
|
||||
else if(typeof define === 'function' && define.amd)
|
||||
define([], factory);
|
||||
else {
|
||||
var a = factory();
|
||||
for(var i in a) (typeof exports === 'object' ? exports : root)[i] = a[i];
|
||||
}
|
||||
})((typeof self !== 'undefined' ? self : this), function() {
|
||||
return /******/ (function() { // webpackBootstrap
|
||||
/******/ "use strict";
|
||||
var __webpack_exports__ = {};
|
||||
|
||||
;// CONCATENATED MODULE: ./contrib/copy-tex/katex2tex.js
|
||||
// Set these to how you want inline and display math to be delimited.
|
||||
const defaultCopyDelimiters = {
|
||||
inline: ['$', '$'],
|
||||
// alternative: ['\(', '\)']
|
||||
display: ['$$', '$$'] // alternative: ['\[', '\]']
|
||||
|
||||
}; // Replace .katex elements with their TeX source (<annotation> element).
|
||||
// Modifies fragment in-place. Useful for writing your own 'copy' handler,
|
||||
// as in copy-tex.js.
|
||||
|
||||
function katexReplaceWithTex(fragment, copyDelimiters) {
|
||||
if (copyDelimiters === void 0) {
|
||||
copyDelimiters = defaultCopyDelimiters;
|
||||
}
|
||||
|
||||
// Remove .katex-html blocks that are preceded by .katex-mathml blocks
|
||||
// (which will get replaced below).
|
||||
const katexHtml = fragment.querySelectorAll('.katex-mathml + .katex-html');
|
||||
|
||||
for (let i = 0; i < katexHtml.length; i++) {
|
||||
const element = katexHtml[i];
|
||||
|
||||
if (element.remove) {
|
||||
element.remove();
|
||||
} else if (element.parentNode) {
|
||||
element.parentNode.removeChild(element);
|
||||
}
|
||||
} // Replace .katex-mathml elements with their annotation (TeX source)
|
||||
// descendant, with inline delimiters.
|
||||
|
||||
|
||||
const katexMathml = fragment.querySelectorAll('.katex-mathml');
|
||||
|
||||
for (let i = 0; i < katexMathml.length; i++) {
|
||||
const element = katexMathml[i];
|
||||
const texSource = element.querySelector('annotation');
|
||||
|
||||
if (texSource) {
|
||||
if (element.replaceWith) {
|
||||
element.replaceWith(texSource);
|
||||
} else if (element.parentNode) {
|
||||
element.parentNode.replaceChild(texSource, element);
|
||||
}
|
||||
|
||||
texSource.innerHTML = copyDelimiters.inline[0] + texSource.innerHTML + copyDelimiters.inline[1];
|
||||
}
|
||||
} // Switch display math to display delimiters.
|
||||
|
||||
|
||||
const displays = fragment.querySelectorAll('.katex-display annotation');
|
||||
|
||||
for (let i = 0; i < displays.length; i++) {
|
||||
const element = displays[i];
|
||||
element.innerHTML = copyDelimiters.display[0] + element.innerHTML.substr(copyDelimiters.inline[0].length, element.innerHTML.length - copyDelimiters.inline[0].length - copyDelimiters.inline[1].length) + copyDelimiters.display[1];
|
||||
}
|
||||
|
||||
return fragment;
|
||||
}
|
||||
/* harmony default export */ var katex2tex = (katexReplaceWithTex);
|
||||
;// CONCATENATED MODULE: ./contrib/copy-tex/copy-tex.js
|
||||
// Return <div class="katex"> element containing node, or null if not found.
|
||||
|
||||
function closestKatex(node) {
|
||||
// If node is a Text Node, for example, go up to containing Element,
|
||||
// where we can apply the `closest` method.
|
||||
const element = node instanceof Element ? node : node.parentElement;
|
||||
return element && element.closest('.katex');
|
||||
} // Global copy handler to modify behavior on/within .katex elements.
|
||||
|
||||
|
||||
document.addEventListener('copy', function (event) {
|
||||
const selection = window.getSelection();
|
||||
|
||||
if (selection.isCollapsed || !event.clipboardData) {
|
||||
return; // default action OK if selection is empty or unchangeable
|
||||
}
|
||||
|
||||
const clipboardData = event.clipboardData;
|
||||
const range = selection.getRangeAt(0); // When start point is within a formula, expand to entire formula.
|
||||
|
||||
const startKatex = closestKatex(range.startContainer);
|
||||
|
||||
if (startKatex) {
|
||||
range.setStartBefore(startKatex);
|
||||
} // Similarly, when end point is within a formula, expand to entire formula.
|
||||
|
||||
|
||||
const endKatex = closestKatex(range.endContainer);
|
||||
|
||||
if (endKatex) {
|
||||
range.setEndAfter(endKatex);
|
||||
}
|
||||
|
||||
const fragment = range.cloneContents();
|
||||
|
||||
if (!fragment.querySelector('.katex-mathml')) {
|
||||
return; // default action OK if no .katex-mathml elements
|
||||
}
|
||||
|
||||
const htmlContents = Array.prototype.map.call(fragment.childNodes, el => el instanceof Text ? el.textContent : el.outerHTML).join(''); // Preserve usual HTML copy/paste behavior.
|
||||
|
||||
clipboardData.setData('text/html', htmlContents); // Rewrite plain-text version.
|
||||
|
||||
clipboardData.setData('text/plain', katex2tex(fragment).textContent); // Prevent normal copy handling.
|
||||
|
||||
event.preventDefault();
|
||||
});
|
||||
__webpack_exports__ = __webpack_exports__["default"];
|
||||
/******/ return __webpack_exports__;
|
||||
/******/ })()
|
||||
;
|
||||
});
|
||||
Vendored
-1
@@ -1 +0,0 @@
|
||||
!function(e,t){if("object"==typeof exports&&"object"==typeof module)module.exports=t();else if("function"==typeof define&&define.amd)define([],t);else{var n=t();for(var o in n)("object"==typeof exports?exports:e)[o]=n[o]}}("undefined"!=typeof self?self:this,(function(){return function(){"use strict";var e={};const t={inline:["$","$"],display:["$$","$$"]};var n=function(e,n){void 0===n&&(n=t);const o=e.querySelectorAll(".katex-mathml + .katex-html");for(let e=0;e<o.length;e++){const t=o[e];t.remove?t.remove():t.parentNode&&t.parentNode.removeChild(t)}const r=e.querySelectorAll(".katex-mathml");for(let e=0;e<r.length;e++){const t=r[e],o=t.querySelector("annotation");o&&(t.replaceWith?t.replaceWith(o):t.parentNode&&t.parentNode.replaceChild(o,t),o.innerHTML=n.inline[0]+o.innerHTML+n.inline[1])}const l=e.querySelectorAll(".katex-display annotation");for(let e=0;e<l.length;e++){const t=l[e];t.innerHTML=n.display[0]+t.innerHTML.substr(n.inline[0].length,t.innerHTML.length-n.inline[0].length-n.inline[1].length)+n.display[1]}return e};function o(e){const t=e instanceof Element?e:e.parentElement;return t&&t.closest(".katex")}return document.addEventListener("copy",(function(e){const t=window.getSelection();if(t.isCollapsed||!e.clipboardData)return;const r=e.clipboardData,l=t.getRangeAt(0),i=o(l.startContainer);i&&l.setStartBefore(i);const a=o(l.endContainer);a&&l.setEndAfter(a);const s=l.cloneContents();if(!s.querySelector(".katex-mathml"))return;const c=Array.prototype.map.call(s.childNodes,(e=>e instanceof Text?e.textContent:e.outerHTML)).join("");r.setData("text/html",c),r.setData("text/plain",n(s).textContent),e.preventDefault()})),e=e.default}()}));
|
||||
@@ -1,105 +0,0 @@
|
||||
// Set these to how you want inline and display math to be delimited.
|
||||
var defaultCopyDelimiters = {
|
||||
inline: ['$', '$'],
|
||||
// alternative: ['\(', '\)']
|
||||
display: ['$$', '$$'] // alternative: ['\[', '\]']
|
||||
|
||||
}; // Replace .katex elements with their TeX source (<annotation> element).
|
||||
// Modifies fragment in-place. Useful for writing your own 'copy' handler,
|
||||
// as in copy-tex.js.
|
||||
|
||||
function katexReplaceWithTex(fragment, copyDelimiters) {
|
||||
if (copyDelimiters === void 0) {
|
||||
copyDelimiters = defaultCopyDelimiters;
|
||||
}
|
||||
|
||||
// Remove .katex-html blocks that are preceded by .katex-mathml blocks
|
||||
// (which will get replaced below).
|
||||
var katexHtml = fragment.querySelectorAll('.katex-mathml + .katex-html');
|
||||
|
||||
for (var i = 0; i < katexHtml.length; i++) {
|
||||
var element = katexHtml[i];
|
||||
|
||||
if (element.remove) {
|
||||
element.remove();
|
||||
} else if (element.parentNode) {
|
||||
element.parentNode.removeChild(element);
|
||||
}
|
||||
} // Replace .katex-mathml elements with their annotation (TeX source)
|
||||
// descendant, with inline delimiters.
|
||||
|
||||
|
||||
var katexMathml = fragment.querySelectorAll('.katex-mathml');
|
||||
|
||||
for (var _i = 0; _i < katexMathml.length; _i++) {
|
||||
var _element = katexMathml[_i];
|
||||
|
||||
var texSource = _element.querySelector('annotation');
|
||||
|
||||
if (texSource) {
|
||||
if (_element.replaceWith) {
|
||||
_element.replaceWith(texSource);
|
||||
} else if (_element.parentNode) {
|
||||
_element.parentNode.replaceChild(texSource, _element);
|
||||
}
|
||||
|
||||
texSource.innerHTML = copyDelimiters.inline[0] + texSource.innerHTML + copyDelimiters.inline[1];
|
||||
}
|
||||
} // Switch display math to display delimiters.
|
||||
|
||||
|
||||
var displays = fragment.querySelectorAll('.katex-display annotation');
|
||||
|
||||
for (var _i2 = 0; _i2 < displays.length; _i2++) {
|
||||
var _element2 = displays[_i2];
|
||||
_element2.innerHTML = copyDelimiters.display[0] + _element2.innerHTML.substr(copyDelimiters.inline[0].length, _element2.innerHTML.length - copyDelimiters.inline[0].length - copyDelimiters.inline[1].length) + copyDelimiters.display[1];
|
||||
}
|
||||
|
||||
return fragment;
|
||||
}
|
||||
|
||||
function closestKatex(node) {
|
||||
// If node is a Text Node, for example, go up to containing Element,
|
||||
// where we can apply the `closest` method.
|
||||
var element = node instanceof Element ? node : node.parentElement;
|
||||
return element && element.closest('.katex');
|
||||
} // Global copy handler to modify behavior on/within .katex elements.
|
||||
|
||||
|
||||
document.addEventListener('copy', function (event) {
|
||||
var selection = window.getSelection();
|
||||
|
||||
if (selection.isCollapsed || !event.clipboardData) {
|
||||
return; // default action OK if selection is empty or unchangeable
|
||||
}
|
||||
|
||||
var clipboardData = event.clipboardData;
|
||||
var range = selection.getRangeAt(0); // When start point is within a formula, expand to entire formula.
|
||||
|
||||
var startKatex = closestKatex(range.startContainer);
|
||||
|
||||
if (startKatex) {
|
||||
range.setStartBefore(startKatex);
|
||||
} // Similarly, when end point is within a formula, expand to entire formula.
|
||||
|
||||
|
||||
var endKatex = closestKatex(range.endContainer);
|
||||
|
||||
if (endKatex) {
|
||||
range.setEndAfter(endKatex);
|
||||
}
|
||||
|
||||
var fragment = range.cloneContents();
|
||||
|
||||
if (!fragment.querySelector('.katex-mathml')) {
|
||||
return; // default action OK if no .katex-mathml elements
|
||||
}
|
||||
|
||||
var htmlContents = Array.prototype.map.call(fragment.childNodes, el => el instanceof Text ? el.textContent : el.outerHTML).join(''); // Preserve usual HTML copy/paste behavior.
|
||||
|
||||
clipboardData.setData('text/html', htmlContents); // Rewrite plain-text version.
|
||||
|
||||
clipboardData.setData('text/plain', katexReplaceWithTex(fragment).textContent); // Prevent normal copy handling.
|
||||
|
||||
event.preventDefault();
|
||||
});
|
||||
@@ -1,112 +0,0 @@
|
||||
(function webpackUniversalModuleDefinition(root, factory) {
|
||||
if(typeof exports === 'object' && typeof module === 'object')
|
||||
module.exports = factory(require("katex"));
|
||||
else if(typeof define === 'function' && define.amd)
|
||||
define(["katex"], factory);
|
||||
else {
|
||||
var a = typeof exports === 'object' ? factory(require("katex")) : factory(root["katex"]);
|
||||
for(var i in a) (typeof exports === 'object' ? exports : root)[i] = a[i];
|
||||
}
|
||||
})((typeof self !== 'undefined' ? self : this), function(__WEBPACK_EXTERNAL_MODULE__771__) {
|
||||
return /******/ (function() { // webpackBootstrap
|
||||
/******/ "use strict";
|
||||
/******/ var __webpack_modules__ = ({
|
||||
|
||||
/***/ 771:
|
||||
/***/ (function(module) {
|
||||
|
||||
module.exports = __WEBPACK_EXTERNAL_MODULE__771__;
|
||||
|
||||
/***/ })
|
||||
|
||||
/******/ });
|
||||
/************************************************************************/
|
||||
/******/ // The module cache
|
||||
/******/ var __webpack_module_cache__ = {};
|
||||
/******/
|
||||
/******/ // The require function
|
||||
/******/ function __webpack_require__(moduleId) {
|
||||
/******/ // Check if module is in cache
|
||||
/******/ var cachedModule = __webpack_module_cache__[moduleId];
|
||||
/******/ if (cachedModule !== undefined) {
|
||||
/******/ return cachedModule.exports;
|
||||
/******/ }
|
||||
/******/ // Create a new module (and put it into the cache)
|
||||
/******/ var module = __webpack_module_cache__[moduleId] = {
|
||||
/******/ // no module.id needed
|
||||
/******/ // no module.loaded needed
|
||||
/******/ exports: {}
|
||||
/******/ };
|
||||
/******/
|
||||
/******/ // Execute the module function
|
||||
/******/ __webpack_modules__[moduleId](module, module.exports, __webpack_require__);
|
||||
/******/
|
||||
/******/ // Return the exports of the module
|
||||
/******/ return module.exports;
|
||||
/******/ }
|
||||
/******/
|
||||
/************************************************************************/
|
||||
/******/ /* webpack/runtime/compat get default export */
|
||||
/******/ !function() {
|
||||
/******/ // getDefaultExport function for compatibility with non-harmony modules
|
||||
/******/ __webpack_require__.n = function(module) {
|
||||
/******/ var getter = module && module.__esModule ?
|
||||
/******/ function() { return module['default']; } :
|
||||
/******/ function() { return module; };
|
||||
/******/ __webpack_require__.d(getter, { a: getter });
|
||||
/******/ return getter;
|
||||
/******/ };
|
||||
/******/ }();
|
||||
/******/
|
||||
/******/ /* webpack/runtime/define property getters */
|
||||
/******/ !function() {
|
||||
/******/ // define getter functions for harmony exports
|
||||
/******/ __webpack_require__.d = function(exports, definition) {
|
||||
/******/ for(var key in definition) {
|
||||
/******/ if(__webpack_require__.o(definition, key) && !__webpack_require__.o(exports, key)) {
|
||||
/******/ Object.defineProperty(exports, key, { enumerable: true, get: definition[key] });
|
||||
/******/ }
|
||||
/******/ }
|
||||
/******/ };
|
||||
/******/ }();
|
||||
/******/
|
||||
/******/ /* webpack/runtime/hasOwnProperty shorthand */
|
||||
/******/ !function() {
|
||||
/******/ __webpack_require__.o = function(obj, prop) { return Object.prototype.hasOwnProperty.call(obj, prop); }
|
||||
/******/ }();
|
||||
/******/
|
||||
/************************************************************************/
|
||||
var __webpack_exports__ = {};
|
||||
// This entry need to be wrapped in an IIFE because it need to be isolated against other modules in the chunk.
|
||||
!function() {
|
||||
/* harmony import */ var katex__WEBPACK_IMPORTED_MODULE_0__ = __webpack_require__(771);
|
||||
/* harmony import */ var katex__WEBPACK_IMPORTED_MODULE_0___default = /*#__PURE__*/__webpack_require__.n(katex__WEBPACK_IMPORTED_MODULE_0__);
|
||||
|
||||
let scripts = document.body.getElementsByTagName("script");
|
||||
scripts = Array.prototype.slice.call(scripts);
|
||||
scripts.forEach(function (script) {
|
||||
if (!script.type || !script.type.match(/math\/tex/i)) {
|
||||
return -1;
|
||||
}
|
||||
|
||||
const display = script.type.match(/mode\s*=\s*display(;|\s|\n|$)/) != null;
|
||||
const katexElement = document.createElement(display ? "div" : "span");
|
||||
katexElement.setAttribute("class", display ? "equation" : "inline-equation");
|
||||
|
||||
try {
|
||||
katex__WEBPACK_IMPORTED_MODULE_0___default().render(script.text, katexElement, {
|
||||
displayMode: display
|
||||
});
|
||||
} catch (err) {
|
||||
//console.error(err); linter doesn't like this
|
||||
katexElement.textContent = script.text;
|
||||
}
|
||||
|
||||
script.parentNode.replaceChild(katexElement, script);
|
||||
});
|
||||
}();
|
||||
__webpack_exports__ = __webpack_exports__["default"];
|
||||
/******/ return __webpack_exports__;
|
||||
/******/ })()
|
||||
;
|
||||
});
|
||||
@@ -1 +0,0 @@
|
||||
!function(e,t){if("object"==typeof exports&&"object"==typeof module)module.exports=t(require("katex"));else if("function"==typeof define&&define.amd)define(["katex"],t);else{var n="object"==typeof exports?t(require("katex")):t(e.katex);for(var r in n)("object"==typeof exports?exports:e)[r]=n[r]}}("undefined"!=typeof self?self:this,(function(e){return function(){"use strict";var t={771:function(t){t.exports=e}},n={};function r(e){var o=n[e];if(void 0!==o)return o.exports;var i=n[e]={exports:{}};return t[e](i,i.exports,r),i.exports}r.n=function(e){var t=e&&e.__esModule?function(){return e.default}:function(){return e};return r.d(t,{a:t}),t},r.d=function(e,t){for(var n in t)r.o(t,n)&&!r.o(e,n)&&Object.defineProperty(e,n,{enumerable:!0,get:t[n]})},r.o=function(e,t){return Object.prototype.hasOwnProperty.call(e,t)};var o={};return function(){var e=r(771),t=r.n(e);let n=document.body.getElementsByTagName("script");n=Array.prototype.slice.call(n),n.forEach((function(e){if(!e.type||!e.type.match(/math\/tex/i))return-1;const n=null!=e.type.match(/mode\s*=\s*display(;|\s|\n|$)/),r=document.createElement(n?"div":"span");r.setAttribute("class",n?"equation":"inline-equation");try{t().render(e.text,r,{displayMode:n})}catch(t){r.textContent=e.text}e.parentNode.replaceChild(r,e)}))}(),o=o.default}()}));
|
||||
@@ -1,24 +0,0 @@
|
||||
import katex from '../katex.mjs';
|
||||
|
||||
var scripts = document.body.getElementsByTagName("script");
|
||||
scripts = Array.prototype.slice.call(scripts);
|
||||
scripts.forEach(function (script) {
|
||||
if (!script.type || !script.type.match(/math\/tex/i)) {
|
||||
return -1;
|
||||
}
|
||||
|
||||
var display = script.type.match(/mode\s*=\s*display(;|\s|\n|$)/) != null;
|
||||
var katexElement = document.createElement(display ? "div" : "span");
|
||||
katexElement.setAttribute("class", display ? "equation" : "inline-equation");
|
||||
|
||||
try {
|
||||
katex.render(script.text, katexElement, {
|
||||
displayMode: display
|
||||
});
|
||||
} catch (err) {
|
||||
//console.error(err); linter doesn't like this
|
||||
katexElement.textContent = script.text;
|
||||
}
|
||||
|
||||
script.parentNode.replaceChild(katexElement, script);
|
||||
});
|
||||
File diff suppressed because it is too large
Load Diff
Vendored
-1
File diff suppressed because one or more lines are too long
File diff suppressed because it is too large
Load Diff
@@ -1,890 +0,0 @@
|
||||
(function webpackUniversalModuleDefinition(root, factory) {
|
||||
if(typeof exports === 'object' && typeof module === 'object')
|
||||
module.exports = factory(require("katex"));
|
||||
else if(typeof define === 'function' && define.amd)
|
||||
define(["katex"], factory);
|
||||
else {
|
||||
var a = typeof exports === 'object' ? factory(require("katex")) : factory(root["katex"]);
|
||||
for(var i in a) (typeof exports === 'object' ? exports : root)[i] = a[i];
|
||||
}
|
||||
})((typeof self !== 'undefined' ? self : this), function(__WEBPACK_EXTERNAL_MODULE__771__) {
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||||
return /******/ (function() { // webpackBootstrap
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||||
/******/ "use strict";
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||||
/******/ var __webpack_modules__ = ({
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||||
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||||
/***/ 771:
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||||
/***/ (function(module) {
|
||||
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||||
module.exports = __WEBPACK_EXTERNAL_MODULE__771__;
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||||
|
||||
/***/ })
|
||||
|
||||
/******/ });
|
||||
/************************************************************************/
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||||
/******/ // The module cache
|
||||
/******/ var __webpack_module_cache__ = {};
|
||||
/******/
|
||||
/******/ // The require function
|
||||
/******/ function __webpack_require__(moduleId) {
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||||
/******/ // Check if module is in cache
|
||||
/******/ var cachedModule = __webpack_module_cache__[moduleId];
|
||||
/******/ if (cachedModule !== undefined) {
|
||||
/******/ return cachedModule.exports;
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||||
/******/ }
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||||
/******/ // Create a new module (and put it into the cache)
|
||||
/******/ var module = __webpack_module_cache__[moduleId] = {
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||||
/******/ // no module.id needed
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||||
/******/ // no module.loaded needed
|
||||
/******/ exports: {}
|
||||
/******/ };
|
||||
/******/
|
||||
/******/ // Execute the module function
|
||||
/******/ __webpack_modules__[moduleId](module, module.exports, __webpack_require__);
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||||
/******/
|
||||
/******/ // Return the exports of the module
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||||
/******/ return module.exports;
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||||
/******/ }
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||||
/******/
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||||
/************************************************************************/
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||||
/******/ /* webpack/runtime/compat get default export */
|
||||
/******/ !function() {
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/******/ // getDefaultExport function for compatibility with non-harmony modules
|
||||
/******/ __webpack_require__.n = function(module) {
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||||
/******/ var getter = module && module.__esModule ?
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||||
/******/ function() { return module['default']; } :
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||||
/******/ function() { return module; };
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||||
/******/ __webpack_require__.d(getter, { a: getter });
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||||
/******/ return getter;
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||||
/******/ };
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/******/ }();
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||||
/******/
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||||
/******/ /* webpack/runtime/define property getters */
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||||
/******/ !function() {
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||||
/******/ // define getter functions for harmony exports
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||||
/******/ __webpack_require__.d = function(exports, definition) {
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||||
/******/ for(var key in definition) {
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||||
/******/ if(__webpack_require__.o(definition, key) && !__webpack_require__.o(exports, key)) {
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||||
/******/ Object.defineProperty(exports, key, { enumerable: true, get: definition[key] });
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/******/ }
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||||
/******/ };
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/******/ }();
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/******/
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/******/ /* webpack/runtime/hasOwnProperty shorthand */
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||||
/******/ !function() {
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/******/ __webpack_require__.o = function(obj, prop) { return Object.prototype.hasOwnProperty.call(obj, prop); }
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||||
/******/ }();
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||||
/******/
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||||
/************************************************************************/
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||||
var __webpack_exports__ = {};
|
||||
// This entry need to be wrapped in an IIFE because it need to be isolated against other modules in the chunk.
|
||||
!function() {
|
||||
/* harmony import */ var katex__WEBPACK_IMPORTED_MODULE_0__ = __webpack_require__(771);
|
||||
/* harmony import */ var katex__WEBPACK_IMPORTED_MODULE_0___default = /*#__PURE__*/__webpack_require__.n(katex__WEBPACK_IMPORTED_MODULE_0__);
|
||||
/**
|
||||
* renderA11yString returns a readable string.
|
||||
*
|
||||
* In some cases the string will have the proper semantic math
|
||||
* meaning,:
|
||||
* renderA11yString("\\frac{1}{2}"")
|
||||
* -> "start fraction, 1, divided by, 2, end fraction"
|
||||
*
|
||||
* However, other cases do not:
|
||||
* renderA11yString("f(x) = x^2")
|
||||
* -> "f, left parenthesis, x, right parenthesis, equals, x, squared"
|
||||
*
|
||||
* The commas in the string aim to increase ease of understanding
|
||||
* when read by a screenreader.
|
||||
*/
|
||||
// NOTE: since we're importing types here these files won't actually be
|
||||
// included in the build.
|
||||
// $FlowIgnore: we import the types directly anyways
|
||||
|
||||
const stringMap = {
|
||||
"(": "left parenthesis",
|
||||
")": "right parenthesis",
|
||||
"[": "open bracket",
|
||||
"]": "close bracket",
|
||||
"\\{": "left brace",
|
||||
"\\}": "right brace",
|
||||
"\\lvert": "open vertical bar",
|
||||
"\\rvert": "close vertical bar",
|
||||
"|": "vertical bar",
|
||||
"\\uparrow": "up arrow",
|
||||
"\\Uparrow": "up arrow",
|
||||
"\\downarrow": "down arrow",
|
||||
"\\Downarrow": "down arrow",
|
||||
"\\updownarrow": "up down arrow",
|
||||
"\\leftarrow": "left arrow",
|
||||
"\\Leftarrow": "left arrow",
|
||||
"\\rightarrow": "right arrow",
|
||||
"\\Rightarrow": "right arrow",
|
||||
"\\langle": "open angle",
|
||||
"\\rangle": "close angle",
|
||||
"\\lfloor": "open floor",
|
||||
"\\rfloor": "close floor",
|
||||
"\\int": "integral",
|
||||
"\\intop": "integral",
|
||||
"\\lim": "limit",
|
||||
"\\ln": "natural log",
|
||||
"\\log": "log",
|
||||
"\\sin": "sine",
|
||||
"\\cos": "cosine",
|
||||
"\\tan": "tangent",
|
||||
"\\cot": "cotangent",
|
||||
"\\sum": "sum",
|
||||
"/": "slash",
|
||||
",": "comma",
|
||||
".": "point",
|
||||
"-": "negative",
|
||||
"+": "plus",
|
||||
"~": "tilde",
|
||||
":": "colon",
|
||||
"?": "question mark",
|
||||
"'": "apostrophe",
|
||||
"\\%": "percent",
|
||||
" ": "space",
|
||||
"\\ ": "space",
|
||||
"\\$": "dollar sign",
|
||||
"\\angle": "angle",
|
||||
"\\degree": "degree",
|
||||
"\\circ": "circle",
|
||||
"\\vec": "vector",
|
||||
"\\triangle": "triangle",
|
||||
"\\pi": "pi",
|
||||
"\\prime": "prime",
|
||||
"\\infty": "infinity",
|
||||
"\\alpha": "alpha",
|
||||
"\\beta": "beta",
|
||||
"\\gamma": "gamma",
|
||||
"\\omega": "omega",
|
||||
"\\theta": "theta",
|
||||
"\\sigma": "sigma",
|
||||
"\\lambda": "lambda",
|
||||
"\\tau": "tau",
|
||||
"\\Delta": "delta",
|
||||
"\\delta": "delta",
|
||||
"\\mu": "mu",
|
||||
"\\rho": "rho",
|
||||
"\\nabla": "del",
|
||||
"\\ell": "ell",
|
||||
"\\ldots": "dots",
|
||||
// TODO: add entries for all accents
|
||||
"\\hat": "hat",
|
||||
"\\acute": "acute"
|
||||
};
|
||||
const powerMap = {
|
||||
"prime": "prime",
|
||||
"degree": "degrees",
|
||||
"circle": "degrees",
|
||||
"2": "squared",
|
||||
"3": "cubed"
|
||||
};
|
||||
const openMap = {
|
||||
"|": "open vertical bar",
|
||||
".": ""
|
||||
};
|
||||
const closeMap = {
|
||||
"|": "close vertical bar",
|
||||
".": ""
|
||||
};
|
||||
const binMap = {
|
||||
"+": "plus",
|
||||
"-": "minus",
|
||||
"\\pm": "plus minus",
|
||||
"\\cdot": "dot",
|
||||
"*": "times",
|
||||
"/": "divided by",
|
||||
"\\times": "times",
|
||||
"\\div": "divided by",
|
||||
"\\circ": "circle",
|
||||
"\\bullet": "bullet"
|
||||
};
|
||||
const relMap = {
|
||||
"=": "equals",
|
||||
"\\approx": "approximately equals",
|
||||
"≠": "does not equal",
|
||||
"\\geq": "is greater than or equal to",
|
||||
"\\ge": "is greater than or equal to",
|
||||
"\\leq": "is less than or equal to",
|
||||
"\\le": "is less than or equal to",
|
||||
">": "is greater than",
|
||||
"<": "is less than",
|
||||
"\\leftarrow": "left arrow",
|
||||
"\\Leftarrow": "left arrow",
|
||||
"\\rightarrow": "right arrow",
|
||||
"\\Rightarrow": "right arrow",
|
||||
":": "colon"
|
||||
};
|
||||
const accentUnderMap = {
|
||||
"\\underleftarrow": "left arrow",
|
||||
"\\underrightarrow": "right arrow",
|
||||
"\\underleftrightarrow": "left-right arrow",
|
||||
"\\undergroup": "group",
|
||||
"\\underlinesegment": "line segment",
|
||||
"\\utilde": "tilde"
|
||||
};
|
||||
|
||||
const buildString = (str, type, a11yStrings) => {
|
||||
if (!str) {
|
||||
return;
|
||||
}
|
||||
|
||||
let ret;
|
||||
|
||||
if (type === "open") {
|
||||
ret = str in openMap ? openMap[str] : stringMap[str] || str;
|
||||
} else if (type === "close") {
|
||||
ret = str in closeMap ? closeMap[str] : stringMap[str] || str;
|
||||
} else if (type === "bin") {
|
||||
ret = binMap[str] || str;
|
||||
} else if (type === "rel") {
|
||||
ret = relMap[str] || str;
|
||||
} else {
|
||||
ret = stringMap[str] || str;
|
||||
} // If the text to add is a number and there is already a string
|
||||
// in the list and the last string is a number then we should
|
||||
// combine them into a single number
|
||||
|
||||
|
||||
if (/^\d+$/.test(ret) && a11yStrings.length > 0 && // TODO(kevinb): check that the last item in a11yStrings is a string
|
||||
// I think we might be able to drop the nested arrays, which would make
|
||||
// this easier to type
|
||||
// $FlowFixMe
|
||||
/^\d+$/.test(a11yStrings[a11yStrings.length - 1])) {
|
||||
a11yStrings[a11yStrings.length - 1] += ret;
|
||||
} else if (ret) {
|
||||
a11yStrings.push(ret);
|
||||
}
|
||||
};
|
||||
|
||||
const buildRegion = (a11yStrings, callback) => {
|
||||
const regionStrings = [];
|
||||
a11yStrings.push(regionStrings);
|
||||
callback(regionStrings);
|
||||
};
|
||||
|
||||
const handleObject = (tree, a11yStrings, atomType) => {
|
||||
// Everything else is assumed to be an object...
|
||||
switch (tree.type) {
|
||||
case "accent":
|
||||
{
|
||||
buildRegion(a11yStrings, a11yStrings => {
|
||||
buildA11yStrings(tree.base, a11yStrings, atomType);
|
||||
a11yStrings.push("with");
|
||||
buildString(tree.label, "normal", a11yStrings);
|
||||
a11yStrings.push("on top");
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "accentUnder":
|
||||
{
|
||||
buildRegion(a11yStrings, a11yStrings => {
|
||||
buildA11yStrings(tree.base, a11yStrings, atomType);
|
||||
a11yStrings.push("with");
|
||||
buildString(accentUnderMap[tree.label], "normal", a11yStrings);
|
||||
a11yStrings.push("underneath");
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "accent-token":
|
||||
{
|
||||
// Used internally by accent symbols.
|
||||
break;
|
||||
}
|
||||
|
||||
case "atom":
|
||||
{
|
||||
const {
|
||||
text
|
||||
} = tree;
|
||||
|
||||
switch (tree.family) {
|
||||
case "bin":
|
||||
{
|
||||
buildString(text, "bin", a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "close":
|
||||
{
|
||||
buildString(text, "close", a11yStrings);
|
||||
break;
|
||||
}
|
||||
// TODO(kevinb): figure out what should be done for inner
|
||||
|
||||
case "inner":
|
||||
{
|
||||
buildString(tree.text, "inner", a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "open":
|
||||
{
|
||||
buildString(text, "open", a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "punct":
|
||||
{
|
||||
buildString(text, "punct", a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "rel":
|
||||
{
|
||||
buildString(text, "rel", a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
default:
|
||||
{
|
||||
tree.family;
|
||||
throw new Error("\"" + tree.family + "\" is not a valid atom type");
|
||||
}
|
||||
}
|
||||
|
||||
break;
|
||||
}
|
||||
|
||||
case "color":
|
||||
{
|
||||
const color = tree.color.replace(/katex-/, "");
|
||||
buildRegion(a11yStrings, regionStrings => {
|
||||
regionStrings.push("start color " + color);
|
||||
buildA11yStrings(tree.body, regionStrings, atomType);
|
||||
regionStrings.push("end color " + color);
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "color-token":
|
||||
{
|
||||
// Used by \color, \colorbox, and \fcolorbox but not directly rendered.
|
||||
// It's a leaf node and has no children so just break.
|
||||
break;
|
||||
}
|
||||
|
||||
case "delimsizing":
|
||||
{
|
||||
if (tree.delim && tree.delim !== ".") {
|
||||
buildString(tree.delim, "normal", a11yStrings);
|
||||
}
|
||||
|
||||
break;
|
||||
}
|
||||
|
||||
case "genfrac":
|
||||
{
|
||||
buildRegion(a11yStrings, regionStrings => {
|
||||
// genfrac can have unbalanced delimiters
|
||||
const {
|
||||
leftDelim,
|
||||
rightDelim
|
||||
} = tree; // NOTE: Not sure if this is a safe assumption
|
||||
// hasBarLine true -> fraction, false -> binomial
|
||||
|
||||
if (tree.hasBarLine) {
|
||||
regionStrings.push("start fraction");
|
||||
leftDelim && buildString(leftDelim, "open", regionStrings);
|
||||
buildA11yStrings(tree.numer, regionStrings, atomType);
|
||||
regionStrings.push("divided by");
|
||||
buildA11yStrings(tree.denom, regionStrings, atomType);
|
||||
rightDelim && buildString(rightDelim, "close", regionStrings);
|
||||
regionStrings.push("end fraction");
|
||||
} else {
|
||||
regionStrings.push("start binomial");
|
||||
leftDelim && buildString(leftDelim, "open", regionStrings);
|
||||
buildA11yStrings(tree.numer, regionStrings, atomType);
|
||||
regionStrings.push("over");
|
||||
buildA11yStrings(tree.denom, regionStrings, atomType);
|
||||
rightDelim && buildString(rightDelim, "close", regionStrings);
|
||||
regionStrings.push("end binomial");
|
||||
}
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "hbox":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "kern":
|
||||
{
|
||||
// No op: we don't attempt to present kerning information
|
||||
// to the screen reader.
|
||||
break;
|
||||
}
|
||||
|
||||
case "leftright":
|
||||
{
|
||||
buildRegion(a11yStrings, regionStrings => {
|
||||
buildString(tree.left, "open", regionStrings);
|
||||
buildA11yStrings(tree.body, regionStrings, atomType);
|
||||
buildString(tree.right, "close", regionStrings);
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "leftright-right":
|
||||
{
|
||||
// TODO: double check that this is a no-op
|
||||
break;
|
||||
}
|
||||
|
||||
case "lap":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "mathord":
|
||||
{
|
||||
buildString(tree.text, "normal", a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "op":
|
||||
{
|
||||
const {
|
||||
body,
|
||||
name
|
||||
} = tree;
|
||||
|
||||
if (body) {
|
||||
buildA11yStrings(body, a11yStrings, atomType);
|
||||
} else if (name) {
|
||||
buildString(name, "normal", a11yStrings);
|
||||
}
|
||||
|
||||
break;
|
||||
}
|
||||
|
||||
case "op-token":
|
||||
{
|
||||
// Used internally by operator symbols.
|
||||
buildString(tree.text, atomType, a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "ordgroup":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "overline":
|
||||
{
|
||||
buildRegion(a11yStrings, function (a11yStrings) {
|
||||
a11yStrings.push("start overline");
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
a11yStrings.push("end overline");
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "pmb":
|
||||
{
|
||||
a11yStrings.push("bold");
|
||||
break;
|
||||
}
|
||||
|
||||
case "phantom":
|
||||
{
|
||||
a11yStrings.push("empty space");
|
||||
break;
|
||||
}
|
||||
|
||||
case "raisebox":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "rule":
|
||||
{
|
||||
a11yStrings.push("rectangle");
|
||||
break;
|
||||
}
|
||||
|
||||
case "sizing":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "spacing":
|
||||
{
|
||||
a11yStrings.push("space");
|
||||
break;
|
||||
}
|
||||
|
||||
case "styling":
|
||||
{
|
||||
// We ignore the styling and just pass through the contents
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "sqrt":
|
||||
{
|
||||
buildRegion(a11yStrings, regionStrings => {
|
||||
const {
|
||||
body,
|
||||
index
|
||||
} = tree;
|
||||
|
||||
if (index) {
|
||||
const indexString = flatten(buildA11yStrings(index, [], atomType)).join(",");
|
||||
|
||||
if (indexString === "3") {
|
||||
regionStrings.push("cube root of");
|
||||
buildA11yStrings(body, regionStrings, atomType);
|
||||
regionStrings.push("end cube root");
|
||||
return;
|
||||
}
|
||||
|
||||
regionStrings.push("root");
|
||||
regionStrings.push("start index");
|
||||
buildA11yStrings(index, regionStrings, atomType);
|
||||
regionStrings.push("end index");
|
||||
return;
|
||||
}
|
||||
|
||||
regionStrings.push("square root of");
|
||||
buildA11yStrings(body, regionStrings, atomType);
|
||||
regionStrings.push("end square root");
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "supsub":
|
||||
{
|
||||
const {
|
||||
base,
|
||||
sub,
|
||||
sup
|
||||
} = tree;
|
||||
let isLog = false;
|
||||
|
||||
if (base) {
|
||||
buildA11yStrings(base, a11yStrings, atomType);
|
||||
isLog = base.type === "op" && base.name === "\\log";
|
||||
}
|
||||
|
||||
if (sub) {
|
||||
const regionName = isLog ? "base" : "subscript";
|
||||
buildRegion(a11yStrings, function (regionStrings) {
|
||||
regionStrings.push("start " + regionName);
|
||||
buildA11yStrings(sub, regionStrings, atomType);
|
||||
regionStrings.push("end " + regionName);
|
||||
});
|
||||
}
|
||||
|
||||
if (sup) {
|
||||
buildRegion(a11yStrings, function (regionStrings) {
|
||||
const supString = flatten(buildA11yStrings(sup, [], atomType)).join(",");
|
||||
|
||||
if (supString in powerMap) {
|
||||
regionStrings.push(powerMap[supString]);
|
||||
return;
|
||||
}
|
||||
|
||||
regionStrings.push("start superscript");
|
||||
buildA11yStrings(sup, regionStrings, atomType);
|
||||
regionStrings.push("end superscript");
|
||||
});
|
||||
}
|
||||
|
||||
break;
|
||||
}
|
||||
|
||||
case "text":
|
||||
{
|
||||
// TODO: handle other fonts
|
||||
if (tree.font === "\\textbf") {
|
||||
buildRegion(a11yStrings, function (regionStrings) {
|
||||
regionStrings.push("start bold text");
|
||||
buildA11yStrings(tree.body, regionStrings, atomType);
|
||||
regionStrings.push("end bold text");
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
buildRegion(a11yStrings, function (regionStrings) {
|
||||
regionStrings.push("start text");
|
||||
buildA11yStrings(tree.body, regionStrings, atomType);
|
||||
regionStrings.push("end text");
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "textord":
|
||||
{
|
||||
buildString(tree.text, atomType, a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "smash":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "enclose":
|
||||
{
|
||||
// TODO: create a map for these.
|
||||
// TODO: differentiate between a body with a single atom, e.g.
|
||||
// "cancel a" instead of "start cancel, a, end cancel"
|
||||
if (/cancel/.test(tree.label)) {
|
||||
buildRegion(a11yStrings, function (regionStrings) {
|
||||
regionStrings.push("start cancel");
|
||||
buildA11yStrings(tree.body, regionStrings, atomType);
|
||||
regionStrings.push("end cancel");
|
||||
});
|
||||
break;
|
||||
} else if (/box/.test(tree.label)) {
|
||||
buildRegion(a11yStrings, function (regionStrings) {
|
||||
regionStrings.push("start box");
|
||||
buildA11yStrings(tree.body, regionStrings, atomType);
|
||||
regionStrings.push("end box");
|
||||
});
|
||||
break;
|
||||
} else if (/sout/.test(tree.label)) {
|
||||
buildRegion(a11yStrings, function (regionStrings) {
|
||||
regionStrings.push("start strikeout");
|
||||
buildA11yStrings(tree.body, regionStrings, atomType);
|
||||
regionStrings.push("end strikeout");
|
||||
});
|
||||
break;
|
||||
} else if (/phase/.test(tree.label)) {
|
||||
buildRegion(a11yStrings, function (regionStrings) {
|
||||
regionStrings.push("start phase angle");
|
||||
buildA11yStrings(tree.body, regionStrings, atomType);
|
||||
regionStrings.push("end phase angle");
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
throw new Error("KaTeX-a11y: enclose node with " + tree.label + " not supported yet");
|
||||
}
|
||||
|
||||
case "vcenter":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "vphantom":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: vphantom not implemented yet");
|
||||
}
|
||||
|
||||
case "hphantom":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: hphantom not implemented yet");
|
||||
}
|
||||
|
||||
case "operatorname":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "array":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: array not implemented yet");
|
||||
}
|
||||
|
||||
case "raw":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: raw not implemented yet");
|
||||
}
|
||||
|
||||
case "size":
|
||||
{
|
||||
// Although there are nodes of type "size" in the parse tree, they have
|
||||
// no semantic meaning and should be ignored.
|
||||
break;
|
||||
}
|
||||
|
||||
case "url":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: url not implemented yet");
|
||||
}
|
||||
|
||||
case "tag":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: tag not implemented yet");
|
||||
}
|
||||
|
||||
case "verb":
|
||||
{
|
||||
buildString("start verbatim", "normal", a11yStrings);
|
||||
buildString(tree.body, "normal", a11yStrings);
|
||||
buildString("end verbatim", "normal", a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "environment":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: environment not implemented yet");
|
||||
}
|
||||
|
||||
case "horizBrace":
|
||||
{
|
||||
buildString("start " + tree.label.slice(1), "normal", a11yStrings);
|
||||
buildA11yStrings(tree.base, a11yStrings, atomType);
|
||||
buildString("end " + tree.label.slice(1), "normal", a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "infix":
|
||||
{
|
||||
// All infix nodes are replace with other nodes.
|
||||
break;
|
||||
}
|
||||
|
||||
case "includegraphics":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: includegraphics not implemented yet");
|
||||
}
|
||||
|
||||
case "font":
|
||||
{
|
||||
// TODO: callout the start/end of specific fonts
|
||||
// TODO: map \BBb{N} to "the naturals" or something like that
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "href":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: href not implemented yet");
|
||||
}
|
||||
|
||||
case "cr":
|
||||
{
|
||||
// This is used by environments.
|
||||
throw new Error("KaTeX-a11y: cr not implemented yet");
|
||||
}
|
||||
|
||||
case "underline":
|
||||
{
|
||||
buildRegion(a11yStrings, function (a11yStrings) {
|
||||
a11yStrings.push("start underline");
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
a11yStrings.push("end underline");
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "xArrow":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: xArrow not implemented yet");
|
||||
}
|
||||
|
||||
case "cdlabel":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: cdlabel not implemented yet");
|
||||
}
|
||||
|
||||
case "cdlabelparent":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: cdlabelparent not implemented yet");
|
||||
}
|
||||
|
||||
case "mclass":
|
||||
{
|
||||
// \neq and \ne are macros so we let "htmlmathml" render the mathmal
|
||||
// side of things and extract the text from that.
|
||||
const atomType = tree.mclass.slice(1); // $FlowFixMe: drop the leading "m" from the values in mclass
|
||||
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "mathchoice":
|
||||
{
|
||||
// TODO: track which style we're using, e.g. display, text, etc.
|
||||
// default to text style if even that may not be the correct style
|
||||
buildA11yStrings(tree.text, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "htmlmathml":
|
||||
{
|
||||
buildA11yStrings(tree.mathml, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "middle":
|
||||
{
|
||||
buildString(tree.delim, atomType, a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "internal":
|
||||
{
|
||||
// internal nodes are never included in the parse tree
|
||||
break;
|
||||
}
|
||||
|
||||
case "html":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
default:
|
||||
tree.type;
|
||||
throw new Error("KaTeX a11y un-recognized type: " + tree.type);
|
||||
}
|
||||
};
|
||||
|
||||
const buildA11yStrings = function (tree, a11yStrings, atomType) {
|
||||
if (a11yStrings === void 0) {
|
||||
a11yStrings = [];
|
||||
}
|
||||
|
||||
if (tree instanceof Array) {
|
||||
for (let i = 0; i < tree.length; i++) {
|
||||
buildA11yStrings(tree[i], a11yStrings, atomType);
|
||||
}
|
||||
} else {
|
||||
handleObject(tree, a11yStrings, atomType);
|
||||
}
|
||||
|
||||
return a11yStrings;
|
||||
};
|
||||
|
||||
const flatten = function (array) {
|
||||
let result = [];
|
||||
array.forEach(function (item) {
|
||||
if (item instanceof Array) {
|
||||
result = result.concat(flatten(item));
|
||||
} else {
|
||||
result.push(item);
|
||||
}
|
||||
});
|
||||
return result;
|
||||
};
|
||||
|
||||
const renderA11yString = function (text, settings) {
|
||||
const tree = katex__WEBPACK_IMPORTED_MODULE_0___default().__parse(text, settings);
|
||||
|
||||
const a11yStrings = buildA11yStrings(tree, [], "normal");
|
||||
return flatten(a11yStrings).join(", ");
|
||||
};
|
||||
|
||||
/* harmony default export */ __webpack_exports__["default"] = (renderA11yString);
|
||||
}();
|
||||
__webpack_exports__ = __webpack_exports__["default"];
|
||||
/******/ return __webpack_exports__;
|
||||
/******/ })()
|
||||
;
|
||||
});
|
||||
File diff suppressed because one or more lines are too long
@@ -1,800 +0,0 @@
|
||||
import katex from '../katex.mjs';
|
||||
|
||||
/**
|
||||
* renderA11yString returns a readable string.
|
||||
*
|
||||
* In some cases the string will have the proper semantic math
|
||||
* meaning,:
|
||||
* renderA11yString("\\frac{1}{2}"")
|
||||
* -> "start fraction, 1, divided by, 2, end fraction"
|
||||
*
|
||||
* However, other cases do not:
|
||||
* renderA11yString("f(x) = x^2")
|
||||
* -> "f, left parenthesis, x, right parenthesis, equals, x, squared"
|
||||
*
|
||||
* The commas in the string aim to increase ease of understanding
|
||||
* when read by a screenreader.
|
||||
*/
|
||||
var stringMap = {
|
||||
"(": "left parenthesis",
|
||||
")": "right parenthesis",
|
||||
"[": "open bracket",
|
||||
"]": "close bracket",
|
||||
"\\{": "left brace",
|
||||
"\\}": "right brace",
|
||||
"\\lvert": "open vertical bar",
|
||||
"\\rvert": "close vertical bar",
|
||||
"|": "vertical bar",
|
||||
"\\uparrow": "up arrow",
|
||||
"\\Uparrow": "up arrow",
|
||||
"\\downarrow": "down arrow",
|
||||
"\\Downarrow": "down arrow",
|
||||
"\\updownarrow": "up down arrow",
|
||||
"\\leftarrow": "left arrow",
|
||||
"\\Leftarrow": "left arrow",
|
||||
"\\rightarrow": "right arrow",
|
||||
"\\Rightarrow": "right arrow",
|
||||
"\\langle": "open angle",
|
||||
"\\rangle": "close angle",
|
||||
"\\lfloor": "open floor",
|
||||
"\\rfloor": "close floor",
|
||||
"\\int": "integral",
|
||||
"\\intop": "integral",
|
||||
"\\lim": "limit",
|
||||
"\\ln": "natural log",
|
||||
"\\log": "log",
|
||||
"\\sin": "sine",
|
||||
"\\cos": "cosine",
|
||||
"\\tan": "tangent",
|
||||
"\\cot": "cotangent",
|
||||
"\\sum": "sum",
|
||||
"/": "slash",
|
||||
",": "comma",
|
||||
".": "point",
|
||||
"-": "negative",
|
||||
"+": "plus",
|
||||
"~": "tilde",
|
||||
":": "colon",
|
||||
"?": "question mark",
|
||||
"'": "apostrophe",
|
||||
"\\%": "percent",
|
||||
" ": "space",
|
||||
"\\ ": "space",
|
||||
"\\$": "dollar sign",
|
||||
"\\angle": "angle",
|
||||
"\\degree": "degree",
|
||||
"\\circ": "circle",
|
||||
"\\vec": "vector",
|
||||
"\\triangle": "triangle",
|
||||
"\\pi": "pi",
|
||||
"\\prime": "prime",
|
||||
"\\infty": "infinity",
|
||||
"\\alpha": "alpha",
|
||||
"\\beta": "beta",
|
||||
"\\gamma": "gamma",
|
||||
"\\omega": "omega",
|
||||
"\\theta": "theta",
|
||||
"\\sigma": "sigma",
|
||||
"\\lambda": "lambda",
|
||||
"\\tau": "tau",
|
||||
"\\Delta": "delta",
|
||||
"\\delta": "delta",
|
||||
"\\mu": "mu",
|
||||
"\\rho": "rho",
|
||||
"\\nabla": "del",
|
||||
"\\ell": "ell",
|
||||
"\\ldots": "dots",
|
||||
// TODO: add entries for all accents
|
||||
"\\hat": "hat",
|
||||
"\\acute": "acute"
|
||||
};
|
||||
var powerMap = {
|
||||
"prime": "prime",
|
||||
"degree": "degrees",
|
||||
"circle": "degrees",
|
||||
"2": "squared",
|
||||
"3": "cubed"
|
||||
};
|
||||
var openMap = {
|
||||
"|": "open vertical bar",
|
||||
".": ""
|
||||
};
|
||||
var closeMap = {
|
||||
"|": "close vertical bar",
|
||||
".": ""
|
||||
};
|
||||
var binMap = {
|
||||
"+": "plus",
|
||||
"-": "minus",
|
||||
"\\pm": "plus minus",
|
||||
"\\cdot": "dot",
|
||||
"*": "times",
|
||||
"/": "divided by",
|
||||
"\\times": "times",
|
||||
"\\div": "divided by",
|
||||
"\\circ": "circle",
|
||||
"\\bullet": "bullet"
|
||||
};
|
||||
var relMap = {
|
||||
"=": "equals",
|
||||
"\\approx": "approximately equals",
|
||||
"≠": "does not equal",
|
||||
"\\geq": "is greater than or equal to",
|
||||
"\\ge": "is greater than or equal to",
|
||||
"\\leq": "is less than or equal to",
|
||||
"\\le": "is less than or equal to",
|
||||
">": "is greater than",
|
||||
"<": "is less than",
|
||||
"\\leftarrow": "left arrow",
|
||||
"\\Leftarrow": "left arrow",
|
||||
"\\rightarrow": "right arrow",
|
||||
"\\Rightarrow": "right arrow",
|
||||
":": "colon"
|
||||
};
|
||||
var accentUnderMap = {
|
||||
"\\underleftarrow": "left arrow",
|
||||
"\\underrightarrow": "right arrow",
|
||||
"\\underleftrightarrow": "left-right arrow",
|
||||
"\\undergroup": "group",
|
||||
"\\underlinesegment": "line segment",
|
||||
"\\utilde": "tilde"
|
||||
};
|
||||
|
||||
var buildString = (str, type, a11yStrings) => {
|
||||
if (!str) {
|
||||
return;
|
||||
}
|
||||
|
||||
var ret;
|
||||
|
||||
if (type === "open") {
|
||||
ret = str in openMap ? openMap[str] : stringMap[str] || str;
|
||||
} else if (type === "close") {
|
||||
ret = str in closeMap ? closeMap[str] : stringMap[str] || str;
|
||||
} else if (type === "bin") {
|
||||
ret = binMap[str] || str;
|
||||
} else if (type === "rel") {
|
||||
ret = relMap[str] || str;
|
||||
} else {
|
||||
ret = stringMap[str] || str;
|
||||
} // If the text to add is a number and there is already a string
|
||||
// in the list and the last string is a number then we should
|
||||
// combine them into a single number
|
||||
|
||||
|
||||
if (/^\d+$/.test(ret) && a11yStrings.length > 0 && // TODO(kevinb): check that the last item in a11yStrings is a string
|
||||
// I think we might be able to drop the nested arrays, which would make
|
||||
// this easier to type
|
||||
// $FlowFixMe
|
||||
/^\d+$/.test(a11yStrings[a11yStrings.length - 1])) {
|
||||
a11yStrings[a11yStrings.length - 1] += ret;
|
||||
} else if (ret) {
|
||||
a11yStrings.push(ret);
|
||||
}
|
||||
};
|
||||
|
||||
var buildRegion = (a11yStrings, callback) => {
|
||||
var regionStrings = [];
|
||||
a11yStrings.push(regionStrings);
|
||||
callback(regionStrings);
|
||||
};
|
||||
|
||||
var handleObject = (tree, a11yStrings, atomType) => {
|
||||
// Everything else is assumed to be an object...
|
||||
switch (tree.type) {
|
||||
case "accent":
|
||||
{
|
||||
buildRegion(a11yStrings, a11yStrings => {
|
||||
buildA11yStrings(tree.base, a11yStrings, atomType);
|
||||
a11yStrings.push("with");
|
||||
buildString(tree.label, "normal", a11yStrings);
|
||||
a11yStrings.push("on top");
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "accentUnder":
|
||||
{
|
||||
buildRegion(a11yStrings, a11yStrings => {
|
||||
buildA11yStrings(tree.base, a11yStrings, atomType);
|
||||
a11yStrings.push("with");
|
||||
buildString(accentUnderMap[tree.label], "normal", a11yStrings);
|
||||
a11yStrings.push("underneath");
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "accent-token":
|
||||
{
|
||||
// Used internally by accent symbols.
|
||||
break;
|
||||
}
|
||||
|
||||
case "atom":
|
||||
{
|
||||
var {
|
||||
text
|
||||
} = tree;
|
||||
|
||||
switch (tree.family) {
|
||||
case "bin":
|
||||
{
|
||||
buildString(text, "bin", a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "close":
|
||||
{
|
||||
buildString(text, "close", a11yStrings);
|
||||
break;
|
||||
}
|
||||
// TODO(kevinb): figure out what should be done for inner
|
||||
|
||||
case "inner":
|
||||
{
|
||||
buildString(tree.text, "inner", a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "open":
|
||||
{
|
||||
buildString(text, "open", a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "punct":
|
||||
{
|
||||
buildString(text, "punct", a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "rel":
|
||||
{
|
||||
buildString(text, "rel", a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
default:
|
||||
{
|
||||
tree.family;
|
||||
throw new Error("\"" + tree.family + "\" is not a valid atom type");
|
||||
}
|
||||
}
|
||||
|
||||
break;
|
||||
}
|
||||
|
||||
case "color":
|
||||
{
|
||||
var color = tree.color.replace(/katex-/, "");
|
||||
buildRegion(a11yStrings, regionStrings => {
|
||||
regionStrings.push("start color " + color);
|
||||
buildA11yStrings(tree.body, regionStrings, atomType);
|
||||
regionStrings.push("end color " + color);
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "color-token":
|
||||
{
|
||||
// Used by \color, \colorbox, and \fcolorbox but not directly rendered.
|
||||
// It's a leaf node and has no children so just break.
|
||||
break;
|
||||
}
|
||||
|
||||
case "delimsizing":
|
||||
{
|
||||
if (tree.delim && tree.delim !== ".") {
|
||||
buildString(tree.delim, "normal", a11yStrings);
|
||||
}
|
||||
|
||||
break;
|
||||
}
|
||||
|
||||
case "genfrac":
|
||||
{
|
||||
buildRegion(a11yStrings, regionStrings => {
|
||||
// genfrac can have unbalanced delimiters
|
||||
var {
|
||||
leftDelim,
|
||||
rightDelim
|
||||
} = tree; // NOTE: Not sure if this is a safe assumption
|
||||
// hasBarLine true -> fraction, false -> binomial
|
||||
|
||||
if (tree.hasBarLine) {
|
||||
regionStrings.push("start fraction");
|
||||
leftDelim && buildString(leftDelim, "open", regionStrings);
|
||||
buildA11yStrings(tree.numer, regionStrings, atomType);
|
||||
regionStrings.push("divided by");
|
||||
buildA11yStrings(tree.denom, regionStrings, atomType);
|
||||
rightDelim && buildString(rightDelim, "close", regionStrings);
|
||||
regionStrings.push("end fraction");
|
||||
} else {
|
||||
regionStrings.push("start binomial");
|
||||
leftDelim && buildString(leftDelim, "open", regionStrings);
|
||||
buildA11yStrings(tree.numer, regionStrings, atomType);
|
||||
regionStrings.push("over");
|
||||
buildA11yStrings(tree.denom, regionStrings, atomType);
|
||||
rightDelim && buildString(rightDelim, "close", regionStrings);
|
||||
regionStrings.push("end binomial");
|
||||
}
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "hbox":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "kern":
|
||||
{
|
||||
// No op: we don't attempt to present kerning information
|
||||
// to the screen reader.
|
||||
break;
|
||||
}
|
||||
|
||||
case "leftright":
|
||||
{
|
||||
buildRegion(a11yStrings, regionStrings => {
|
||||
buildString(tree.left, "open", regionStrings);
|
||||
buildA11yStrings(tree.body, regionStrings, atomType);
|
||||
buildString(tree.right, "close", regionStrings);
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "leftright-right":
|
||||
{
|
||||
// TODO: double check that this is a no-op
|
||||
break;
|
||||
}
|
||||
|
||||
case "lap":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "mathord":
|
||||
{
|
||||
buildString(tree.text, "normal", a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "op":
|
||||
{
|
||||
var {
|
||||
body,
|
||||
name
|
||||
} = tree;
|
||||
|
||||
if (body) {
|
||||
buildA11yStrings(body, a11yStrings, atomType);
|
||||
} else if (name) {
|
||||
buildString(name, "normal", a11yStrings);
|
||||
}
|
||||
|
||||
break;
|
||||
}
|
||||
|
||||
case "op-token":
|
||||
{
|
||||
// Used internally by operator symbols.
|
||||
buildString(tree.text, atomType, a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "ordgroup":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "overline":
|
||||
{
|
||||
buildRegion(a11yStrings, function (a11yStrings) {
|
||||
a11yStrings.push("start overline");
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
a11yStrings.push("end overline");
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "pmb":
|
||||
{
|
||||
a11yStrings.push("bold");
|
||||
break;
|
||||
}
|
||||
|
||||
case "phantom":
|
||||
{
|
||||
a11yStrings.push("empty space");
|
||||
break;
|
||||
}
|
||||
|
||||
case "raisebox":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "rule":
|
||||
{
|
||||
a11yStrings.push("rectangle");
|
||||
break;
|
||||
}
|
||||
|
||||
case "sizing":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "spacing":
|
||||
{
|
||||
a11yStrings.push("space");
|
||||
break;
|
||||
}
|
||||
|
||||
case "styling":
|
||||
{
|
||||
// We ignore the styling and just pass through the contents
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "sqrt":
|
||||
{
|
||||
buildRegion(a11yStrings, regionStrings => {
|
||||
var {
|
||||
body,
|
||||
index
|
||||
} = tree;
|
||||
|
||||
if (index) {
|
||||
var indexString = flatten(buildA11yStrings(index, [], atomType)).join(",");
|
||||
|
||||
if (indexString === "3") {
|
||||
regionStrings.push("cube root of");
|
||||
buildA11yStrings(body, regionStrings, atomType);
|
||||
regionStrings.push("end cube root");
|
||||
return;
|
||||
}
|
||||
|
||||
regionStrings.push("root");
|
||||
regionStrings.push("start index");
|
||||
buildA11yStrings(index, regionStrings, atomType);
|
||||
regionStrings.push("end index");
|
||||
return;
|
||||
}
|
||||
|
||||
regionStrings.push("square root of");
|
||||
buildA11yStrings(body, regionStrings, atomType);
|
||||
regionStrings.push("end square root");
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "supsub":
|
||||
{
|
||||
var {
|
||||
base,
|
||||
sub,
|
||||
sup
|
||||
} = tree;
|
||||
var isLog = false;
|
||||
|
||||
if (base) {
|
||||
buildA11yStrings(base, a11yStrings, atomType);
|
||||
isLog = base.type === "op" && base.name === "\\log";
|
||||
}
|
||||
|
||||
if (sub) {
|
||||
var regionName = isLog ? "base" : "subscript";
|
||||
buildRegion(a11yStrings, function (regionStrings) {
|
||||
regionStrings.push("start " + regionName);
|
||||
buildA11yStrings(sub, regionStrings, atomType);
|
||||
regionStrings.push("end " + regionName);
|
||||
});
|
||||
}
|
||||
|
||||
if (sup) {
|
||||
buildRegion(a11yStrings, function (regionStrings) {
|
||||
var supString = flatten(buildA11yStrings(sup, [], atomType)).join(",");
|
||||
|
||||
if (supString in powerMap) {
|
||||
regionStrings.push(powerMap[supString]);
|
||||
return;
|
||||
}
|
||||
|
||||
regionStrings.push("start superscript");
|
||||
buildA11yStrings(sup, regionStrings, atomType);
|
||||
regionStrings.push("end superscript");
|
||||
});
|
||||
}
|
||||
|
||||
break;
|
||||
}
|
||||
|
||||
case "text":
|
||||
{
|
||||
// TODO: handle other fonts
|
||||
if (tree.font === "\\textbf") {
|
||||
buildRegion(a11yStrings, function (regionStrings) {
|
||||
regionStrings.push("start bold text");
|
||||
buildA11yStrings(tree.body, regionStrings, atomType);
|
||||
regionStrings.push("end bold text");
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
buildRegion(a11yStrings, function (regionStrings) {
|
||||
regionStrings.push("start text");
|
||||
buildA11yStrings(tree.body, regionStrings, atomType);
|
||||
regionStrings.push("end text");
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "textord":
|
||||
{
|
||||
buildString(tree.text, atomType, a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "smash":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "enclose":
|
||||
{
|
||||
// TODO: create a map for these.
|
||||
// TODO: differentiate between a body with a single atom, e.g.
|
||||
// "cancel a" instead of "start cancel, a, end cancel"
|
||||
if (/cancel/.test(tree.label)) {
|
||||
buildRegion(a11yStrings, function (regionStrings) {
|
||||
regionStrings.push("start cancel");
|
||||
buildA11yStrings(tree.body, regionStrings, atomType);
|
||||
regionStrings.push("end cancel");
|
||||
});
|
||||
break;
|
||||
} else if (/box/.test(tree.label)) {
|
||||
buildRegion(a11yStrings, function (regionStrings) {
|
||||
regionStrings.push("start box");
|
||||
buildA11yStrings(tree.body, regionStrings, atomType);
|
||||
regionStrings.push("end box");
|
||||
});
|
||||
break;
|
||||
} else if (/sout/.test(tree.label)) {
|
||||
buildRegion(a11yStrings, function (regionStrings) {
|
||||
regionStrings.push("start strikeout");
|
||||
buildA11yStrings(tree.body, regionStrings, atomType);
|
||||
regionStrings.push("end strikeout");
|
||||
});
|
||||
break;
|
||||
} else if (/phase/.test(tree.label)) {
|
||||
buildRegion(a11yStrings, function (regionStrings) {
|
||||
regionStrings.push("start phase angle");
|
||||
buildA11yStrings(tree.body, regionStrings, atomType);
|
||||
regionStrings.push("end phase angle");
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
throw new Error("KaTeX-a11y: enclose node with " + tree.label + " not supported yet");
|
||||
}
|
||||
|
||||
case "vcenter":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "vphantom":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: vphantom not implemented yet");
|
||||
}
|
||||
|
||||
case "hphantom":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: hphantom not implemented yet");
|
||||
}
|
||||
|
||||
case "operatorname":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "array":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: array not implemented yet");
|
||||
}
|
||||
|
||||
case "raw":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: raw not implemented yet");
|
||||
}
|
||||
|
||||
case "size":
|
||||
{
|
||||
// Although there are nodes of type "size" in the parse tree, they have
|
||||
// no semantic meaning and should be ignored.
|
||||
break;
|
||||
}
|
||||
|
||||
case "url":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: url not implemented yet");
|
||||
}
|
||||
|
||||
case "tag":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: tag not implemented yet");
|
||||
}
|
||||
|
||||
case "verb":
|
||||
{
|
||||
buildString("start verbatim", "normal", a11yStrings);
|
||||
buildString(tree.body, "normal", a11yStrings);
|
||||
buildString("end verbatim", "normal", a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "environment":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: environment not implemented yet");
|
||||
}
|
||||
|
||||
case "horizBrace":
|
||||
{
|
||||
buildString("start " + tree.label.slice(1), "normal", a11yStrings);
|
||||
buildA11yStrings(tree.base, a11yStrings, atomType);
|
||||
buildString("end " + tree.label.slice(1), "normal", a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "infix":
|
||||
{
|
||||
// All infix nodes are replace with other nodes.
|
||||
break;
|
||||
}
|
||||
|
||||
case "includegraphics":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: includegraphics not implemented yet");
|
||||
}
|
||||
|
||||
case "font":
|
||||
{
|
||||
// TODO: callout the start/end of specific fonts
|
||||
// TODO: map \BBb{N} to "the naturals" or something like that
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "href":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: href not implemented yet");
|
||||
}
|
||||
|
||||
case "cr":
|
||||
{
|
||||
// This is used by environments.
|
||||
throw new Error("KaTeX-a11y: cr not implemented yet");
|
||||
}
|
||||
|
||||
case "underline":
|
||||
{
|
||||
buildRegion(a11yStrings, function (a11yStrings) {
|
||||
a11yStrings.push("start underline");
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
a11yStrings.push("end underline");
|
||||
});
|
||||
break;
|
||||
}
|
||||
|
||||
case "xArrow":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: xArrow not implemented yet");
|
||||
}
|
||||
|
||||
case "cdlabel":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: cdlabel not implemented yet");
|
||||
}
|
||||
|
||||
case "cdlabelparent":
|
||||
{
|
||||
throw new Error("KaTeX-a11y: cdlabelparent not implemented yet");
|
||||
}
|
||||
|
||||
case "mclass":
|
||||
{
|
||||
// \neq and \ne are macros so we let "htmlmathml" render the mathmal
|
||||
// side of things and extract the text from that.
|
||||
var _atomType = tree.mclass.slice(1); // $FlowFixMe: drop the leading "m" from the values in mclass
|
||||
|
||||
|
||||
buildA11yStrings(tree.body, a11yStrings, _atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "mathchoice":
|
||||
{
|
||||
// TODO: track which style we're using, e.g. display, text, etc.
|
||||
// default to text style if even that may not be the correct style
|
||||
buildA11yStrings(tree.text, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "htmlmathml":
|
||||
{
|
||||
buildA11yStrings(tree.mathml, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
case "middle":
|
||||
{
|
||||
buildString(tree.delim, atomType, a11yStrings);
|
||||
break;
|
||||
}
|
||||
|
||||
case "internal":
|
||||
{
|
||||
// internal nodes are never included in the parse tree
|
||||
break;
|
||||
}
|
||||
|
||||
case "html":
|
||||
{
|
||||
buildA11yStrings(tree.body, a11yStrings, atomType);
|
||||
break;
|
||||
}
|
||||
|
||||
default:
|
||||
tree.type;
|
||||
throw new Error("KaTeX a11y un-recognized type: " + tree.type);
|
||||
}
|
||||
};
|
||||
|
||||
var buildA11yStrings = function buildA11yStrings(tree, a11yStrings, atomType) {
|
||||
if (a11yStrings === void 0) {
|
||||
a11yStrings = [];
|
||||
}
|
||||
|
||||
if (tree instanceof Array) {
|
||||
for (var i = 0; i < tree.length; i++) {
|
||||
buildA11yStrings(tree[i], a11yStrings, atomType);
|
||||
}
|
||||
} else {
|
||||
handleObject(tree, a11yStrings, atomType);
|
||||
}
|
||||
|
||||
return a11yStrings;
|
||||
};
|
||||
|
||||
var flatten = function flatten(array) {
|
||||
var result = [];
|
||||
array.forEach(function (item) {
|
||||
if (item instanceof Array) {
|
||||
result = result.concat(flatten(item));
|
||||
} else {
|
||||
result.push(item);
|
||||
}
|
||||
});
|
||||
return result;
|
||||
};
|
||||
|
||||
var renderA11yString = function renderA11yString(text, settings) {
|
||||
var tree = katex.__parse(text, settings);
|
||||
|
||||
var a11yStrings = buildA11yStrings(tree, [], "normal");
|
||||
return flatten(a11yStrings).join(", ");
|
||||
};
|
||||
|
||||
export { renderA11yString as default };
|
||||
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File diff suppressed because it is too large
Load Diff
-18998
File diff suppressed because it is too large
Load Diff
Vendored
-1
File diff suppressed because one or more lines are too long
Vendored
-1
File diff suppressed because one or more lines are too long
-18458
File diff suppressed because it is too large
Load Diff
@@ -1,8 +0,0 @@
|
||||
document.addEventListener("DOMContentLoaded", () => {
|
||||
for (const m of document.querySelectorAll(".math.inline")) {
|
||||
katex.render(m.textContent, m, {throwOnError: false, displayMode: false});
|
||||
}
|
||||
for (const m of document.querySelectorAll(".math.display")) {
|
||||
katex.render(m.textContent, m, {throwOnError: false, displayMode: true});
|
||||
}
|
||||
});
|
||||
Reference in New Issue
Block a user