Math.LaTeX.Prelude

Use in documents

toMathLaTeX :: forall σ l. (LaTeXC l, Num l, SymbolClass σ, SCConstraint σ l) => CAS (Infix l) (Encapsulation l) (SymbolD σ l) -> l

(>$) :: (LaTeXC r, SymbolClass σ, SCConstraint σ LaTeX) => r -> CAS (Infix LaTeX) (Encapsulation LaTeX) (SymbolD σ LaTeX) -> r infixl 1

dmaths

Arguments

:: (LaTeXC r, SymbolClass σ, SCConstraint σ LaTeX)

=> [[CAS (Infix LaTeX) (Encapsulation LaTeX) (SymbolD σ LaTeX)]]

Equations to show.

-> String

“Terminator” – this can include punctuation (when an equation is at the end of a sentence in the preceding text).

-> r

Include a formula / equation system as a LaTeX display. If it's a single equation, automatic line breaks are inserted (requires the breqn LaTeX package).

maths

Arguments

:: (LaTeXC r, SymbolClass σ, SCConstraint σ LaTeX)

=> [[CAS (Infix LaTeX) (Encapsulation LaTeX) (SymbolD σ LaTeX)]]

Equations to show.

-> String

“Terminator” – this can include punctuation (when an equation is at the end of a sentence in the preceding text).

-> r

Include a formula / equation system as a LaTeX display.

dcalculation

Arguments

:: (LaTeXC (m ()), SymbolClass σ, SCConstraint σ LaTeX, Functor m)

=> CAS (Infix LaTeX) (Encapsulation LaTeX) (SymbolD σ LaTeX)

Computation chain to display.

-> String

“Terminator” – this can include punctuation (when an equation is at the end of a sentence in the preceding text).

-> m (CAS (Infix LaTeX) (Encapsulation LaTeX) (SymbolD σ LaTeX))

Yield the rightmost expression in the displayed computation (i.e. usually the final result in a chain of algebraic equalities).

Display an equation and also extract the final result. As with dmaths, automatic line breaks are inserted by breqn.

Primitive symbols

module CAS.Dumb.Symbols.Unicode.MathLatin_RomanGreek__BopomofoGaps

Modifiers

(%$>) :: (SymbolClass σ, SCConstraint σ c) => (c -> c') -> CAS' γ s² s¹ (SymbolD σ c) -> CAS' γ s² s¹ (SymbolD σ c') infixl 4

Transform the symbols of an expression, in their underlying representation.

(map succ%$> 𝑎+𝑝) * 𝑥  ≡  (𝑏+𝑞) * 𝑥

prime :: LaTeXC l => l -> l

bar :: LaTeXC l => l -> l

Add a bar accent above a symbol.

hat :: LaTeXC l => l -> l

Add a hat accent above a symbol.

vec :: LaTeXC l => l -> l

Add a vector arrow accent above a symbol.

underline :: LaTeXC l => l -> l

tilde :: LaTeXC l => l -> l

Add a tilde accent above a symbol.

Operators

(°) :: MathsInfix infixl 7

(⁀) :: MathsInfix infixr 9

(...) :: MathsInfix infixr 0

(،..،) :: MathsInfix infixr 0

(،) :: MathsInfix infixr 0

(⸪=) :: MathsInfix infixl 4

(=⸪) :: MathsInfix infixl 4

(␣) :: MathsInfix infixr 0

(+..+) :: MathsInfix infixl 6

(*..*) :: MathsInfix infixl 7

(×) :: MathsInfix infixl 7

(⊗) :: MathsInfix infixl 7

(∘) :: MathsInfix infixl 7

factorial :: LaTeXC l => CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l)

(◝) :: MathsInfix infixr 9

(◝⁀) :: MathsInfix infixr 9

(◞) :: MathsInfix infixr 9

(◞◝) :: LaTeXC s => CAS' γ (Infix s) (Encapsulation s) (SymbolD σ s) -> (CAS' γ (Infix s) (Encapsulation s) (SymbolD σ s), CAS' γ (Infix s) (Encapsulation s) (SymbolD σ s)) -> CAS' γ (Infix s) (Encapsulation s) (SymbolD σ s) infixl 8

(|◞) :: MathsInfix infixl 8

(|◝) :: LaTeXC s => CAS' γ (Infix s) (Encapsulation s) (SymbolD σ s) -> CAS' γ (Infix s) (Encapsulation s) (SymbolD σ s) -> CAS' γ (Infix s) (Encapsulation s) (SymbolD σ s) infixl 8

(|◞◝) :: LaTeXC s => CAS' γ (Infix s) (Encapsulation s) (SymbolD σ s) -> (CAS' γ (Infix s) (Encapsulation s) (SymbolD σ s), CAS' γ (Infix s) (Encapsulation s) (SymbolD σ s)) -> CAS' γ (Infix s) (Encapsulation s) (SymbolD σ s) infixl 8

(⩵) :: MathsInfix infixl 4

(≡) :: MathsInfix infixl 4

(⩵!) :: MathsInfix infixl 4

(≠) :: MathsInfix infixl 4

(⪡) :: MathsInfix infixl 4

(⪢) :: MathsInfix infixl 4

(≤) :: MathsInfix infixl 4

(≥) :: MathsInfix infixl 4

(≪) :: MathsInfix infixl 4

(≫) :: MathsInfix infixl 4

(₌₌) :: MathsInfix infixl 8

(=→) :: MathsInfix infixl 4

(≈) :: MathsInfix infixl 4

(∼) :: MathsInfix infixl 4

(⊂) :: MathsInfix infixl 4

(/⊂) :: MathsInfix infixl 4

(⊆) :: MathsInfix infixl 4

(⊃) :: MathsInfix infixl 4

(⊇) :: MathsInfix infixl 4

(∋) :: MathsInfix infixl 4

(∌) :: MathsInfix infixl 4

(∈) :: MathsInfix infixl 4

(∉) :: MathsInfix infixl 4

(∩) :: MathsInfix infixr 3

(∪) :: MathsInfix infixr 2

(-\-) :: MathsInfix infixl 2

(⸪) :: MathsInfix infixr 5

(⊕) :: MathsInfix infixl 6

(∀:) :: MathsInfix infix 2

(∃:) :: MathsInfix infix 2

(-→) :: MathsInfix infixr 5

(↦) :: MathsInfix infixl 4

(↪) :: MathsInfix infixr 5

(==>) :: MathsInfix infixl 1

(<==) :: MathsInfix infixl 1

(<=>) :: MathsInfix infixl 1

(∧) :: MathsInfix infixr 3

(∨) :: MathsInfix infixr 3

(∫) :: LaTeXC l => (CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l), CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l)) -> Integrand γ (Infix l) (Encapsulation l) (SymbolD σ l) -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) infixr 8

(◞∫) :: LaTeXC l => CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) -> Integrand γ (Infix l) (Encapsulation l) (SymbolD σ l) -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) infixr 8

(◞∮) :: LaTeXC l => CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) -> Integrand γ (Infix l) (Encapsulation l) (SymbolD σ l) -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) infixr 8

d :: LaTeXC l => CAS' γ (Infix l) (Encapsulation l) s⁰ -> CAS' γ (Infix l) (Encapsulation l) s⁰ -> Integrand γ (Infix l) (Encapsulation l) s⁰

(∑) :: LaTeXC l => (CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l), CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l)) -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) infixr 8

(◞∑) :: LaTeXC l => CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) infixr 8

(∏) :: LaTeXC l => (CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l), CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l)) -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) infixr 8

(◞∏) :: LaTeXC l => CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) infixr 8

del :: (SymbolClass σ, SCConstraint σ LaTeX) => CAS' γ s² s¹ (SymbolD σ LaTeX)

nabla :: (SymbolClass σ, SCConstraint σ LaTeX) => CAS' γ s² s¹ (SymbolD σ LaTeX)

(<.<) :: MathsInfix infix 5

(≤.<) :: MathsInfix infix 5

(<.≤) :: MathsInfix infix 5

(≤.≤) :: MathsInfix infix 5

(±) :: MathsInfix infixl 6

(∓) :: MathsInfix infixl 6

set :: LaTeXC l => CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l)

tup :: LaTeXC l => CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l)

intv :: LaTeXC l => CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l)

infty :: (SymbolClass σ, SCConstraint σ LaTeX) => CAS' γ s² s¹ (SymbolD σ LaTeX)

norm :: LaTeXC l => CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l)

nobreaks :: LaTeXC l => CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l)

matrix :: LaTeXC l => [[CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l)]] -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l)

cases :: LaTeXC l => [(CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l), LaTeX)] -> CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l)

Algebraic manipulation

(&~~!) :: (Eq l, Eq (Encapsulation l), SymbolClass σ, SCConstraint σ l, Show (AlgebraExpr σ l), Show (AlgebraPattern σ l)) => AlgebraExpr σ l -> [AlgebraPattern σ l] -> AlgebraExpr σ l infixl 1

Apply a sequence of pattern-transformations and yield the result concatenated to the original via the corresponding chain-operator. Because only the rightmost expression in a chain is processed, this can be iterated, giving a chain of intermediate results.

If one of the patterns does not match, this manipulator will raise an error.

(&~~:) :: (Eq l, Eq (Encapsulation l), SymbolClass σ, SCConstraint σ l, Show (AlgebraExpr σ l), Show (AlgebraPattern σ l)) => AlgebraExpr σ l -> [AlgebraPattern σ l] -> AlgebraExpr σ l infixl 1

Apply a sequence of pattern-transformations, each in every spot possible, and yield the result concatenated to the original via the corresponding chain-operator. Because only the rightmost expression in a chain is processed, this can be iterated, giving a chain of intermediate results.

continueExpr

Arguments

:: (Eq l, Monoid l)

=> (AlgebraExpr' γ σ l -> AlgebraExpr' γ σ l -> AlgebraExpr' γ σ l)

Combinator to use for chaining the new expression to the old ones

-> (AlgebraExpr' γ σ l -> AlgebraExpr' γ σ l)

Transformation to apply to the rightmost expression in the previous chain

-> AlgebraExpr' γ σ l

Transformation which appends the result.

-> AlgebraExpr' γ σ l

(&) :: a -> (a -> b) -> b

(&~:) :: (Eq s⁰, Eq s¹, Eq s²) => CAS s² s¹ s⁰ -> Eqspattern s² s¹ s⁰ -> CAS s² s¹ s⁰ infixl 1

expr &~: pat :=: rep replaces every occurence of pat within expr with rep.

For example, 𝑎·𝑏 − 𝑐·𝑑 &~: ㄅ·ㄘ :=: ㄘ·ㄅ yields 𝑏·𝑎 − 𝑑·𝑐.

(&~?) :: (Eq s⁰, Eq s¹, Eq s²) => CAS s² s¹ s⁰ -> Eqspattern s² s¹ s⁰ -> [CAS s² s¹ s⁰] infixl 1

expr &~? pat :=: rep gives every possible way pat can be replaced exactly once within expr.

For example, 𝑎·𝑏 − 𝑐·𝑑 &~? ㄅ·ㄘ :=: ㄘ·ㄅ yields [𝑏·𝑎 − 𝑐·𝑑, 𝑎·𝑏 − 𝑑·𝑐].

(&~!) :: (Eq s⁰, Eq s¹, Eq s², Show (CAS s² s¹ s⁰), Show (CAS' GapId s² s¹ s⁰)) => CAS s² s¹ s⁰ -> Eqspattern s² s¹ s⁰ -> CAS s² s¹ s⁰ infixl 1

expr &~! pat :=: rep replaces pat exactly once in expr. If this is not possible, an error is raised. If multiple occurences match, the leftmost is preferred.

(|->) :: CAS' γ s² s¹ s⁰ -> CAS' γ s² s¹ s⁰ -> Equality' γ s² s¹ s⁰ infix 2