LaTeXSpec.hs

-- |
-- Description: Tests for Symtegration.Symbolic.LaTeX.
-- Copyright: Copyright 2024 Yoo Chung
-- License: Apache-2.0
-- Maintainer: dev@chungyc.org
module Symtegration.Symbolic.LaTeXSpec (spec) where

import Symtegration.Symbolic.Arbitrary ()
import Symtegration.Symbolic.LaTeX
import Test.Hspec
import Test.Hspec.QuickCheck
import Test.QuickCheck

spec :: Spec
spec = parallel $ describe "toLaTeX" $ do
  -- Full-fledged property-based tests would be nice, but for now,
  -- check only for totality property and test with specific examples instead.
  prop "is total" $ \e -> total (toLaTeX e)

  describe "addition" $ do
    it "-(1 + a)" $ toLaTeX (-(1 + "a")) `shouldBe` "-\\left(1 + a\\right)"

    it "1 + 5" $ toLaTeX (1 + 5) `shouldBe` "1 + 5"

    it "1 + 2 + 3" $ toLaTeX (1 + 2 + 3) `shouldBe` "1 + 2 + 3"

    it "x * y + u * v" $ toLaTeX ("x" * "y" + "u" * "v") `shouldBe` "x y + u v"

    it "x + u * v" $ toLaTeX ("x" + "u" * "v") `shouldBe` "x + u v"

    it "(x - y) + (u - v)" $ toLaTeX (("x" - "y") + ("u" - "v")) `shouldBe` "x - y + u - v"

    it "(-1) + (-4)" $ toLaTeX ((-1) + (-4)) `shouldBe` "-1 - 4"

    it "(-x) + y" $ toLaTeX ((-"x") + "y") `shouldBe` "-x + y"

    it "(-x) + (-y)" $ toLaTeX ((-"x") + (-"y")) `shouldBe` "-x - y"

    it "sin x + cos y" $ toLaTeX (sin "x" + cos "y") `shouldBe` "\\sin x + \\cos y"

    it "10 + (-4)" $ toLaTeX (10 + (-4)) `shouldBe` "10 - 4"

    it "x + (-y)" $ toLaTeX ("x" + (-"y")) `shouldBe` "x - y"

    it "x + 3 * x ** 2 + 2" $ toLaTeX ("x" + 3 * "x" ** 2 + 2) `shouldBe` "x + 3 x^{2} + 2"

  describe "subtraction" $ do
    it "x - y" $ toLaTeX ("x" - "y") `shouldBe` "x - y"

    it "(x + y) - z" $ toLaTeX (("x" + "y") - "z") `shouldBe` "x + y - z"

    it "x - (y + z)" $ toLaTeX ("x" - ("y" + "z")) `shouldBe` "x - \\left(y + z\\right)"

    it "x - (y - z)" $ toLaTeX ("x" - ("y" - "z")) `shouldBe` "x - \\left(y - z\\right)"

    it "x - (y * z)" $ toLaTeX ("x" - ("y" * "z")) `shouldBe` "x - y z"

    it "(-x) - y" $ toLaTeX ((-"x") - "y") `shouldBe` "-x - y"

    it "x - 3 * x ** 2 + 2" $ toLaTeX ("x" - 3 * "x" ** 2 + 2) `shouldBe` "x - 3 x^{2} + 2"

  describe "multiplication" $ do
    it "2 * 5" $ toLaTeX (2 * 5) `shouldBe` "2 \\times 5"

    it "2 * 3 * 4 * 6" $ toLaTeX (2 * 3 * 4 * 6) `shouldBe` "2 \\times 3 \\times 4 \\times 6"

    it "(2 * 3) * (4 * 6)" $ toLaTeX ((2 * 3) * (4 * 6)) `shouldBe` "2 \\times 3 \\times 4 \\times 6"

    it "2 * (4 * 6)" $ toLaTeX (2 * (4 * 6)) `shouldBe` "2 \\times 4 \\times 6"

    it "sin x * 3" $ toLaTeX (sin "x" * 3) `shouldBe` "\\sin x \\times 3"

    it "abs x * y" $ toLaTeX (abs "x" * "y") `shouldBe` "\\left\\lvert x \\right\\rvert y"

    it "signum x * y" $ toLaTeX (signum "x" * "y") `shouldBe` "\\mathrm{signum}\\left(x\\right) y"

    it "exp x * y" $ toLaTeX (exp "x" * "y") `shouldBe` "e^{x} y"

    it "sin x * y" $ toLaTeX (sin "x" * "y") `shouldBe` "\\left(\\sin x\\right) y"

    it "(-2) * (-5)" $ toLaTeX ((-2) * (-5)) `shouldBe` "\\left(-2\\right) \\left(-5\\right)"

    it "sin x * cos y" $ toLaTeX (sin "x" * cos "y") `shouldBe` "\\sin x \\cos y"

    it "4 * sin x" $ toLaTeX (4 * sin "x") `shouldBe` "4 \\sin x"

    it "x * y" $ toLaTeX ("x" * "y") `shouldBe` "x y"

    it "x * y ** z" $ toLaTeX ("x" * "y" ** "z") `shouldBe` "x y^{z}"

    it "log x * y" $ toLaTeX (log "x" * "y") `shouldBe` "\\left(\\log x\\right) y"

    it "logBase x y * z" $ toLaTeX (logBase "x" "y" * "z") `shouldBe` "\\left(\\log_{x}y\\right) z"

  describe "negation" $ do
    it "-a" $ toLaTeX (-"a") `shouldBe` "-a"

    it "-19" $ toLaTeX (negate 19) `shouldBe` "-19"

    it "-x" $ toLaTeX (negate "x") `shouldBe` "-x"

    it "-(-x)" $ toLaTeX (negate (negate "x")) `shouldBe` "-\\left(-x\\right)"

    it "-(x + y)" $ toLaTeX (negate ("x" + "y")) `shouldBe` "-\\left(x + y\\right)"

    it "-(x - y)" $ toLaTeX (negate ("x" - "y")) `shouldBe` "-\\left(x - y\\right)"

    it "-(sin x)" $ toLaTeX (negate (sin "x")) `shouldBe` "-\\sin x"

    it "-(x * sin x)" $ toLaTeX (negate ("x" * sin "x")) `shouldBe` "-x \\sin x"

    it "x * negate (sin x)" $ toLaTeX ("x" * negate (sin "x")) `shouldBe` "x \\left(-\\sin x\\right)"

  describe "unary function arguments" $ do
    it "cos (log x)" $ toLaTeX (cos (log "x")) `shouldBe` "\\cos \\left(\\log x\\right)"

    it "tan (pi * x)" $ toLaTeX (tan (pi * "x")) `shouldBe` "\\tan \\left(\\pi x\\right)"