def test_trigintegrate_mixed(): assert trigintegrate(sin(x) * sec(x), x) == -log(sin(x)**2 - 1) / 2 assert trigintegrate(sin(x) * csc(x), x) == x assert trigintegrate(sin(x) * cot(x), x) == sin(x) assert trigintegrate(cos(x) * sec(x), x) == x assert trigintegrate(cos(x) * csc(x), x) == log(cos(x)**2 - 1) / 2 assert trigintegrate(cos(x) * tan(x), x) == -cos(x) assert trigintegrate(cos(x)*cot(x), x) == log(cos(x) - 1)/2 \ - log(cos(x) + 1)/2 + cos(x)
def test_trigintegrate_mixed(): assert trigintegrate(sin(x)*sec(x), x) == -log(sin(x)**2 - 1)/2 assert trigintegrate(sin(x)*csc(x), x) == x assert trigintegrate(sin(x)*cot(x), x) == sin(x) assert trigintegrate(cos(x)*sec(x), x) == x assert trigintegrate(cos(x)*csc(x), x) == log(cos(x)**2 - 1)/2 assert trigintegrate(cos(x)*tan(x), x) == -cos(x) assert trigintegrate(cos(x)*cot(x), x) == log(cos(x) - 1)/2 \ - log(cos(x) + 1)/2 + cos(x)
def test_Function(): assert mcode(f(x, y, z)) == "f[x, y, z]" assert mcode(sin(x)**cos(x)) == "Sin[x]^Cos[x]" assert mcode(sec(x) * acsc(x)) == "ArcCsc[x]*Sec[x]" assert mcode(atan2(x, y)) == "ArcTan[x, y]" assert mcode(conjugate(x)) == "Conjugate[x]" assert mcode(Max(x, y, z) * Min(y, z)) == "Max[x, y, z]*Min[y, z]" assert mcode(fresnelc(x)) == "FresnelC[x]" assert mcode(fresnels(x)) == "FresnelS[x]" assert mcode(gamma(x)) == "Gamma[x]" assert mcode(uppergamma(x, y)) == "Gamma[x, y]" assert mcode(polygamma(x, y)) == "PolyGamma[x, y]" assert mcode(loggamma(x)) == "LogGamma[x]" assert mcode(erf(x)) == "Erf[x]" assert mcode(erfc(x)) == "Erfc[x]" assert mcode(erfi(x)) == "Erfi[x]" assert mcode(erf2(x, y)) == "Erf[x, y]" assert mcode(expint(x, y)) == "ExpIntegralE[x, y]" assert mcode(erfcinv(x)) == "InverseErfc[x]" assert mcode(erfinv(x)) == "InverseErf[x]" assert mcode(erf2inv(x, y)) == "InverseErf[x, y]" assert mcode(Ei(x)) == "ExpIntegralEi[x]" assert mcode(Ci(x)) == "CosIntegral[x]" assert mcode(li(x)) == "LogIntegral[x]" assert mcode(Si(x)) == "SinIntegral[x]" assert mcode(Shi(x)) == "SinhIntegral[x]" assert mcode(Chi(x)) == "CoshIntegral[x]" assert mcode(beta(x, y)) == "Beta[x, y]" assert mcode(factorial(x)) == "Factorial[x]" assert mcode(factorial2(x)) == "Factorial2[x]" assert mcode(subfactorial(x)) == "Subfactorial[x]" assert mcode(FallingFactorial(x, y)) == "FactorialPower[x, y]" assert mcode(RisingFactorial(x, y)) == "Pochhammer[x, y]" assert mcode(catalan(x)) == "CatalanNumber[x]" assert mcode(harmonic(x)) == "HarmonicNumber[x]" assert mcode(harmonic(x, y)) == "HarmonicNumber[x, y]" assert mcode(Li(x)) == "LogIntegral[x] - LogIntegral[2]" assert mcode(LambertW(x)) == "ProductLog[x]" assert mcode(LambertW(x, -1)) == "ProductLog[-1, x]" assert mcode(LambertW(x, y)) == "ProductLog[y, x]"
def Trig_Check(s): if sin(s.args[0])/s is S.One or cos(s.args[0])/s is S.One \ or csc(s.args[0])/s is S.One or sec(s.args[0])/s is S.One \ or tan(s.args[0])/s is S.One or cot(s.args[0])/s is S.One: return True