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f():=[];//Echo(CurrentFile()," line ",CurrentLine());
Testing("UnaryFunctionInverses");
Verify(Sin(ArcSin(a)),a); f();
Verify(Cos(ArcCos(a)),a); f();
//TODO ??? Verify(Tan(ArcTan(a)),a);
Verify(ArcSin(Sin(a)),a); f();
Verify(ArcCos(Cos(a)),a); f();
//TODO ??? this is not always the correct answer! Verify(ArcTan(Tan(a)),a);
Verify(Tan(Pi/2),Infinity); f();
Verify(Tan(Pi),0); f();
Verify( Limit(x,Infinity) Sin(x), Undefined ); f();
Verify( Limit(x,Infinity) Cos(x), Undefined ); f();
Verify( Limit(x,Infinity) Tan(x), Undefined ); f();
Verify( Limit(x,Infinity) Gamma(x), Infinity ); f();
Verify( Limit(x,Infinity) Abs(x), Infinity ); f();
Verify( Limit(x,Infinity) x!, Infinity); f();
Verify( Sin(x)/Cos(x), Tan(x) ); f();
Verify( TrigSimpCombine(Sin(x)^2 + Cos(x)^2), 1 ); f();
Verify( Sinh(x)-Cosh(x), Exp(-x)); f();
Verify( Sinh(x)+Cosh(x), Exp(x) ); f();
Verify( Sinh(x)/Cosh(x), Tanh(x) ); f();
Verify( Sinh(Infinity), Infinity); f();
Verify( Sinh(x)*Csch(x), 1); f();
Verify( 1/Coth(x), Tanh(x) ); f();
Verify(2+I*3,Complex(2,3)); f();
Verify(Magnitude(I+1),Sqrt(2)); f();
Verify(Re(2+I*3),2); f();
Verify(Im(2+I*3),3); f();
// Shouldn't these be in linalg.yts?
Verify(ZeroVector(3),{0,0,0}); f();
Verify(BaseVector(2,3),{0,1,0}); f();
Verify(Identity(3),{{1,0,0},{0,1,0},{0,0,1}}); f();
Testing("Derivatives");
Verify(D(x) a,0); f();
Verify(D(x) x,1); f();
Verify(D(x) (x+x),2); f();
Verify(D(x) (x*x),2*x); f();
Verify(D(x) D(x) Sin(x),-Sin(x)); f();
Testing("Limits");
Verify( Limit(x,0,Right) Ln(x)*Sin(x), 0 ); f();
KnownFailure( Limit(k,Infinity) ((k-phi)/k)^(k+1/2) = Exp(-phi) ); f();
[
Local(z);
// This function satisfies Laplaces eqn: D(x,2)z + D(y,2)z = 0
z:= ArcTan((2*x*y)/(x^2 - y^2)); f();
//TODO, this test is disabled, should it be re-enabled?
// Hangs
// Verify(Simplify((D(x,2) z) + D(y,2) z), 0 );
];
Testing("Pslq");
VerifyPslq(left,right):=
[
If(left=right,
Verify(True,True),
`Verify(@left,-(@right)));
];
VerifyPslq(Pslq({ Pi+2*Exp(1) , Pi , Exp(1) },20),{1,-1,-2}); f();
VerifyPslq(Pslq({ 2*Pi+3*Exp(1) , Pi , Exp(1) },20),{1,-2,-3}); f();
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