Suppose you have some functions like:

S^1 --> S^1: w(x,y) = (x^2 - y^2, 2xy)

Then this is equivalent of

w(exp(i 2Pi t)) = exp(i 4 Pi t)

Or if I have S^1 --> S^1: w(x,y) = (-y,x), we would get:

w(exp(i 2Pi t)) = exp(i 2 Pi (t+1/4))

How can I obtain the second form of the expression in Maple given the first one?

I would like to compute the euler-lagrange equations using the index notation in quantum field theory. So for example given the Lagrangian here:

Is there a way to derive the Euler-Lagrange equation in maple?

Often times I run into calculations like these:

Where d denotes the exterior derivative. Now I know that it is possible to compute the exterior derivative of a function (using the DifferentialGeometry package). But is there a way to compute and simplify them with tensor products as above?

Suppose I have the equation C := y^2*z + yz^2 = x^2, then I want to test for which triples (x,y,z) with x,y,z in {0,1} the equation is satisfied? Is there a quick way of doing this in Maple?

Hi I am trying to compute the series approximation for the difference between these two divergent integrals

M := int(cosh(p)^2/sqrt(cosh(p)^2 - (1 + x)^2*sinh(p)^2), p = 0 .. 1/2*ln(1/x));

N := int((1 + x)*sinh(p)^2/sqrt(cosh(p)^2 - (1 + x)^2*sinh(p)^2), p = 0 .. 1/2*ln(1/x))

where x,p are positive and x is approaching zero. I would like to get a series expansion of M-N, but I am not quite if this is possible.