Hi,
I am trying to simplify the expression s as given below. (I am not sure why it comes up with all the vector caclulus notation in it but it should display okay when you enter it)
Because of the presence of the exponential imaginary fucntions I thought evalc might be useful but when I use it I get a huge expression with csgn appearing in it. To my knowledge csgn appears when assumptions are not correctly specified - is this so? I can't see any assumption that I would need to specify and the ones I have tried have made no difference (beta is real, k is an integer, sigma >= 0) . How can I use evalc or otherwise simplify s. In particular I suspect the exponentials in s may be turned into trig functions but I don't want to convert the whole thing to a trig fucntion by using convert. (I want to do it in a similar way to what was done in the original post). Any thoughts ?
s := VectorCalculus[`*`](1/4, VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`+`](Pi^2, VectorCalculus[`*`](1/4, beta^2)), Q), VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](1/2, Pi), VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](1/8, VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`-`](I), VectorCalculus[`*`](I, (exp(VectorCalculus[`*`](VectorCalculus[`*`](I, k), theta)))^2)), exp(VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](1/2, sigma^2), k^2)))), VectorCalculus[`*`](VectorCalculus[`*`](2, exp(VectorCalculus[`*`](VectorCalculus[`*`](I, k), theta))), sin(VectorCalculus[`*`](k, theta))))), Pi), Q^2), beta^2), sqrt(VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](16, beta^2), Q^2)), VectorCalculus[`-`](16)), Pi^4), VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](16, I), beta^3), Q^2), Pi^3)), VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`*`](4, beta^4), Q^2), VectorCalculus[`-`](VectorCalculus[`*`](8, beta^2))), Pi^2)), VectorCalculus[`-`](beta^4)))), VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](1/4, VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](2, Q^3), beta^3)), 1), VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](2, beta), Q))), Pi^3), VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](I, VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`-`](VectorCalculus[`*`](beta, Q)), VectorCalculus[`*`](Q^3, beta^3)), 1/2)), beta), Pi^2)), VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`*`](1/4, beta^2), VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](1/2, Q), beta^3))), Pi)), VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](1/4, I), VectorCalculus[`+`](VectorCalculus[`*`](beta, Q), VectorCalculus[`-`](1/2))), beta^3)))), VectorCalculus[`+`](exp(VectorCalculus[`*`](VectorCalculus[`*`](I, k), theta)), 1)), VectorCalculus[`+`](exp(VectorCalculus[`*`](VectorCalculus[`*`](I, k), theta)), VectorCalculus[`-`](1))), exp(VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](1/2, sigma^2), k^2))))), VectorCalculus[`*`](VectorCalculus[`*`](sin(VectorCalculus[`*`](k, theta)), exp(VectorCalculus[`*`](VectorCalculus[`*`](I, k), theta))), VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`*`](I, beta), Q), VectorCalculus[`*`](VectorCalculus[`*`](I, beta^3), Q^3)), VectorCalculus[`-`](VectorCalculus[`*`](1/2, I))), Pi^3), VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](1/2, beta^2), Q)), VectorCalculus[`*`](VectorCalculus[`*`](1/2, beta^4), Q^3)), VectorCalculus[`*`](1/4, beta)), Pi^2)), VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](1/4, I), VectorCalculus[`+`](VectorCalculus[`*`](beta, Q), VectorCalculus[`-`](1/2))), beta^2), Pi)), VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](1/8, beta^4), Q))), VectorCalculus[`*`](1/16, beta^3))))), sqrt(VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](16, beta^2), Q^2)), VectorCalculus[`-`](16)), Pi^4), VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](16, I), beta^3), Q^2), Pi^3))), VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`*`](4, beta^4), Q^2), VectorCalculus[`-`](VectorCalculus[`*`](8, beta^2))), Pi^2)), VectorCalculus[`-`](beta^4))))), VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](1/2, Pi), VectorCalculus[`+`](VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](1/4, VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`+`](1, VectorCalculus[`*`](VectorCalculus[`*`](2, Q^3), beta^3)), VectorCalculus[`*`](VectorCalculus[`*`](2, beta), Q)), Pi^3), VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](I, VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`-`](1/2), VectorCalculus[`-`](VectorCalculus[`*`](beta, Q))), VectorCalculus[`*`](Q^3, beta^3))), beta), Pi^2)), VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`*`](1/2, Q), beta^3), VectorCalculus[`*`](1/4, beta^2)), Pi)), VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](1/4, I), VectorCalculus[`+`](VectorCalculus[`*`](beta, Q), 1/2)), beta^3)))), VectorCalculus[`+`](exp(VectorCalculus[`*`](VectorCalculus[`*`](I, k), theta)), 1)), VectorCalculus[`+`](exp(VectorCalculus[`*`](VectorCalculus[`*`](I, k), theta)), VectorCalculus[`-`](1))), exp(VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](1/2, sigma^2), k^2))))), VectorCalculus[`*`](VectorCalculus[`*`](sin(VectorCalculus[`*`](k, theta)), exp(VectorCalculus[`*`](VectorCalculus[`*`](I, k), theta))), VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`*`](I, beta), Q), VectorCalculus[`*`](VectorCalculus[`*`](I, beta^3), Q^3)), VectorCalculus[`*`](1/2, I)), Pi^3), VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`*`](1/2, beta^2), Q), VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](1/2, beta^4), Q^3))), VectorCalculus[`*`](1/4, beta)), Pi^2)), VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](1/4, I), VectorCalculus[`+`](VectorCalculus[`*`](beta, Q), 1/2)), beta^2), Pi)), VectorCalculus[`*`](VectorCalculus[`*`](1/8, beta^4), Q)), VectorCalculus[`*`](1/16, beta^3))))), sqrt(VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](16, beta^2), Q^2)), VectorCalculus[`-`](16)), Pi^4), VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](16, I), beta^3), Q^2), Pi^3)), VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`*`](4, beta^4), Q^2), VectorCalculus[`-`](VectorCalculus[`*`](8, beta^2))), Pi^2)), VectorCalculus[`-`](beta^4)))))), VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`*`](I, VectorCalculus[`+`](VectorCalculus[`*`](beta^2, Q^2), 1)^2), Pi^4), VectorCalculus[`*`](VectorCalculus[`*`](Pi^3, Q), beta^2)), VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`*`](1/2, I), beta^2), VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](1/2, I), beta^4), Q^2))), Pi^2)), VectorCalculus[`*`](VectorCalculus[`*`](1/16, I), beta^4)), VectorCalculus[`+`](exp(VectorCalculus[`*`](VectorCalculus[`*`](I, k), theta)), 1)), VectorCalculus[`+`](exp(VectorCalculus[`*`](VectorCalculus[`*`](I, k), theta)), VectorCalculus[`-`](1))), exp(VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](1/2, sigma^2), k^2)))), VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](2, sin(VectorCalculus[`*`](k, theta))), exp(VectorCalculus[`*`](VectorCalculus[`*`](I, k), theta))), VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`*`](beta^2, Q^2), 1)^2, Pi^4)), VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](I, Pi^3), beta^2), Q)), VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`*`](1/2, beta^4), Q^2), VectorCalculus[`-`](VectorCalculus[`*`](1/2, beta^2))), Pi^2)), VectorCalculus[`-`](VectorCalculus[`*`](1/16, beta^4)))))), VectorCalculus[`+`](Pi^2, VectorCalculus[`*`](1/4, beta^2))))), t), 1/VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](1/4, Pi), VectorCalculus[`+`](VectorCalculus[`*`](I, Pi), VectorCalculus[`-`](VectorCalculus[`*`](1/2, beta)))), beta), Q), sqrt(VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](16, beta^2), Q^2)), VectorCalculus[`-`](16)), Pi^4), VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](16, I), beta^3), Q^2), Pi^3))), VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`*`](4, beta^4), Q^2), VectorCalculus[`-`](VectorCalculus[`*`](8, beta^2))), Pi^2)), VectorCalculus[`-`](beta^4))))), VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`*`](beta^2, Q^2), 1), Pi^4)), VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](I, beta^3), Q^2), Pi^3)), VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](1/4, beta^4), Q^2)), VectorCalculus[`*`](1/2, beta^2)), Pi^2)), VectorCalculus[`*`](1/16, beta^4)), exp(VectorCalculus[`*`](VectorCalculus[`*`](I, k), theta))), VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](1/4, Pi), Q), VectorCalculus[`+`](VectorCalculus[`*`](I, Pi), VectorCalculus[`*`](1/2, beta))), beta), sqrt(VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](16, beta^2), Q^2)), VectorCalculus[`-`](16)), Pi^4), VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](16, I), beta^3), Q^2), Pi^3)), VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`*`](4, beta^4), Q^2), VectorCalculus[`-`](VectorCalculus[`*`](8, beta^2))), Pi^2)), VectorCalculus[`-`](beta^4)))), VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`-`](VectorCalculus[`*`](beta^2, Q^2)), VectorCalculus[`-`](1)), Pi^4)), VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](I, beta^3), Q^2), Pi^3)), VectorCalculus[`*`](VectorCalculus[`+`](VectorCalculus[`*`](VectorCalculus[`*`](1/4, beta^4), Q^2), VectorCalculus[`-`](VectorCalculus[`*`](1/2, beta^2))), Pi^2)), VectorCalculus[`-`](VectorCalculus[`*`](1/16, beta^4)))), beta^2)));
