I want construst a vector with 2^62 entries. Only 2^20+1=2049 entries are non-null complex numbers and others are all zero. Maple tells me the memory is not enough.

construct a vector with entries of symmetric real parts and anti-symatric imaginary parts,such as v:=<1+2I,5+3I,9+4I,9-4I,5-3I,1-2I>;DiscreteTransforms[FourierTransform](v);By property of fourier transform,the result should be real numbers,but it is not this. Imaginary parts not vanish

for example:
array1:=Vector(10,0): 

for i from -0.5 to 0.5 by 0.1 do

print(sin(i)):

end do:

I want to write the 10 results of sin(i) into array1 in sequence

How to make it?

Additionally, if I don't want to write the 6th (i=0) value to array2:=Vector(9,0), what should I do?

Thank you

k:=<1,2,3>:

mu:=<4,5,6>:

sigma:=<7,8,9>:

solutions:=<1,2,3,4>

product(add(1/((I*.5)*exp(solutions[i]*sqrt(2)*sigma[j]+mu[j]-ln(k[j]))+1)^k[j], i = 1 .. 4), j = 2 .. 3);

 

returns "Error, bad index into Vector"

As showed in attached file

the laurent series of exp(1/z) at z=1 is equal to the taylor series of exp(z) at z=1