Creating symmetric polynomials of squares of variables?
I have five variables: a,b,c,d,e, for which I want to use the elementary symmetric polynomials of their squares:
s1 = a^2+b^2+c^2+d^2+e^2
s2 = a^2b^2 + a^2c^2 + ... + d^2e^2
and so on, to:
s5 = a^2b^2c^2d^2e^2.
Now, I can do this by hand, or by pulling out the coefficients of the polynomial
P = (x+a^2)(x+b^2)...(x+e^2)
However, is there a nicer way which uses Sage's own extensive symmetric polynomial functionality?