> Can I do this in Sage?
Sure. Here you have some tips:
{{{id=1|
#Create n variables with names x1, x2 ... xn
#and store them in a list vs
n = 5
vs = var(' '.join('x%d'%j for j in range(5)))
vs
///
(x0, x1, x2, x3, x4)
}}}
{{{id=6|
def pot(vs,ds):
return prod(v^d for v,d in zip(vs,ds))
pot(vs,[1,2,3])
///
x0*x1^2*x2^3
}}}
{{{id=2|
def generating_function(cs):
return prod(1 + c*pot(vs,ds) for ds,c in cs.items())
generating_function({(1,1,0,0,1):3, (1,1,0,0,0):5})
///
(5*x0*x1 + 1)*(3*x0*x1*x4 + 1)
}}}
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