In Python generally, "X = Y" doesn't modify the *object* which is named X,
it just rebinds the name, saying that "X" now refers to the object given by
the expression Y. So in general,
for something in someloop:
something = something_else
isn't going to do much. (I want to say "nothing" but I guess there could
be side effects of computing something_else.)
You can arrive at your goal in lots of ways. You could sum the component
monomials, which is short but less general:
sage: R.<x1,x2,x3> = QQbar[]
sage: P = x1^2 + 2*x1*x2 + x2^2 + 2*x1*x3 + 2*x2*x3 + x3^2 + 2*x1 + 2*x2 +
2*x3 + 1
sage: sum(P.monomials())
x1^2 + x1*x2 + x2^2 + x1*x3 + x2*x3 + x3^2 + x1 + x2 + x3 + 1
Another way to get what you want would be to use map_coefficients, which
applies the function you pass it to all the coefficients, which is clear
but doesn't give you access to the corresponding term:
sage: P = x1^2 + 2*x1*x2 + x2^2 + 2*x1*x3 + 2*x2*x3 + x3^2 + 2*x1 + 2*x2 +
2*x3 + 1
sage: P.map_coefficients(lambda x: 1)
x1^2 + x1*x2 + x2^2 + x1*x3 + x2*x3 + x3^2 + x1 + x2 + x3 + 1
Or in the most general way, you could loop over the coefficients and their
monomials and build a new polynomial from each term:
sage: list(P)
[(1, x1^2),
(2, x1*x2),
(1, x2^2),
(2, x1*x3),
(2, x2*x3),
(1, x3^2),
(2, x1),
(2, x2),
(2, x3),
(1, 1)]
sage: sum(mon for coeff, mon in P)
x1^2 + x1*x2 + x2^2 + x1*x3 + x2*x3 + x3^2 + x1 + x2 + x3 + 1
Doug
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