![]() | 1 | initial version |
Yep, see the coefficients()
method:
...
sage: g = f^3
sage: g.coefficients()
[b2^3, 3*b1*b2^2, a0*b2^2 + 2*b1^2*b2 + (2*a0*b2 + b1^2)*b2, 2*a0*b1*b2 + a1*b2^2 + (2*a0*b2 + b1^2)*b1 + 2*(a0*b1 + a1*b2)*b2, 2*a1*b1*b2 + a2*b2^2 + (2*a0*b2 + b1^2)*a0 + 2*(a0*b1 + a1*b2)*b1 + (a0^2 + 2*a1*b1 + 2*a2*b2)*b2, 2*a2*b1*b2 + a3*b2^2 + (2*a0*b2 + b1^2)*a1 + 2*(a0*b1 + a1*b2)*a0 + 2*(a0*a1 + a2*b1 + a3*b2)*b2 + (a0^2 + 2*a1*b1 + 2*a2*b2)*b1, 2*a3*b1*b2 + a4*b2^2 + (2*a0*b2 + b1^2)*a2 + 2*(a0*b1 + a1*b2)*a1 + 2*(a0*a1 + a2*b1 + a3*b2)*b1 + (a0^2 + 2*a1*b1 + 2*a2*b2)*a0 + (2*a0*a2 + a1^2 + 2*a3*b1 + 2*a4*b2)*b2]
![]() | 2 | No.2 Revision |
Yep, see the coefficients()
method:
...
sage: g = f^3
sage: g.coefficients()
[b2^3, 3*b1*b2^2, a0*b2^2 + 2*b1^2*b2 + (2*a0*b2 + b1^2)*b2, 2*a0*b1*b2 + a1*b2^2 + (2*a0*b2 + b1^2)*b1 + 2*(a0*b1 + a1*b2)*b2, 2*a1*b1*b2 + a2*b2^2 + (2*a0*b2 + b1^2)*a0 + 2*(a0*b1 + a1*b2)*b1 + (a0^2 + 2*a1*b1 + 2*a2*b2)*b2, 2*a2*b1*b2 + a3*b2^2 + (2*a0*b2 + b1^2)*a1 + 2*(a0*b1 + a1*b2)*a0 + 2*(a0*a1 + a2*b1 + a3*b2)*b2 + (a0^2 + 2*a1*b1 + 2*a2*b2)*b1, 2*a3*b1*b2 + a4*b2^2 + (2*a0*b2 + b1^2)*a2 + 2*(a0*b1 + a1*b2)*a1 + 2*(a0*a1 + a2*b1 + a3*b2)*b1 + (a0^2 + 2*a1*b1 + 2*a2*b2)*a0 + (2*a0*a2 + a1^2 + 2*a3*b1 + 2*a4*b2)*b2]
--- edit
Sorry, I answered the wrong question. If you want to simplify the coefficients, you can map the simplify
function over your list:
sage: g = f^3
sage: map(simplify, g.coefficients())
[b2^3,
3*b1*b2^2,
a0*b2^2 + 2*b1^2*b2 + (2*a0*b2 + b1^2)*b2,
2*a0*b1*b2 + a1*b2^2 + (2*a0*b2 + b1^2)*b1 + 2*(a0*b1 + a1*b2)*b2,
2*a1*b1*b2 + a2*b2^2 + (2*a0*b2 + b1^2)*a0 + 2*(a0*b1 + a1*b2)*b1 + (a0^2 + 2*a1*b1 + 2*a2*b2)*b2,
2*a2*b1*b2 + a3*b2^2 + (2*a0*b2 + b1^2)*a1 + 2*(a0*b1 + a1*b2)*a0 + 2*(a0*a1 + a2*b1 + a3*b2)*b2 + (a0^2 + 2*a1*b1 + 2*a2*b2)*b1,
2*a3*b1*b2 + a4*b2^2 + (2*a0*b2 + b1^2)*a2 + 2*(a0*b1 + a1*b2)*a1 + 2*(a0*a1 + a2*b1 + a3*b2)*b1 + (a0^2 + 2*a1*b1 + 2*a2*b2)*a0 + (2*a0*a2 + a1^2 + 2*a3*b1 + 2*a4*b2)*b2]
But, if you look at the resulting list you'll see that it's identical to g.coefficients()
, so the coefficients are "simplified". Maybe what you really want is to expand the coefficients (which is less simple that the factored form by some definition):
sage: map(expand, g.coefficients())
[b2^3,
3*b1*b2^2,
3*a0*b2^2 + 3*b1^2*b2,
6*a0*b1*b2 + 3*a1*b2^2 + b1^3,
3*a0^2*b2 + 3*a0*b1^2 + 6*a1*b1*b2 + 3*a2*b2^2,
3*a0^2*b1 + 6*a0*a1*b2 + 3*a1*b1^2 + 6*a2*b1*b2 + 3*a3*b2^2,
a0^3 + 6*a0*a1*b1 + 6*a0*a2*b2 + 3*a1^2*b2 + 3*a2*b1^2 + 6*a3*b1*b2 + 3*a4*b2^2]
If you're curious about other powerful list operations, check out map
, reduce
, and filter
here.