On Tuesday, June 25, 2019 at 10:03:03 AM UTC+2, Peter Luschny wrote: > > How that? Look at the output above. Sage *knows* that the terms of the sum > are polynomials. So it should return the zero of that ring, which is the > null polynomial. > > Not in the first case, look at what are you passing to sum as argument
sage: sage: R=ZZ['x'] sage: R=ZZ['x'] sage: def ib(m, n): return [binomial(m*n-1, m*k)*cyclotomic_polynomial(m*(k+1)) for k in (0..n-1)] sage: for n in (0..6): ....: print(ib(2,n)) ....: [] [x + 1] [x + 1, 3*x^2 + 3] [x + 1, 10*x^2 + 10, 5*x^2 - 5*x + 5] [x + 1, 21*x^2 + 21, 35*x^2 - 35*x + 35, 7*x^4 + 7] [x + 1, 36*x^2 + 36, 126*x^2 - 126*x + 126, 84*x^4 + 84, 9*x^4 - 9*x^3 + 9*x^2 - 9*x + 9] [x + 1, 55*x^2 + 55, 330*x^2 - 330*x + 330, 462*x^4 + 462, 165*x^4 - 165*x^3 + 165*x^2 - 165*x + 165, 11*x^4 - 11*x^2 + 11] When n =0, k ranges from 0 to -1 so there is no k and the list constructed in ib(n,m) is just the empty list. Not an empty list of polynomials, just an empty list. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/f26ea001-2dda-4d8f-a1fd-36d794d3bc41%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
