Hi Robert! On Nov 26, 10:20 am, Robert Bradshaw <rober...@math.washington.edu> wrote: [...] > With over-allocation one might not even need the dense/sparse > distinction--creating 1000 variables in a "sparse" manner would only > need 10 reallocations. (There could still be the question of how > expensive it is to do arithmetic between very old and very new > variables, without timing and looking at the actual code I'm not sure > if this is a concern.)
I just remembered one important detail: In the sparse implementation, any element of an InfinitePolynomialRing has its own underlying polynomial ring. Continuing the example from my post above: sage: x[100].polynomial().parent() Univariate Polynomial Ring in x100 over Real Field with 53 bits of precision sage: x[1].polynomial().parent() Univariate Polynomial Ring in x1 over Real Field with 53 bits of precision sage: x[10].polynomial().parent() Univariate Polynomial Ring in x10 over Real Field with 53 bits of precision sage: (x[1]+x[10]).polynomial().parent() Multivariate Polynomial Ring in x10, x1 over Real Field with 53 bits of precision sage: x[5].polynomial().parent() Univariate Polynomial Ring in x5 over Real Field with 53 bits of precision sage: (x[5]+x[10]).polynomial().parent() Multivariate Polynomial Ring in x10, x5 over Real Field with 53 bits of precision This is why the sparse implementation is so slow. In the dense implementation, the InfinitePolynomialRing has an underlying ring by itself: sage: Y.polynomial_ring() Multivariate Polynomial Ring in b10, b9, b8, b7, b6, b5, b4, b3, b2, b1, b0, a10, a9, a8, a7, a6, a5, a4, a3, a2, a1, a0 over Real Field with 53 bits of precision Perhaps it would be better if the InfinitePolynomialRing had a *common* underlying ring also in the sparse implementation? In the sparse implementation that ring would just be slimmer than in the dense implementation? Provided that I find the time, I'll try to implement it. Thank you for pointing me to it! Cheers, Simon -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
