ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 04 Nov 2011 11:46:03 -0500Speeding up matrix multiplication?http://ask.sagemath.org/question/8438/speeding-up-matrix-multiplication/I'm currently trying write code to compute with overconvergent modular symbols. In iterating a Hecke operator, the key (i.e. most time consuming) operation that is performed tons of times is simply taking the product of a large dense matrix say $M$ with a vector $v$, both with integral entries.
More precisely, let $p$ be a (relatively small) prime (think $p=11$) and $N$ some integer (think 100). I have an $N$ by $N$ matrix and am interested in quickly computing the product $M \cdot v$ modulo $p^N$.
I am simply using the intrinsic SAGE command of multiplying a matrix by a vector, and I was surprised to see that working with matrices over ${\bf Z}/p^n{\bf Z}$ was much (i.e. 10 times) slower than working with matrices over ${\bf Z}$.
My question: is there a faster way to do this computation than using SAGE's intrinsic matrix times a vector command over ${\bf Z}$?
Robert PollackFri, 04 Nov 2011 11:46:03 -0500http://ask.sagemath.org/question/8438/