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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 with a vector, both with integral entries. The matrix is say 100 by 100 and the entries are on the order of $10^{100}$.

Is there any faster way to do this computation than use SAGE's intrinsic matrix times a vector command?

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 with a vector, both with integral entries. The matrix is say 100 by 100 and the entries are on the order of $10^{100}$.

Is there any faster way to do this computation than use using SAGE's intrinsic matrix times a vector command?

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, vector $v$, both with integral entries. The

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 is say 100 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 100 a vector, and the entries are on the order of $10^{100}$. 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 ${\bf Z}$.

Is My question: is there any a faster way to do this computation than using SAGE's intrinsic matrix times a vector command?command over ${\bf Z}$?