On Mon, Dec 15, 2008 at 8:05 AM, John H Palmieri <[email protected]> wrote: > > On Dec 14, 11:16 pm, "William Stein" <[email protected]> wrote: >> On Sun, Dec 14, 2008 at 10:53 PM, John H Palmieri >> >> <[email protected]> wrote: >> >> > I have some code which generates a bunch of expressions of the form >> > Sum (n_i a_i) where each n_i is an integer and each a_i is an unknown >> > in a field, and I'm most interested in the case when the field is GF >> > (p). Set each of these expressions equal to zero. What's the best way >> > in Sage to solve the resulting system of equations for the a_i's? >> >> > For example, I can't figure out how to use 'solve', because I can't >> > figure out how to insist that the variables be treated as elements of >> > a particular field. Is the only way to convert everything to a matrix >> > equation? >> >> Is p big or small? Just to be clear above, are you *really* just >> solving a system of linear equations modulo p? > > p is small. For each prime p >= 2 and for each integer n >= 3, I have > a system of equations modulo p in n-1 variables. I am interested in > solving the system for each pair (p,n) for all values of p and n. I > understand the characteristic zero situation, and I know about how big > the coefficients are, so I understand what happens if p is large > relative to n; I want to see what happens in the other case. (For what > it's worth, the number of equations is equal to the number of > partitions of n into three parts.) > > And yes, I'm solving a homogeneous linear system mod p.
The only reasonable way to solve this in Sage right now is to create a matrix and solve the matrix equation, i.e., to encode this as a linear algebra problem. William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
