ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 08 Apr 2018 20:40:45 +0200A way of checking that a multivariate system of equations has a solution?https://ask.sagemath.org/question/41913/a-way-of-checking-that-a-multivariate-system-of-equations-has-a-solution/Is there a way to check that a multivariate system of polynomial equations does indeed have a solution(or not)? The context i am using this in is as follows: say i have a system of multivariate polynomial equations over a finite field, i then put values in for some of the variables, and then i need to check if the resulting system in the remaining unassigned variables has a solution or not? If not, then i will reassign different values to the other variables until a system with a solution is yielded. Of course because the assigning of these values is random there is a high chance the system has a solution anyway, but in the event that it does not is where i need a way to check whether a solution exists or not.DalvirSun, 08 Apr 2018 20:40:45 +0200https://ask.sagemath.org/question/41913/Symbolic Linear Algebrahttps://ask.sagemath.org/question/26952/symbolic-linear-algebra/I'd like to manipulate symbolic expression in linear algebra. More specifically, suppose that A,B, etc. are matrices and v,w,.. etc are column vectors. I have various expressions in them that I'd like expanded and grouped. It also should know about transpose (that it's an involution). For example, if I write the expression:
transpose(v-w)*A*(v-w). It should be able to expand this to
transpose(v)*A*v - transpose(v)*A*w - transpose(w)*A*v + transpose(w)*A*w
Also, I'd like to specify that A is symmetric -- A == transpose(A). In that case the above would simplify to
transpose(v)*A*v - 2*transpose(v)*A*w + transpose(w)*A*w
if we idenfity a 1 by 1 matrix with a scalar. It would also be nice, if we could specify symbolic scalars, and, for example to say that A in hom(V,W), where V,W are some vector spaces. In that case if we try to multiply things that are incompatible we would get an error. This looks like it should be part of some sort of universal algebra package. Does such a thing exist in SAGE?VictorWed, 27 May 2015 16:59:07 +0200https://ask.sagemath.org/question/26952/