Thanks very much Daniel for your reply. If Solve
is not accelerated in a parallel computing environment, does that also mean that running it on a single multi-core processor with a greater number of cores would also not reduce execution time, and that the only way to reduce execution time is to use a faster processor?
Also, re the Groebner basis, I have noted your published work on that topic. I am only generally familiar with it and its application in solving simultaneous equations, but I gather from your reply that the computation of a Groebner basis is not amenable to parallelization. In addition to my earlier description of the type of equations I am working with (polynomials with terms consisting of a coefficient and multiple variables involving only multiplication), I will also note that I am interested in numeric, not symbolic solutions, and further, that all variable values are integers. Also, in some of these systems all of the variables in the polynomial terms are only to the first power. I don't know if that makes a difference with regard to the need to generate a Groebner basis by Solve
or if other methods might be used internally that are amenable to parallelization. Is there a way to ascertain which solution methods are being used by Solve
in a particular instance?
Also, in some earlier work on smaller sets of these equations, I have successfully used the simple substitution method to obtain solutions using custom algorithms. Being familiar with that method, I can see that parallelization is possible, since different processors can be working on different substitutions. Can Mathematica be instructed to try that method? Is there a function for it? If so, can that function / method make use of multiple processors and/or GPUs? Or is it the case that none of the computer algebra functions in Mathematica are able to benefit from multi-processor / multi-core computational resources because the computational steps can only be executed sequentially? Thanks in advance to Daniel and to all for your assistance!