Solving singular matrix quadratic form using Groebner basis
sc719 ยท Fri Mar 01, 2019 6:46 pm
(Previous Post modified)
As an economist who is not familiar with math and singular, I've been struggling to find a general way of solving the following type of problems. I really hope that someone can help me out.
Def: A_ij, B_j are n by n real-valued matrices - may well be singular.
Question: Solve for all solutions for (X1,X2) to the following system of multivariate matrix quadratic form using Groebner basis.
===========================
A_11*X1^2 + A12*X2*X1 - X1 + B1 = 0;
A_21*X1*X2 + A22*X2^2 -X2 + B2 = 0;
===========================
Ideally, I want to have a matlab code for this problem, only to fail. I used the built-in vpasolve.m. It didn't work.
So can anyone write a sample code for this in Singular and show how to run the code?
Solving this problem is so important to my research.
Thank you
As an economist who is not familiar with math and singular, I've been struggling to find a general way of solving the following type of problems. I really hope that someone can help me out.
Def: A_ij, B_j are n by n real-valued matrices - may well be singular.
Question: Solve for all solutions for (X1,X2) to the following system of multivariate matrix quadratic form using Groebner basis.
===========================
A_11*X1^2 + A12*X2*X1 - X1 + B1 = 0;
A_21*X1*X2 + A22*X2^2 -X2 + B2 = 0;
===========================
Ideally, I want to have a matlab code for this problem, only to fail. I used the built-in vpasolve.m. It didn't work.
So can anyone write a sample code for this in Singular and show how to run the code?
Solving this problem is so important to my research.
Thank you