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Solving singular matrix quadratic form using Groebner basis

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[quote="sc719"](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_11X1^2 + A12X2X1 - X1 + B1 = 0; A_21X1X2 + A22X2^2 -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[/quote]

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Topic review - Solving singular matrix quadratic form using Groebner basis

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sc719

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Solving singular matrix quadratic form using Groebner basis

(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

Posted: Fri Mar 01, 2019 6:46 pm

It is currently Fri May 13, 2022 10:54 am

Singular

Solving singular matrix quadratic form using Groebner basis

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