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| Solving singular matrix quadratic form using Groebner basis https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2829 |
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| Author: | sc719 [ Fri Mar 01, 2019 6:46 pm ] |
| Post subject: | 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 |
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