Re:SageMath – Open-Source Mathematical Software System
by enriquto on Saturday June 13, 2020 @04:54PM
(#23512640)
> Can Grobner basis techniques be used to solve a set of quadratic inequalities?
One application of Gröbner bases is to solve systems of polynomial equations [0], and characterize their solutions. In many circumstances it is not however the best method, for example if you are content with a numerical solution you can use other techniques.
Notice that this concerns equations, not inequalities. After a cursory search, I cannot find any "big" reference for solving polynomial inequalities using Gröbner bases. There is this [1], still, not sure how serious it is.
One application of Gröbner bases is to solve systems of polynomial equations [0], and characterize their solutions. In many circumstances it is not however the best method, for example if you are content with a numerical solution you can use other techniques.
Notice that this concerns equations, not inequalities. After a cursory search, I cannot find any "big" reference for solving polynomial inequalities using Gröbner bases. There is this [1], still, not sure how serious it is.
[0] https://en.wikipedia.org/wiki/Gr%C3%B6bner_basis#Solutions_o...
[1] https://arxiv.org/abs/1603.01183