ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 08 Apr 2018 20:42:28 -0500A way of checking that a multivariate system of equations has a solution?https://ask.sagemath.org/question/41913/a-way-of-checking-that-a-multivariate-system-of-equations-has-a-solution/Is there a way to check that a multivariate system of polynomial equations does indeed have a solution(or not)? The context i am using this in is as follows: say i have a system of multivariate polynomial equations over a finite field, i then put values in for some of the variables, and then i need to check if the resulting system in the remaining unassigned variables has a solution or not? If not, then i will reassign different values to the other variables until a system with a solution is yielded. Of course because the assigning of these values is random there is a high chance the system has a solution anyway, but in the event that it does not is where i need a way to check whether a solution exists or not.Sun, 08 Apr 2018 13:40:45 -0500https://ask.sagemath.org/question/41913/a-way-of-checking-that-a-multivariate-system-of-equations-has-a-solution/Comment by slelievre for <p>Is there a way to check that a multivariate system of polynomial equations does indeed have a solution(or not)? The context i am using this in is as follows: say i have a system of multivariate polynomial equations over a finite field, i then put values in for some of the variables, and then i need to check if the resulting system in the remaining unassigned variables has a solution or not? If not, then i will reassign different values to the other variables until a system with a solution is yielded. Of course because the assigning of these values is random there is a high chance the system has a solution anyway, but in the event that it does not is where i need a way to check whether a solution exists or not.</p>
https://ask.sagemath.org/question/41913/a-way-of-checking-that-a-multivariate-system-of-equations-has-a-solution/?comment=41932#post-id-41932I concur with @tmonteil -- please provide an example of input of
a polynomial system that other users can copy paste to get started
exploring your question.Sun, 08 Apr 2018 20:41:39 -0500https://ask.sagemath.org/question/41913/a-way-of-checking-that-a-multivariate-system-of-equations-has-a-solution/?comment=41932#post-id-41932Comment by tmonteil for <p>Is there a way to check that a multivariate system of polynomial equations does indeed have a solution(or not)? The context i am using this in is as follows: say i have a system of multivariate polynomial equations over a finite field, i then put values in for some of the variables, and then i need to check if the resulting system in the remaining unassigned variables has a solution or not? If not, then i will reassign different values to the other variables until a system with a solution is yielded. Of course because the assigning of these values is random there is a high chance the system has a solution anyway, but in the event that it does not is where i need a way to check whether a solution exists or not.</p>
https://ask.sagemath.org/question/41913/a-way-of-checking-that-a-multivariate-system-of-equations-has-a-solution/?comment=41914#post-id-41914There are ways to do that in Sage, but please provide a concrete example, it will be easier for us to show how to !Sun, 08 Apr 2018 14:06:52 -0500https://ask.sagemath.org/question/41913/a-way-of-checking-that-a-multivariate-system-of-equations-has-a-solution/?comment=41914#post-id-41914Answer by slelievre for <p>Is there a way to check that a multivariate system of polynomial equations does indeed have a solution(or not)? The context i am using this in is as follows: say i have a system of multivariate polynomial equations over a finite field, i then put values in for some of the variables, and then i need to check if the resulting system in the remaining unassigned variables has a solution or not? If not, then i will reassign different values to the other variables until a system with a solution is yielded. Of course because the assigning of these values is random there is a high chance the system has a solution anyway, but in the event that it does not is where i need a way to check whether a solution exists or not.</p>
https://ask.sagemath.org/question/41913/a-way-of-checking-that-a-multivariate-system-of-equations-has-a-solution/?answer=41934#post-id-41934It's possible that the answers to other questions about polynomial systems can help you,
adapting them to the case of finite fields.
For instance, the answers to this question invite to use ideals and varieties:
- [Find algebraic solutions to system-of-polynomial-equations](https://ask.sagemath.org/question/11070/find-algebraic-solutions-to-system-of-polynomial-equations/)Sun, 08 Apr 2018 20:42:28 -0500https://ask.sagemath.org/question/41913/a-way-of-checking-that-a-multivariate-system-of-equations-has-a-solution/?answer=41934#post-id-41934