ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 03 Dec 2012 04:15:56 +0100System of polynomial inequalitieshttps://ask.sagemath.org/question/9596/system-of-polynomial-inequalities/I heard that something called a Groebner Basis can be used to find the solutions of a system of polynomial equations like $p_1(x_1,\ldots,x_m)=0,\ldots,p_n(x_1,\ldots,x_m)=0$
Is there something analgous that can find solutions when inequalities are also involved such as
$$p_1(x_1,\ldots,x_m)=0,\ldots,p_n(x_1,\ldots,x_m)=0$$
$$q_1(x_1,\ldots,x_m)>0,\ldots,q_r(x_1,\ldots,x_m)>0$$
and is there a way to do this in Sage?Sat, 01 Dec 2012 21:56:21 +0100https://ask.sagemath.org/question/9596/system-of-polynomial-inequalities/Answer by burcin for <p>I heard that something called a Groebner Basis can be used to find the solutions of a system of polynomial equations like $p_1(x_1,\ldots,x_m)=0,\ldots,p_n(x_1,\ldots,x_m)=0$</p>
<p>Is there something analgous that can find solutions when inequalities are also involved such as</p>
<p>$$p_1(x_1,\ldots,x_m)=0,\ldots,p_n(x_1,\ldots,x_m)=0$$
$$q_1(x_1,\ldots,x_m)>0,\ldots,q_r(x_1,\ldots,x_m)>0$$</p>
<p>and is there a way to do this in Sage?</p>
https://ask.sagemath.org/question/9596/system-of-polynomial-inequalities/?answer=14340#post-id-14340You can use the cylindirical algebraic decomposition (CAD) method to solve a system of polynomials with inequalities. Sage has an optional package for [QEPCAD](http://www.usna.edu/cs/~qepcad/B/QEPCAD.html). See the output of
sage: qepcad?
and try
./sage -i qepcad
from the command line to install QEPCAD. Note that the version we have (`1.50`) is quite old. The latest version on the web site is `1.69`.Mon, 03 Dec 2012 04:15:56 +0100https://ask.sagemath.org/question/9596/system-of-polynomial-inequalities/?answer=14340#post-id-14340