Ask Your Question

System of polynomial inequalities

asked 2012-12-01 21:56:21 +0200

anonymous user


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?

edit retag flag offensive close merge delete

1 Answer

Sort by ยป oldest newest most voted

answered 2012-12-03 04:15:56 +0200

You can use the cylindirical algebraic decomposition (CAD) method to solve a system of polynomials with inequalities. Sage has an optional package for QEPCAD. 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.

edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools


Asked: 2012-12-01 21:56:21 +0200

Seen: 450 times

Last updated: Dec 03 '12