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System of polynomial inequalities

asked 2012-12-01 14:56:21 -0600

anonymous user

Anonymous

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?

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answered 2012-12-02 21:15:56 -0600

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.

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Asked: 2012-12-01 14:56:21 -0600

Seen: 202 times

Last updated: Dec 02 '12