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Groebner basis computation

asked 2019-02-06 00:49:28 -0500

MMumtaz gravatar image

How we can use SageMath for computing Groebner basis? e.g. we have 35 multivariate polynomial equations, is it possible to compute groebner basis at a time?

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answered 2019-02-06 06:31:21 -0500

Sébastien gravatar image

updated 2019-02-06 06:33:29 -0500

You may do something like:

sage: R = QQ['x,y,z']
sage: R
Multivariate Polynomial Ring in x, y, z over Rational Field
sage: x,y,z = R.gens()
sage: I = ideal(x^5 + y^4 + z^3 - 1,  x^3 + y^3 + z^2 - 1)
sage: B = I.groebner_basis()
sage: B
[y^6 + x*y^4 + 2*y^3*z^2 + x*z^3 + z^4 - 2*y^3 - 2*z^2 - x + 1, 
 x^2*y^3 - y^4 + x^2*z^2 - z^3 - x^2 + 1, 
 x^3 + y^3 + z^2 - 1]

This example was taken from the documentation on Ideals in multivariate polynomial rings

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Asked: 2019-02-06 00:49:28 -0500

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Last updated: Feb 06