# Groebner basis computation

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?

Groebner basis computation

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2

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

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

Seen: **124 times**

Last updated: **Feb 06 '19**

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