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gb -- compute a Gröbner basis

Synopsis

Description

See Gröbner bases for more information and examples.

The returned value is not the Gröbner basis itself. The matrix whose columns form a sorted, auto-reduced Gröbner basis are obtained by applying generators (synonym: gens) to the result of gb.

i1 : R = QQ[a..d]

o1 = R

o1 : PolynomialRing
i2 : I = ideal(a^3-b^2*c, b*c^2-c*d^2, c^3)

             3    2      2      2   3
o2 = ideal (a  - b c, b*c  - c*d , c )

o2 : Ideal of R
i3 : G = gens gb I

o3 = | c3 bc2-cd2 a3-b2c c2d2 cd4 |

             1       5
o3 : Matrix R  <--- R

See also

Ways to use gb :