# Difference between revisions of "Package sagbi/SB.SAGBI"

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<short_description>Computes a finite SAGBI-basis of a subalgebra if existing.</short_description> | <short_description>Computes a finite SAGBI-basis of a subalgebra if existing.</short_description> | ||

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<description> | <description> | ||

This function computes a finite SAGBI-basis of a subalgebra <tt>S</tt> generated by the polynomials of the list <tt>G</tt>, if a finite SAGBI-basis of <tt>S</tt> is existing. Then a list of polynomials is returned which form a SAGBI-basis of <tt>S</tt>. Otherwise the computation runs until it is interrupted. | This function computes a finite SAGBI-basis of a subalgebra <tt>S</tt> generated by the polynomials of the list <tt>G</tt>, if a finite SAGBI-basis of <tt>S</tt> is existing. Then a list of polynomials is returned which form a SAGBI-basis of <tt>S</tt>. Otherwise the computation runs until it is interrupted. |

## Revision as of 08:51, 28 October 2020

This article is about a function from ApCoCoA-2. If you are looking for the ApCoCoA-1 version of it, see ApCoCoA-1:SB.Sagbi and ApCoCoA-1:SB.ReducedSagbi. |

## SB.SAGBI

Computes a finite SAGBI-basis of a subalgebra if existing.

### Syntax

SB.SAGBI(G:LIST of POLY):LIST of POLY

### Description

This function computes a finite SAGBI-basis of a subalgebra `S` generated by the polynomials of the list `G`, if a finite SAGBI-basis of `S` is existing. Then a list of polynomials is returned which form a SAGBI-basis of `S`. Otherwise the computation runs until it is interrupted.

@param

*G*A list of polynomials which generates a subalgebra.@return A list of polynomials which form a finite SAGBI-basis of the subalgebra generated by

`G`.

#### Example

Use QQ[x,y,z], DegRevLex; S := SB.SAGBI([x^2 -z^2, x*y +z^2, y^2 -2*z^2]); indent(S); -- [ -- y^2 -2*z^2, -- x*y +z^2, -- x^2 -z^2, -- x^2*z^2 +x*y*z^2 +(1/2)*y^2*z^2 +(-1/2)*z^4 -- ]

### See also

Package sagbi/SB.GetTruncSAGBI