# Difference between revisions of "ApCoCoA-1:SB.IsSagbiOf"

From ApCoCoAWiki

(New page: <command> <title>SB.IsSagbiOf</title> <short_description>Checks if a set of polynomials is a SAGBI-basis of a given subalgebra.</short_description> <syntax> SB.IsSagbiOf(Gens:LIST o...) |
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− | This function if the given list of polynomials <tt>Basis</tt> is a SAGBI- | + | This function checks if the given list of polynomials <tt>Basis</tt> forms a SAGBI-basis of the subalgebra <tt>S</tt> generated by the polynomials of the list <tt>Gens</tt>, i.e. it is checked if <tt>Basis</tt> is a SAGBI-Basis and if <tt>Basis</tt> also generates the subalgebra <tt>S</tt>. Then the corresponding boolean value is returned. |

<itemize> | <itemize> |

## Revision as of 10:14, 21 May 2010

## SB.IsSagbiOf

Checks if a set of polynomials is a SAGBI-basis of a given subalgebra.

### Syntax

SB.IsSagbiOf(Gens:LIST of POLY, Basis:LIST of POLY):BOOL

### Description

This function checks if the given list of polynomials `Basis` forms a SAGBI-basis of the subalgebra `S` generated by the polynomials of the list `Gens`, i.e. it is checked if `Basis` is a SAGBI-Basis and if `Basis` also generates the subalgebra `S`. Then the corresponding boolean value is returned.

@param

*Gens*A list of polynomials, which are the generators of the current subalgebra.@param

*Basis*A list of polynomials, possibly a SAGBI-basis of the current subalgebra.@return The corresponding boolean value.

#### Example

Set Indentation; Use R::=QQ[x,y], DegLex; G:=[x^2-y^2,x^2y,x^2y^2-y^4,x^2y^4,y^6x^2y^6-y^8]; SBasis:=SB.Sagbi(G); SBasis; SB.IsSagbiOf(G,SBasis); -- This SAGBI-basis generates the same subalgebra as the -- the polynomials of the set G [ x^2 - y^2, x^2y, x^2y^2 - y^4, x^2y^4, x^2y^12 - y^8, y^6, x^2y^6 - y^8, x^2y^16 + x^4y^8 - y^12, x^2y^10 - 3/8y^12, y^14 - y^8, y^14 - y^8] ------------------------------- TRUE ------------------------------- -- Done. -------------------------------

#### Example

Set Indentation; Use R::=QQ[x,y], DegLex; G:=[x+y,xy]; SBasis:=SB.Sagbi(G); SBasis; SB.IsSagbiOf(G,SBasis); -- This SAGBI-basis generates the same subalgebra as the -- the polynomials of the set G [ x + y, xy] ------------------------------- TRUE ------------------------------- -- Done. -------------------------------

#### Example

Set Indentation; Use R::=QQ[x,y], DegLex; G:=[x+y,xy]; Basis:=[x^3+x^2y]; -- The polynomial y^3+x^2y is not a member of K[G]. -- Therefore it is impossible that the given Basis generates -- the same subalgebra. SB.IsSagbiOf(G,Basis); FALSE ------------------------------- -- Done. -------------------------------