Difference between revisions of "Package sagbi/SB.IsSAGBIOf"

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   <short_description>This function checks whether a given list of polynomials is a SAGBI basis of a specific subalgebra.</short_description>
 
   <short_description>This function checks whether a given list of polynomials is a SAGBI basis of a specific subalgebra.</short_description>
 
    
 
    
   <syntax>SB.IsSAGBIOf(G: LIST of POLY, S: TAGGED(<quotes>$apcocoa/sagbi.Subalgebra</quotes>)): BOOL</syntax>
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   <syntax>SB.IsSAGBIOf(G: LIST of POLY, S: TAGGED("$apcocoa/sagbi.Subalgebra")): BOOL</syntax>
 
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Latest revision as of 13:22, 29 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.IsSagbiOf.

SB.IsSAGBIOf

This function checks whether a given list of polynomials is a SAGBI basis of a specific subalgebra.

Syntax

SB.IsSAGBIOf(G: LIST of POLY, S: TAGGED("$apcocoa/sagbi.Subalgebra")): BOOL

Description

  • @param G A list of polynomials all of the same ring R

  • @param S A subalgebra of R

  • @return true if G is a SAGBI basis of S and false if not.

Example

Use R ::= QQ[x,y];
fs := [x^2*y,  x^2 -y^2,  x^2*y^2 -y^4,  x^2*y^4];
S := SB.Subalgebra(R,fs);
G := [x^2 -y^2,  x^2*y,  x^2*y^2 -y^4,  y^6,  x^2*y^4];
SB.IsSAGBIOf(fs,S); -- false
SB.IsSAGBIOf(G,S); -- true

See also

Package sagbi/SB.Subalgebra

Package sagbi/SB.SAGBI