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...) |
Andraschko (talk | contribs) (added version info) |
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| + | {{Version|1|[[Package sagbi/SB.IsSAGBIOf]]}} | ||
<command> | <command> | ||
<title>SB.IsSagbiOf</title> | <title>SB.IsSagbiOf</title> | ||
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</syntax> | </syntax> | ||
<description> | <description> | ||
| − | 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> | ||
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SB.IsSagbiOf(G,SBasis); | SB.IsSagbiOf(G,SBasis); | ||
| + | |||
| + | ------------------------------------------------------- | ||
| + | -- output: | ||
-- This SAGBI-basis generates the same subalgebra as the | -- This SAGBI-basis generates the same subalgebra as the | ||
| Line 54: | Line 58: | ||
SB.IsSagbiOf(G,SBasis); | SB.IsSagbiOf(G,SBasis); | ||
| + | |||
| + | ------------------------------------------------------- | ||
| + | -- output: | ||
-- This SAGBI-basis generates the same subalgebra as the | -- This SAGBI-basis generates the same subalgebra as the | ||
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SB.IsSagbiOf(G,Basis); | SB.IsSagbiOf(G,Basis); | ||
| + | |||
| + | ------------------------------------------------------- | ||
| + | -- output: | ||
FALSE | FALSE | ||
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</example> | </example> | ||
</description> | </description> | ||
| − | <see>SB.Sagbi</see> | + | <see>ApCoCoA-1:SB.Sagbi|SB.Sagbi</see> |
| − | <see>SB.IsSagbi</see> | + | <see>ApCoCoA-1:SB.IsSagbi|SB.IsSagbi</see> |
<types> | <types> | ||
<type>sagbi</type> | <type>sagbi</type> | ||
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<key>sb.issagbiof</key> | <key>sb.issagbiof</key> | ||
<key>sagbi.issagbiof</key> | <key>sagbi.issagbiof</key> | ||
| − | <wiki-category>Package_sagbi</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_sagbi</wiki-category> |
</command> | </command> | ||
Latest revision as of 17:45, 27 October 2020
| This article is about a function from ApCoCoA-1. If you are looking for the ApCoCoA-2 version of it, see Package sagbi/SB.IsSAGBIOf. |
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); ------------------------------------------------------- -- output: -- 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); ------------------------------------------------------- -- output: -- 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); ------------------------------------------------------- -- output: FALSE ------------------------------- -- Done. -------------------------------
