ApCoCoA:SB.IsSagbiOf

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<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 of POLY, Basis:LIST of POLY):BOOL </syntax>

 <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.

<itemize>

 <item>@param Gens A list of polynomials, which are the generators of the current subalgebra.</item>
 <item>@param Basis A list of polynomials, possibly a SAGBI-basis of the current subalgebra.</item>
 <item>@return The corresponding boolean value.</item>

</itemize>

<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> <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> <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.


</example>

 </description>

<see>SB.Sagbi</see> <see>SB.IsSagbi</see>

 <types>
   <type>sagbi</type>
 </types>
 <key>issagbiof</key>
 <key>sb.issagbiof</key>
 <key>sagbi.issagbiof</key>
 <wiki-category>Package_sagbi</wiki-category>

</command>