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{{Version|2|[[ApCoCoA-1:SB.Sagbi]] and [[ApCoCoA-1:SB.ReducedSagbi]]}} | |||
<command> | |||
<title>SB.SAGBI</title> | |||
<short_description>Computes a finite SAGBI-basis of a subalgebra if existing.</short_description> | |||
<syntax>SB.SAGBI(G:LIST of POLY):LIST of POLY</syntax> | |||
<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> exists. Then a list of polynomials is returned which form a SAGBI-basis of <tt>S</tt>. Otherwise the computation runs until it is interrupted. | |||
<itemize> | |||
<item>@param <em>G</em> A list of polynomials which generates a subalgebra.</item> | |||
<item>@return A list of polynomials which form a finite SAGBI-basis of the subalgebra generated by <tt>G</tt>.</item> | |||
</itemize> | |||
<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 | |||
-- ]</example> | |||
</description> | |||
<seealso> | |||
<see>Package sagbi/SB.TruncSAGBI</see> | |||
<see>Package sagbi/SB.SAGBITimeout</see> | |||
<see>Package sagbi/SB.IsSAGBIOf</see> | |||
<see>Package sagbi/SB.GetSAGBI</see> | |||
<see>Package sagbi/SB.GetTruncSAGBI</see> | |||
</seealso> | |||
<types> | |||
<type>sagbi</type> | |||
<type>poly</type> | |||
</types> | |||
<key>SAGBI</key> | |||
<key>SB.SAGBI</key> | |||
<key>apcocoa/sagbi.SAGBI</key> | |||
<wiki-category>Package sagbi</wiki-category> | |||
</command> | |||
Revision as of 18:30, 17 November 2022
| 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 exists. 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
