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

From ApCoCoAWiki
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{{Version|2|[[ApCoCoA-1:SB.Sagbi]] and [[ApCoCoA-1:SB.ReducedSagbi]]}}
 
{{Version|2|[[ApCoCoA-1:SB.Sagbi]] and [[ApCoCoA-1:SB.ReducedSagbi]]}}
 
 
<command>
 
<command>
 
   <title>SB.SAGBI</title>
 
   <title>SB.SAGBI</title>
 
   <short_description>Computes a finite SAGBI-basis of a subalgebra if existing.</short_description>
 
   <short_description>Computes a finite SAGBI-basis of a subalgebra if existing.</short_description>
    
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<syntax>
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   <syntax>
 
SB.SAGBI(G:LIST of POLY):LIST of POLY
 
SB.SAGBI(G:LIST of POLY):LIST of POLY
</syntax>
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  </syntax>
 
   <description>
 
   <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> is existing. Then a list of polynomials is returned which form a SAGBI-basis of <tt>S</tt>. Otherwise the computation runs until it is interrupted.
 
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> is existing. 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>
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    <itemize>
  <item>@param <em>G</em> A list of polynomials which generates a subalgebra.</item>
+
      <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>
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      <item>@return A list of polynomials which form a finite SAGBI-basis of the subalgebra generated by <tt>G</tt>.</item>
</itemize>
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    </itemize>
  
<example>
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    <example>
 
Use QQ[x,y,z], DegRevLex;
 
Use QQ[x,y,z], DegRevLex;
 
S := SB.SAGBI([x^2 -z^2,  x*y +z^2,  y^2 -2*z^2]);
 
S := SB.SAGBI([x^2 -z^2,  x*y +z^2,  y^2 -2*z^2]);
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--  x^2 -z^2,
 
--  x^2 -z^2,
 
--  x^2*z^2 +x*y*z^2 +(1/2)*y^2*z^2 +(-1/2)*z^4
 
--  x^2*z^2 +x*y*z^2 +(1/2)*y^2*z^2 +(-1/2)*z^4
-- ]
+
-- ]</example>
</example>
 
 
   </description>
 
   </description>
 +
 
   <seealso>
 
   <seealso>
 
     <see>Package sagbi/SB.TruncSAGBI</see>
 
     <see>Package sagbi/SB.TruncSAGBI</see>
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     <see>Package sagbi/SB.GetTruncSAGBI</see>
 
     <see>Package sagbi/SB.GetTruncSAGBI</see>
 
   </seealso>
 
   </seealso>
 +
 
   <types>
 
   <types>
 
     <type>sagbi</type>
 
     <type>sagbi</type>
 
     <type>poly</type>
 
     <type>poly</type>
 
   </types>
 
   </types>
 +
 
   <key>SAGBI</key>
 
   <key>SAGBI</key>
 
   <key>SB.SAGBI</key>
 
   <key>SB.SAGBI</key>
 
   <key>apcocoa/sagbi.SAGBI</key>
 
   <key>apcocoa/sagbi.SAGBI</key>
 +
 
   <wiki-category>Package sagbi</wiki-category>
 
   <wiki-category>Package sagbi</wiki-category>
 
</command>
 
</command>

Revision as of 08:49, 28 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.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 is existing. 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.TruncSAGBI

Package sagbi/SB.SAGBITimeout

Package sagbi/SB.IsSAGBIOf

Package sagbi/SB.GetSAGBI

Package sagbi/SB.GetTruncSAGBI