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

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{| cellspacing="8" cellpadding="0" style="background-color:#eeeeff; width:100%; font-size:95%; border-bottom: 2px solid blue; border-top: 2px solid blue; position:top; clear:both;"
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{{Version|2|[[ApCoCoA-1:SB.Sagbi]] and [[ApCoCoA-1:SB.ReducedSagbi]]}}
| This article is about the function in [[ApCoCoA:Downloads#ApCoCoA-2.0 Beta|ApCoCoA-2.0]]. If you are looking for the [[ApCoCoA:What is ApCoCoA|ApCoCoA-1.0]] version of it, see [[ApCoCoA:SB.Sagbi]].
 
|}
 
 
 
 
<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</syntax>
SB.SAGBI(G:LIST of POLY):LIST of POLY
 
</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.
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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>
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    <itemize>
  <item>@param <em>G</em> A list of polynomials which generates a subalgebra.</item>
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      <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[1..3]];
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Use QQ[x,y,z], DegRevLex;
S := SB.SAGBI([x[1]^2-x[3]^2,x[1]*x[2]+x[3]^2,x[2]^2-2*x[3]^2]);
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S := SB.SAGBI([x^2 -z^2, x*y +z^2, y^2 -2*z^2]);
 
indent(S);
 
indent(S);
-----------------------------------------------------------------------------
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-- [
[
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--  y^2 -2*z^2,
   x[2]^2 -2*x[3]^2,
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--   x*y +z^2,
   x[1]*x[2] +x[3]^2,
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--   x^2 -z^2,
   x[1]^2 -x[3]^2,
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--   x^2*z^2 +x*y*z^2 +(1/2)*y^2*z^2 +(-1/2)*z^4
   x[1]^2*x[3]^2 +x[1]*x[2]*x[3]^2 +(1/2)*x[2]^2*x[3]^2 +(-1/2)*x[3]^4
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-- ]</example>
]
 
</example>
 
 
   </description>
 
   </description>
<!-- <see>SB.IsSagbi</see> -->
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<!-- <see>SB.IsSagbiOf</see> -->
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  <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>
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    <see>Package sagbi/SB.GetTruncSAGBI</see>
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  </seealso>
 +
 
 
   <types>
 
   <types>
 
     <type>sagbi</type>
 
     <type>sagbi</type>
 
     <type>poly</type>
 
     <type>poly</type>
 
   </types>
 
   </types>
   <key>sagbi</key>
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   <key>sb.sagbi</key>
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   <key>SAGBI</key>
   <key>sagbi.sagbi</key>
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   <key>SB.SAGBI</key>
   <wiki-category>ApCoCoA-2.0/Package_sagbi</wiki-category>
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   <key>apcocoa/sagbi.SAGBI</key>
 +
 
 +
   <wiki-category>Package sagbi</wiki-category>
 
</command>
 
</command>

Latest revision as of 15:56, 9 February 2021

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.TruncSAGBI

Package sagbi/SB.SAGBITimeout

Package sagbi/SB.IsSAGBIOf

Package sagbi/SB.GetSAGBI

Package sagbi/SB.GetTruncSAGBI