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

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{{Version|2}}
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{{Version|2|[[ApCoCoA-1:SB.IsInSubalgebra]]}}
 
<command>
 
<command>
 
   <title>SB.IsInSubalgebra_SAGBI</title>
 
   <title>SB.IsInSubalgebra_SAGBI</title>
 
   <short_description>Tests whether a polynomial is in a standard-graded subalgebra using SAGBI bases.</short_description>
 
   <short_description>Tests whether a polynomial is in a standard-graded subalgebra using SAGBI bases.</short_description>
 
    
 
    
<syntax>
+
  <syntax>SB.IsInSubalgebra_SAGBI(f:POLY, G:LIST of POLY):BOOL</syntax>
SB.IsInSubalgebra_SAGBI(f:POLY, G:LIST of POLY):BOOL
 
</syntax>
 
 
   <description>
 
   <description>
 
This function takes a polynomials <tt>f</tt> and a list of homogeneous polynomials <tt>G</tt> and checks whether <tt>F</tt> is in the algebra generated by the polynomials in <tt>G</tt> using truncated SAGBI bases.
 
This function takes a polynomials <tt>f</tt> and a list of homogeneous polynomials <tt>G</tt> and checks whether <tt>F</tt> is in the algebra generated by the polynomials in <tt>G</tt> using truncated SAGBI bases.
<itemize>
+
    <itemize>
  <item>@param <em>f</em> A polynomial.</item>
+
      <item>@param <em>f</em> A polynomial.</item>
  <item>@param <em>G</em> A list of homogeneous polynomials which generate a subalgebra.</item>
+
      <item>@param <em>G</em> A list of homogeneous polynomials which generate a subalgebra.</item>
  <item>@return <tt>true</tt> if <tt>f</tt> is in the subalgebra generated by <tt>G</tt>, <tt>false</tt> elsewise.</item>
+
      <item>@return <tt>true</tt> if <tt>f</tt> is in the subalgebra generated by <tt>G</tt>, <tt>false</tt> elsewise.</item>
</itemize>
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    </itemize>
  
<example>
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    <example>
 
Use QQ[x[1..2]];
 
Use QQ[x[1..2]];
 
G := [x[1]-x[2], x[1]*x[2]-x[2]^2, x[1]*x[2]^2];
 
G := [x[1]-x[2], x[1]*x[2]-x[2]^2, x[1]*x[2]^2];
 
SB.IsInSubalgebra_SAGBI(x[1]*x[2]^4-x[2]^5, G);
 
SB.IsInSubalgebra_SAGBI(x[1]*x[2]^4-x[2]^5, G);
-----------------------------------------------------------------------------
+
-- true</example>
true
 
</example>
 
  
<example>
+
    <example>
 
Use QQ[y[1..3]];
 
Use QQ[y[1..3]];
 
G := [y[1]^2-y[3]^2, y[1]*y[2]+y[3]^2, y[2]^2-2*y[3]^2];
 
G := [y[1]^2-y[3]^2, y[1]*y[2]+y[3]^2, y[2]^2-2*y[3]^2];
 
SB.IsInSubalgebra_SAGBI(y[3]^4, G);
 
SB.IsInSubalgebra_SAGBI(y[3]^4, G);
-----------------------------------------------------------------------------
+
-- false</example>
false
 
</example>
 
 
   </description>
 
   </description>
 +
 +
  <seealso>
 +
    <see>Package sagbi/SB.IsInSubalgebra</see>
 +
    <see>Package sagbi/SB.IsInSA</see>
 +
    <see>Package sagbi/SB.IsInSA_SAGBI</see>
 +
    <see>Package sagbi/SB.IsInToricRing</see>
 +
  </seealso>
 +
 
   <types>
 
   <types>
 
     <type>sagbi</type>
 
     <type>sagbi</type>
 
     <type>poly</type>
 
     <type>poly</type>
 
   </types>
 
   </types>
   <key>sagbi</key>
+
 
   <key>sb.sagbi</key>
+
   <key>IsInSubalgebra_SAGBI</key>
   <key>sagbi.sagbi</key>
+
   <key>SB.IsInSubalgebra_SAGBI</key>
   <wiki-category>ApCoCoA-2.0/Package_sagbi</wiki-category>
+
   <key>apcocoa/sagbi.IsInSubalgebra_SAGBI</key>
 +
   <wiki-category>Package_sagbi</wiki-category>
 
</command>
 
</command>

Latest revision as of 17:40, 27 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.IsInSubalgebra.

SB.IsInSubalgebra_SAGBI

Tests whether a polynomial is in a standard-graded subalgebra using SAGBI bases.

Syntax

SB.IsInSubalgebra_SAGBI(f:POLY, G:LIST of POLY):BOOL

Description

This function takes a polynomials f and a list of homogeneous polynomials G and checks whether F is in the algebra generated by the polynomials in G using truncated SAGBI bases.

  • @param f A polynomial.

  • @param G A list of homogeneous polynomials which generate a subalgebra.

  • @return true if f is in the subalgebra generated by G, false elsewise.

Example

Use QQ[x[1..2]];
G := [x[1]-x[2], x[1]*x[2]-x[2]^2, x[1]*x[2]^2];
SB.IsInSubalgebra_SAGBI(x[1]*x[2]^4-x[2]^5, G);
-- true

Example

Use QQ[y[1..3]];
G := [y[1]^2-y[3]^2, y[1]*y[2]+y[3]^2, y[2]^2-2*y[3]^2];
SB.IsInSubalgebra_SAGBI(y[3]^4, G);
-- false

See also

Package sagbi/SB.IsInSubalgebra

Package sagbi/SB.IsInSA

Package sagbi/SB.IsInSA_SAGBI

Package sagbi/SB.IsInToricRing