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

From ApCoCoAWiki
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(various)
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   <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
 
SB.IsInSubalgebra_SAGBI(f:POLY, G:LIST of POLY):BOOL
</syntax>
+
  </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>
+
    </itemize>
  
<example>
+
    <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];
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-----------------------------------------------------------------------------
 
-----------------------------------------------------------------------------
 
true
 
true
</example>
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    </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];
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-----------------------------------------------------------------------------
 
-----------------------------------------------------------------------------
 
false
 
false
</example>
+
    </example>
 
   </description>
 
   </description>
 +
 +
  <seealso>
 +
    <see>SB.IsInSubalgebra</see>
 +
    <see>SB.IsInSA</see>
 +
    <see>SB.IsInSA_SAGBI</see>
 +
    <see>SB.IsInToricRing</see>
 +
  </seealso>
 +
 
   <types>
 
   <types>
 
     <type>sagbi</type>
 
     <type>sagbi</type>
 
     <type>poly</type>
 
     <type>poly</type>
 
   </types>
 
   </types>
  <seealso>
+
 
  <see>Package sagbi/SB.IsInSubalgebra</see>
+
   <key>IsInSubalgebra_SAGBI</key>
  </seealso>
+
   <key>SB.IsInSubalgebra_SAGBI</key>
   <key>sagbi</key>
+
   <key>apcocoa/sagbi.IsInSubalgebra_SAGBI</key>
   <key>sb.sagbi</key>
 
   <key>sagbi.sagbi</key>
 
 
   <wiki-category>Package_sagbi</wiki-category>
 
   <wiki-category>Package_sagbi</wiki-category>
 
</command>
 
</command>

Revision as of 12:22, 26 October 2020

This article is about a function from ApCoCoA-2.

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

SB.IsInSubalgebra

SB.IsInSA

SB.IsInSA_SAGBI

SB.IsInToricRing