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

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   <title>SB.IsInSA</title>
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   <title>SB.IsInSA_SAGBI</title>
 
   <short_description>This function tests whether a polynomial is in a given standard-graded subalgebra.</short_description>
 
   <short_description>This function tests whether a polynomial is in a given standard-graded subalgebra.</short_description>
 
    
 
    
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   <description>
 
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This function takes a polynomial <em>f</em> and a subalgebra <em>S</em> and tests whether <em>f</em> is an element of <em>S</em> using truncated SAGBI bases.
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This function takes a polynomial <tt>f</tt> and a subalgebra <tt>S</tt> and tests whether <tt>f</tt> is an element of <tt>S</tt> using truncated SAGBI bases.
 
     <itemize>
 
     <itemize>
       <item>@param <em>f</em> A polynomial </item>
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       <item>@param <tt>f</tt> A polynomial </item>
       <item>@param <em>S</em> A standard-graded subalgebra, i.e. of type <em>TAGGED("$apcocoa/sagbi.Subalgebra")</em> and the generators of f are homogeneous polynomials with respect to the standard grading.</item>
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       <item>@param <tt>S</tt> A standard-graded subalgebra, i.e. of type <tt>TAGGED("$apcocoa/sagbi.Subalgebra")</tt> and the generators of f are homogeneous polynomials with respect to the standard grading.</item>
       <item>@return <em>true</em> if <em>f</em> is an element of <em>S</em> and <em>false</em> if not.</item>
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       <item>@return <tt>true</tt> if <tt>f</tt> is an element of <tt>S</tt> and <tt>false</tt> if not.</item>
 
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Revision as of 12:04, 26 October 2020

This article is about a function from ApCoCoA-2.

SB.IsInSA_SAGBI

This function tests whether a polynomial is in a given standard-graded subalgebra.

Syntax

SB.IsInSA(f: RINGELEM,S: TAGGED("$apcocoa/sagbi.Subalgebra")): BOOL
  

Description

This function takes a polynomial f and a subalgebra S and tests whether f is an element of S using truncated SAGBI bases.

  • @param f A polynomial

  • @param S A standard-graded subalgebra, i.e. of type TAGGED("$apcocoa/sagbi.Subalgebra") and the generators of f are homogeneous polynomials with respect to the standard grading.

  • @return true if f is an element of S and false if not.

Example

Use R ::= QQ[x,y,z];
S := SB.Subalgebra(R,[x^2,y+z]);
f := x^4 +2*x^3*y +x^2*y^2 +x^2 +2*x*y +y^2;
SB.IsInSA_SAGBI(f,S); -- true
    

See also

Package sagbi/SB.IsInSA

Package sagbi/SB.IsInSubalgebra

Package sagbi/SB.IsInSubalgebra_SAGBI