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

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{{Version|2}}
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{{Version|2|[[ApCoCoA-1:SB.IsInSubalgebra]]}}
 
<command>
 
<command>
 
   <title>SB.IsInSA_SAGBI</title>
 
   <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>
 
    
 
    
   <syntax>SB.IsInSA(f: RINGELEM,S: TAGGED("$apcocoa/sagbi.Subalgebra")): BOOL</syntax>
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   <syntax>SB.IsInSA(f: RINGELEM,ref S: TAGGED("$apcocoa/sagbi.Subalgebra")): BOOL</syntax>
 
   <description>
 
   <description>
 
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.
 
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.
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S := SB.Subalgebra(R,[x^2,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;
 
f := x^4 +2*x^3*y +x^2*y^2 +x^2 +2*x*y +y^2;
SB.IsInSA_SAGBI(f,S); -- true</example>
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SB.IsInSA_SAGBI(f,ref S); -- true</example>
 
   </description>
 
   </description>
  

Latest revision as of 13:22, 29 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.IsInSA_SAGBI

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

Syntax

SB.IsInSA(f: RINGELEM,ref 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,ref S); -- true

See also

Package sagbi/SB.Subalgebra

Package sagbi/SB.IsInSA

Package sagbi/SB.IsInSubalgebra

Package sagbi/SB.IsInSubalgebra_SAGBI

Package sagbi/SB.IsInToricRing