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

From ApCoCoAWiki
m (typos)
(no new line for </syntax> and </example>)
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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</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.
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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);
-----------------------------------------------------------------------------
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-- true</example>
true
 
    </example>
 
  
 
     <example>
 
     <example>
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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>
  

Revision as of 12:55, 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

Package sagbi/SB.IsInSubalgebra

Package sagbi/SB.IsInSA

Package sagbi/SB.IsInSA_SAGBI

Package sagbi/SB.IsInToricRing