Package sagbi/SB.IsInSubalgebra SAGBI: Difference between revisions
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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>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> | |||
</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> | </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> | ||
<key>IsInSubalgebra_SAGBI</key> | |||
<key>SB.IsInSubalgebra_SAGBI</key> | |||
<key> | <key>apcocoa/sagbi.IsInSubalgebra_SAGBI</key> | ||
<key> | |||
<key>sagbi. | |||
<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
