Difference between revisions of "Package sagbi/SB.IsInSubalgebra SAGBI"
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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]; | ||
| Line 21: | Line 21: | ||
----------------------------------------------------------------------------- | ----------------------------------------------------------------------------- | ||
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]; | ||
| Line 29: | Line 29: | ||
----------------------------------------------------------------------------- | ----------------------------------------------------------------------------- | ||
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
