Package sagbi/SB.IsInSubalgebra: Difference between revisions
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{{Version|2|[[ApCoCoA-1:SB.IsInSubalgebra]]}} | {{Version|2|[[ApCoCoA-1:SB.IsInSubalgebra]]}} | ||
<command> | <command> | ||
<title>SB.IsInSubalgebra</title> | <title>SB.IsInSubalgebra</title> | ||
<short_description>Tests whether a polynomial is in a subalgebra.</short_description> | <short_description>Tests whether a polynomial is in a subalgebra.</short_description> | ||
<syntax> | <syntax> | ||
SB.IsInSubalgebra(f:POLY, G:LIST of POLY):BOOL | SB.IsInSubalgebra(f:POLY, G:LIST of POLY):BOOL | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
This function takes a polynomials <tt>f</tt> and a list of polynomials <tt>G</tt> and checks whether <tt>F</tt> is in the algebra generated by the polynomials in <tt>G</tt>. | This function takes a polynomials <tt>f</tt> and a list of polynomials <tt>G</tt> and checks whether <tt>F</tt> is in the algebra generated by the polynomials in <tt>G</tt>. | ||
<itemize> | <itemize> | ||
<item>@param <tt>f</tt> A polynomial.</item> | |||
<item>@param <tt>G</tt> A list of 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]; | ||
SB.IsInSubalgebra(x[1]*x[2]^4-x[2]^5, G); | SB.IsInSubalgebra(x[1]*x[2]^4-x[2]^5, G); | ||
-- | -- 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]; | ||
SB.IsInSubalgebra(y[3]^4, G); | SB.IsInSubalgebra(y[3]^4, G); | ||
-- | -- false | ||
false | </example> | ||
</example> | |||
</description> | </description> | ||
<seealso> | |||
<see>SB.IsInSubalgebra_SAGBI</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> | |||
<key> | <key>IsInSubalgebra</key> | ||
<key>sagbi. | <key>SB.IsInSubalgebra</key> | ||
<key>apcocoa/sagbi.IsInSubalgebra</key> | |||
<wiki-category>Package_sagbi</wiki-category> | <wiki-category>Package_sagbi</wiki-category> | ||
</command> | </command> | ||
Revision as of 12:20, 26 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.IsInSubalgebra
Tests whether a polynomial is in a subalgebra.
Syntax
SB.IsInSubalgebra(f:POLY, G:LIST of POLY):BOOL
Description
This function takes a polynomials f and a list of polynomials G and checks whether F is in the algebra generated by the polynomials in G.
@param f A polynomial.
@param G A list of 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(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(y[3]^4, G);
-- false
See also
