Package sagbi/SB.IsInSubalgebra SAGBI: Difference between revisions
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{| | {{Version|2|[[ApCoCoA-1:SB.IsInSubalgebra]]}} | ||
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<command> | <command> | ||
<title>SB.IsInSubalgebra_SAGBI</title> | <title>SB.IsInSubalgebra_SAGBI</title> | ||
<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. | ||
<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]; | ||
SB.IsInSubalgebra_SAGBI(x[1]*x[2]^4-x[2]^5, G); | SB.IsInSubalgebra_SAGBI(x[1]*x[2]^4-x[2]^5, G); | ||
-- | -- true</example> | ||
true | |||
</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_SAGBI(y[3]^4, G); | SB.IsInSubalgebra_SAGBI(y[3]^4, G); | ||
-- | -- false</example> | ||
false | |||
</example> | |||
</description> | </description> | ||
<seealso> | |||
<see>Package sagbi/SB.IsInSubalgebra</see> | |||
<see>Package sagbi/SB.IsInSA</see> | |||
<see>Package sagbi/SB.IsInSA_SAGBI</see> | |||
<see>Package sagbi/SB.IsInToricRing</see> | |||
</seealso> | |||
<types> | <types> | ||
<type>sagbi</type> | <type>sagbi</type> | ||
<type>poly</type> | <type>poly</type> | ||
</types> | </types> | ||
<key> | |||
<key> | <key>IsInSubalgebra_SAGBI</key> | ||
<key>sagbi. | <key>SB.IsInSubalgebra_SAGBI</key> | ||
<wiki-category> | <key>apcocoa/sagbi.IsInSubalgebra_SAGBI</key> | ||
<wiki-category>Package_sagbi</wiki-category> | |||
</command> | </command> | ||
Latest revision as of 17:40, 27 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_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.IsInToricRing
