Difference between revisions of "Package sagbi/SB.IsInSubalgebra SAGBI"
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Andraschko (talk | contribs) m (Andraschko moved page User:Andraschko/SB.IsInSubalgebra SAGBI to SB.IsInSubalgebra SAGBI without leaving a redirect) |
Andraschko (talk | contribs) (added version info) |
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| − | {{Version|2}} | + | {{Version|2|[[ApCoCoA-1:SB.IsInSubalgebra]]}} |
<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
