ApCoCoA-1:BB.GenMultMat: Difference between revisions
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{{Version|1}} | |||
<command> | <command> | ||
<title>BB.GenMultMat</title> | |||
<short_description>Computes a generic multiplication matrix.</short_description> | |||
<syntax> | <syntax> | ||
BB.GenMultMat(I:INT,OO:LIST):MAT | BB.GenMultMat(I:INT,OO:LIST):MAT | ||
</syntax> | </syntax> | ||
<description> | |||
Computes the generic multiplication matrix for < | Computes the generic multiplication matrix for the <tt>I</tt>-th indeterminate with respect to an order ideal. The second element of <tt>OO</tt> must be a non-constant polynomial. The output is a matrix of size <ref>CoCoA:Len|Len</ref>(OO) x <ref>CoCoA:Len|Len</ref>(OO) over the ring <tt>BBS=K[c_{ij}]</tt>. | ||
<itemize> | <itemize> | ||
<item>@param <em>I</em> | <item>@param <em>I</em> An integer which specifies the indeterminate for which the generic multiplication matrix will be computed.</item> | ||
<item>@param <em>OO</em> A list of terms representing an order ideal.</item> | <item>@param <em>OO</em> A list of terms representing an order ideal.</item> | ||
<item>@return The generic multiplication matrix | <item>@return The generic multiplication matrix.</item> | ||
</itemize> | </itemize> | ||
</ | <example> | ||
<key> | Use QQ[x, y, z], DegRevLex; | ||
BB.GenMultMat(1, [1, x, y, z]); | |||
------------------------------- | |||
Mat([ | |||
[0, BBS :: c[1,6], BBS :: c[1,5], BBS :: c[1,3]], | |||
[1, BBS :: c[2,6], BBS :: c[2,5], BBS :: c[2,3]], | |||
[0, BBS :: c[3,6], BBS :: c[3,5], BBS :: c[3,3]], | |||
[0, BBS :: c[4,6], BBS :: c[4,5], BBS :: c[4,3]] | |||
]) | |||
------------------------------- | |||
</example> | |||
</description> | |||
<types> | |||
<type>borderbasis</type> | |||
<type>matrix</type> | |||
</types> | |||
<key>GenMultMat</key> | |||
<key>BB.GenMultMat</key> | |||
<key>borderbasis.GenMultMat</key> | |||
<wiki-category>ApCoCoA-1:Package_borderbasis</wiki-category> | |||
</command> | </command> | ||
Latest revision as of 09:40, 7 October 2020
| This article is about a function from ApCoCoA-1. |
BB.GenMultMat
Computes a generic multiplication matrix.
Syntax
BB.GenMultMat(I:INT,OO:LIST):MAT
Description
Computes the generic multiplication matrix for the I-th indeterminate with respect to an order ideal. The second element of OO must be a non-constant polynomial. The output is a matrix of size Len(OO) x Len(OO) over the ring BBS=K[c_{ij}].
@param I An integer which specifies the indeterminate for which the generic multiplication matrix will be computed.
@param OO A list of terms representing an order ideal.
@return The generic multiplication matrix.
Example
Use QQ[x, y, z], DegRevLex; BB.GenMultMat(1, [1, x, y, z]); ------------------------------- Mat([ [0, BBS :: c[1,6], BBS :: c[1,5], BBS :: c[1,3]], [1, BBS :: c[2,6], BBS :: c[2,5], BBS :: c[2,3]], [0, BBS :: c[3,6], BBS :: c[3,5], BBS :: c[3,3]], [0, BBS :: c[4,6], BBS :: c[4,5], BBS :: c[4,3]] ]) -------------------------------
