Difference between revisions of "ApCoCoA-1:BB.MultMat"
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<command> | <command> | ||
<title>BB.MultMat</title> | <title>BB.MultMat</title> | ||
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</syntax> | </syntax> | ||
<description> | <description> | ||
| − | Computes the <tt>I</tt>-th multiplication matrix associated to the given input <tt>OO</tt>-border basis <tt>BB</tt> where <tt>I</tt> is an index number in the range 1..<ref>NumIndets</ref>(). | + | Computes the <tt>I</tt>-th multiplication matrix associated to the given input <tt>OO</tt>-border basis <tt>BB</tt> of the ideal generated by the polynomials of <tt>BB</tt> where <tt>I</tt> is an index number in the range 1..<ref>ApCoCoA-1:NumIndets|NumIndets</ref>(). |
The output is a matrix. | The output is a matrix. | ||
<itemize> | <itemize> | ||
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<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>@param <em>BB</em> A list of terms representing the <tt>OO</tt>-border basis of the ideal generated by the polynomials of <tt>BB</tt>.</item> | <item>@param <em>BB</em> A list of terms representing the <tt>OO</tt>-border basis of the ideal generated by the polynomials of <tt>BB</tt>.</item> | ||
| − | <item>@return | + | <item>@return The <tt>I</tt>-th multiplication matrix.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
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[xy^2, x^3 + xy, y^4, xy^3, x^2y^2, x^3y]); | [xy^2, x^3 + xy, y^4, xy^3, x^2y^2, x^3y]); | ||
| + | ------------------------------- | ||
Mat([ | Mat([ | ||
[0, 0, 0, 0, 0, 0, 0, 0], | [0, 0, 0, 0, 0, 0, 0, 0], | ||
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<types> | <types> | ||
<type>borderbasis</type> | <type>borderbasis</type> | ||
| − | |||
<type>matrix</type> | <type>matrix</type> | ||
</types> | </types> | ||
| − | <see>BB.BBasis</see> | + | <see>ApCoCoA-1:BB.BBasis|BB.BBasis</see> |
| − | <see>BB.BBasisForOI</see> | + | <see>ApCoCoA-1:BB.BBasisForOI|BB.BBasisForOI</see> |
| − | <see>BB.GenMultMat</see> | + | <see>ApCoCoA-1:BB.GenMultMat|BB.GenMultMat</see> |
<key>MultMat</key> | <key>MultMat</key> | ||
<key>BB.MultMat</key> | <key>BB.MultMat</key> | ||
<key>borderbasis.MultMat</key> | <key>borderbasis.MultMat</key> | ||
| − | <wiki-category>Package_borderbasis</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_borderbasis</wiki-category> |
</command> | </command> | ||
Latest revision as of 09:42, 7 October 2020
| This article is about a function from ApCoCoA-1. |
BB.MultMat
Computes the i-th multiplication matrix associated to a border basis.
Syntax
BB.MultMat(I:INT, OO:LIST, BB:LIST):MAT
Description
Computes the I-th multiplication matrix associated to the given input OO-border basis BB of the ideal generated by the polynomials of BB where I is an index number in the range 1..NumIndets().
The output is a matrix.
@param I Index of indeterminate.
@param OO A list of terms representing an order ideal.
@param BB A list of terms representing the OO-border basis of the ideal generated by the polynomials of BB.
@return The I-th multiplication matrix.
Example
Use QQ[x,y];
BB.MultMat(1,
[1, y, y^2, y^3, x, xy, x^2, x^2y],
[xy^2, x^3 + xy, y^4, xy^3, x^2y^2, x^3y]);
-------------------------------
Mat([
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[1, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, -1, 0],
[0, 0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0]
])
-------------------------------
