Difference between revisions of "ApCoCoA-1:NC.Mul"
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(New page: <command> <title>NC.Multiply</title> <short_description> Multiplication of two polynomials in a non-commutative polynomial ring. </short_description> <syntax> NC.Mul(F1:LIST, F2:LIST):LIST...) |
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<command> | <command> | ||
| − | <title>NC. | + | <title>NC.Mul</title> |
<short_description> | <short_description> | ||
Multiplication of two polynomials in a non-commutative polynomial ring. | Multiplication of two polynomials in a non-commutative polynomial ring. | ||
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<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | ||
<par/> | <par/> | ||
| − | Please set ring | + | Please set non-commutative polynomial ring (via the command <ref>ApCoCoA-1:Use|Use</ref>) and word ordering (via the function <ref>ApCoCoA-1:NC.SetOrdering|NC.SetOrdering</ref>) before calling this function. The default word ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant commands and functions. |
<itemize> | <itemize> | ||
| − | <item>@param <em>F1, F2:</em> two polynomials | + | <item>@param <em>F1, F2:</em> two non-commutative polynomials, which are left and right operands of multiplication respectively. Each polynomial is represented as a LIST of LISTs, and each element in every inner LIST involves only one indeterminate or none (a constant). For example, the polynomial <tt>f=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5</tt> is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> |
<item>@return: a LIST which represents the polynomial equal to <tt>F1*F2</tt>.</item> | <item>@return: a LIST which represents the polynomial equal to <tt>F1*F2</tt>.</item> | ||
</itemize> | </itemize> | ||
<example> | <example> | ||
| − | + | USE ZZ/(31)[x[1..2],y[1..2]]; | |
| − | + | F1:= [[2x[1],x[2]], [13y[2]], [5]]; -- 2x[1]x[2]+13y[2]+5 | |
| − | NC. | + | F2:= [[2y[1],y[2]], [19y[2]], [2]]; -- 2y[1]y[2]+19y[2]+2 |
| − | + | NC.Mul(F1,F2); | |
| − | + | ||
| − | + | [[4x[1], x[2], y[1], y[2]], [7x[1], x[2], y[2]], [4x[1], x[2]], [-5y[2], y[1], y[2]], [10y[1], y[2]], [-y[2]^2], [-3y[2]], [10]] | |
------------------------------- | ------------------------------- | ||
| − | F1 | + | NC.Mul(F2,F1); |
| − | + | ||
| − | + | [[4y[1], y[2], x[1], x[2]], [7y[2], x[1], x[2]], [4x[1], x[2]], [-5y[1], y[2]^2], [10y[1], y[2]], [-y[2]^2], [-3y[2]], [10]] | |
| − | [[2 | ||
------------------------------- | ------------------------------- | ||
| − | NC. | + | NC.Mul([],F1); |
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[ ] | [ ] | ||
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------------------------------- | ------------------------------- | ||
</example> | </example> | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>Introduction to CoCoAServer</see> | + | <see>ApCoCoA-1:Use|Use</see> |
| + | <see>ApCoCoA-1:NC.SetOrdering|NC.SetOrdering</see> | ||
| + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> | ||
</seealso> | </seealso> | ||
<types> | <types> | ||
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<key>NC.Mul</key> | <key>NC.Mul</key> | ||
<key>Mul</key> | <key>Mul</key> | ||
| − | <wiki-category>Package_ncpoly</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_ncpoly</wiki-category> |
</command> | </command> | ||
Latest revision as of 13:35, 29 October 2020
| This article is about a function from ApCoCoA-1. |
NC.Mul
Multiplication of two polynomials in a non-commutative polynomial ring.
Syntax
NC.Mul(F1:LIST, F2:LIST):LIST
Description
Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
Please set non-commutative polynomial ring (via the command Use) and word ordering (via the function NC.SetOrdering) before calling this function. The default word ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant commands and functions.
@param F1, F2: two non-commutative polynomials, which are left and right operands of multiplication respectively. Each polynomial is represented as a LIST of LISTs, and each element in every inner LIST involves only one indeterminate or none (a constant). For example, the polynomial f=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5 is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. The zero polynomial 0 is represented as the empty LIST [].
@return: a LIST which represents the polynomial equal to F1*F2.
Example
USE ZZ/(31)[x[1..2],y[1..2]]; F1:= [[2x[1],x[2]], [13y[2]], [5]]; -- 2x[1]x[2]+13y[2]+5 F2:= [[2y[1],y[2]], [19y[2]], [2]]; -- 2y[1]y[2]+19y[2]+2 NC.Mul(F1,F2); [[4x[1], x[2], y[1], y[2]], [7x[1], x[2], y[2]], [4x[1], x[2]], [-5y[2], y[1], y[2]], [10y[1], y[2]], [-y[2]^2], [-3y[2]], [10]] ------------------------------- NC.Mul(F2,F1); [[4y[1], y[2], x[1], x[2]], [7y[2], x[1], x[2]], [4x[1], x[2]], [-5y[1], y[2]^2], [10y[1], y[2]], [-y[2]^2], [-3y[2]], [10]] ------------------------------- NC.Mul([],F1); [ ] -------------------------------
See also
