Difference between revisions of "ApCoCoA-1:NC.Add"
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(New page: <command> <title>Gbmr.MRAdd</title> <short_description> Addition of two polynomials over a monoid ring. </short_description> <syntax> Gbmr.MRAdd(X:STRING, Ordering:STRING, R:LIST, F1:LIST,...) |
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<command> | <command> | ||
| − | <title> | + | <title>NC.Add</title> |
<short_description> | <short_description> | ||
| − | Addition of two polynomials | + | Addition of two polynomials in a non-commutative polynomial ring. |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
| − | + | NC.Add(F1:LIST, F2:LIST):LIST | |
</syntax> | </syntax> | ||
<description> | <description> | ||
<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/> | ||
| + | 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 non-commutative polynomials, which are left and right operands of addition 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>@param <em>F1, F2:</em> two polynomials, | ||
| − | <item>@return: a LIST which represents | ||
</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 | |
| − | + | F2:= [[2y[1],y[2]], [19y[2]], [2]]; -- 2y[1]y[2]+19y[2]+2 | |
| − | + | NC.Add(F1,F2); | |
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| − | [ ] | ||
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| − | + | [[2x[1], x[2]], [2y[1], y[2]], [y[2]], [7]] | |
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------------------------------- | ------------------------------- | ||
| − | + | </example> | |
| − | |||
</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <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> | |
| − | |||
| − | <see> | ||
| − | |||
| − | <see>Introduction to CoCoAServer</see> | ||
</seealso> | </seealso> | ||
<types> | <types> | ||
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
| − | <type> | + | <type>polynomial</type> |
| + | <type>non_commutative</type> | ||
</types> | </types> | ||
| − | <key> | + | <key>ncpoly.Add</key> |
| − | <key> | + | <key>NC.Add</key> |
| − | <wiki-category> | + | <key>Add</key> |
| + | <wiki-category>ApCoCoA-1:Package_ncpoly</wiki-category> | ||
</command> | </command> | ||
Latest revision as of 13:33, 29 October 2020
| This article is about a function from ApCoCoA-1. |
NC.Add
Addition of two polynomials in a non-commutative polynomial ring.
Syntax
NC.Add(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 addition 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.Add(F1,F2); [[2x[1], x[2]], [2y[1], y[2]], [y[2]], [7]] -------------------------------
See also
