Difference between revisions of "ApCoCoA-1:NC.Sub"
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(New page: <command> <title>NC.Subtract</title> <short_description> Subtraction of two polynomials in a non-commutative polynomial ring. </short_description> <syntax> NC.Sub(F1:LIST, F2:LIST):LIST </...) |
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<command> | <command> | ||
| − | <title>NC. | + | <title>NC.Sub</title> |
<short_description> | <short_description> | ||
Subtraction of two polynomials in a non-commutative polynomial ring. | Subtraction 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 subtraction 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 | |
| − | F1 := [[1, | + | F2:= [[2y[1],y[2]], [19y[2]], [2]]; -- 2y[1]y[2]+19y[2]+2 |
| − | F2 := [[ | + | NC.Sub(F1,F2); |
| − | NC. | + | |
| − | [[ | + | [[2x[1], x[2]], [-2y[1], y[2]], [-6y[2]], [3]] |
------------------------------- | ------------------------------- | ||
| − | NC. | + | NC.Sub([],F2); -- 0-F2 |
| − | + | ||
| − | + | [[-2y[1], y[2]], [12y[2]], [-2]] | |
| − | |||
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| − | [ ] | ||
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>Introduction to CoCoAServer</see></seealso> | + | <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> | ||
<types> | <types> | ||
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
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<type>non_commutative</type> | <type>non_commutative</type> | ||
</types> | </types> | ||
| − | <key>ncpoly. | + | <key>ncpoly.Sub</key> |
| − | <key>NC. | + | <key>NC.Sub</key> |
| − | <key> | + | <key>Sub</key> |
| − | <wiki-category>Package_ncpoly</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_ncpoly</wiki-category> |
</command> | </command> | ||
Latest revision as of 13:36, 29 October 2020
| This article is about a function from ApCoCoA-1. |
NC.Sub
Subtraction of two polynomials in a non-commutative polynomial ring.
Syntax
NC.Sub(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 subtraction 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.Sub(F1,F2); [[2x[1], x[2]], [-2y[1], y[2]], [-6y[2]], [3]] ------------------------------- NC.Sub([],F2); -- 0-F2 [[-2y[1], y[2]], [12y[2]], [-2]] -------------------------------
See also
