Difference between revisions of "ApCoCoA-1:NC.FindPolys"
From ApCoCoAWiki
(New page: <command> <title>NC.FindPolys</title> <short_description> Find polynomials with specified indeterminates from a LIST of polynomials. </short_description> <syntax> NC.FindPolys(Alphabet:ST...) |
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</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
| − | NC.FindPolys( | + | NC.FindPolys(Polys:LIST, Inds:LIST):LIST |
</syntax> | </syntax> | ||
<description> | <description> | ||
| + | Please set non-commutative polynomial ring (via the command <ref>Use</ref>) before calling this function. For more information, please check the relevant commands and functions. | ||
<itemize> | <itemize> | ||
| − | <item>@param <em> | + | <item>@param <em>Polys</em>: a LIST of non-commutative polynomials. 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>@ | + | <item>@param <em>Inds</em>: a LIST of specified indeterminates.</item> |
| + | <item>@return: a LIST of non-commutative polynomials, which are in Inds.</item> | ||
</itemize> | </itemize> | ||
<example> | <example> | ||
| Line 50: | Line 52: | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see> | + | <see>Use</see> |
</seealso> | </seealso> | ||
<types> | <types> | ||
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
| + | <type>polynomial</type> | ||
<type>non_commutative</type> | <type>non_commutative</type> | ||
| − | |||
</types> | </types> | ||
<key>ncpoly.FindPolys</key> | <key>ncpoly.FindPolys</key> | ||
Revision as of 12:30, 29 April 2013
NC.FindPolys
Find polynomials with specified indeterminates from a LIST of polynomials.
Syntax
NC.FindPolys(Polys:LIST, Inds:LIST):LIST
Description
Please set non-commutative polynomial ring (via the command Use) before calling this function. For more information, please check the relevant commands and functions.
@param Polys: a LIST of non-commutative polynomials. 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 [].
@param Inds: a LIST of specified indeterminates.
@return: a LIST of non-commutative polynomials, which are in Inds.
Example
Polynomials:=[[[1,<quotes>a</quotes>], [1,<quotes>b</quotes>], [1,<quotes>c</quotes>]], [[1,<quotes>b</quotes>]]]; NC.FindPolynomials(<quotes>abc</quotes>, Polynomials); [[[1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes>c</quotes>]], [[1, <quotes>b</quotes>]]] ------------------------------- NC.FindPolynomials(<quotes>a</quotes>, Polynomials); [ ] ------------------------------- NC.FindPolynomials(<quotes>b</quotes>, Polynomials); [[[1, <quotes>b</quotes>]]] ------------------------------- NC.FindPolynomials(<quotes>ab</quotes>, Polynomials); [[[1, <quotes>b</quotes>]]] ------------------------------- NC.SetX(<quotes>txyz</quotes>); NC.SetOrdering(<quotes>ELIM</quotes>); -- ELIM will eliminate t, x, y, z one after another F1 := [[1,<quotes>xx</quotes>], [-1,<quotes>yx</quotes>]]; F2 := [[1,<quotes>xy</quotes>], [-1,<quotes>ty</quotes>]]; F3 := [[1,<quotes>xt</quotes>], [-1, <quotes>tx</quotes>]]; F4 := [[1,<quotes>yt</quotes>], [-1, <quotes>ty</quotes>]]; G := [F1, F2,F3,F4]; Gb := NC.GB(G); -- compute Groebner basis of <G> w.r.t. ELIM Gb; NC.FindPolynomials(<quotes>xyz</quotes>,Gb); -- compute Groebner basis of the intersection of <G> and K<x,y,z> w.r.t. ELIM [[[1, <quotes>xx</quotes>], [2, <quotes>yx</quotes>]], [[1, <quotes>ty</quotes>], [2, <quotes>xy</quotes>]], [[1, <quotes>yt</quotes>], [2, <quotes>xy</quotes>]], [[1, <quotes>tx</quotes>], [2, <quotes>xt</quotes>]], [[1, <quotes>xyx</quotes>], [2, <quotes>yyx</quotes>]], [[1, <quotes>xyy</quotes>], [2, <quotes>yxy</quotes>]], [[1, <quotes>yxt</quotes>], [2, <quotes>yyx</quotes>]]] ------------------------------- [[[1, <quotes>xx</quotes>], [2, <quotes>yx</quotes>]], [[1, <quotes>xyx</quotes>], [2, <quotes>yyx</quotes>]], [[1, <quotes>xyy</quotes>], [2, <quotes>yxy</quotes>]]] -------------------------------
See also
