Difference between revisions of "ApCoCoA-1:NCo.BInterreduction"
(New page: <command> <title>NCo.BInterreduction</title> <short_description> Interreduce a LIST of polynomials in a free monoid ring over the binary field. <par/> Note that, given a word ordering, a ...) |
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Interreduce a LIST of polynomials in a free monoid ring over the binary field. | Interreduce a LIST of polynomials in a free monoid ring over the binary field. | ||
<par/> | <par/> | ||
| − | Note that, given a word ordering, a set <tt>G</tt> of non-zero polynomials is called <em>interreduced</em> if no element of <tt>Supp(g)</tt> is contained in the leading word ideal <tt> | + | Note that, given a word ordering, a set <tt>G</tt> of non-zero polynomials is called <em>interreduced</em> if no element of <tt>Supp(g)</tt> is contained in the leading word ideal <tt>BLW(G\{g})</tt> for all <tt>g</tt> in <tt>G</tt>. |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
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</description> | </description> | ||
<seealso> | <seealso> | ||
| + | <see>NCo.BLW</see> | ||
<see>NCo.SetOrdering</see> | <see>NCo.SetOrdering</see> | ||
<see>NCo.SetX</see> | <see>NCo.SetX</see> | ||
Revision as of 18:27, 30 April 2013
NCo.BInterreduction
Interreduce a LIST of polynomials in a free monoid ring over the binary field.
Note that, given a word ordering, a set G of non-zero polynomials is called interreduced if no element of Supp(g) is contained in the leading word ideal BLW(G\{g}) for all g in G.
Syntax
NCo.BInterreduction(G: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 ring environment alphabet (or set of indeterminates) X and word ordering via the functions NCo.SetX and NCo.SetOrdering, respectively, before calling this function. The default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param G: a LIST of polynomials in the free monoid ring F_{2}<X>. Each polynomial is represented as a LIST of words (or terms) in <X>. Each word is represented as a STRING. For example, xy^2x is represented as "xyyx", and the identity is represented as the empty string "". Thus, the polynomial f=xy-y+1 is represented as F:=["xy", "y", ""]. The zero polynomial 0 is represented as the empty LIST [].
@return: a LIST of interreduced polynomials.
Example
NCo.SetX(<quotes>abc</quotes>); NCo.SetOrdering(<quotes>ELIM</quotes>); Polynomials:=[[<quotes>ba</quotes>,<quotes>c</quotes>],[<quotes>b</quotes>,<quotes></quotes>], [<quotes>c</quotes>]]; NCo.BInterreduction(Polynomials); [[<quotes>a</quotes>], [<quotes>b</quotes>, <quotes></quotes>], [<quotes>c</quotes>]] -------------------------------
See also
