Difference between revisions of "ApCoCoA-1:NCo.BInterreduction"
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<command> | <command> | ||
<title>NCo.BInterreduction</title> | <title>NCo.BInterreduction</title> | ||
<short_description> | <short_description> | ||
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. | ||
| − | |||
| − | |||
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
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</syntax> | </syntax> | ||
<description> | <description> | ||
| + | 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>. | ||
| + | <par/> | ||
<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 environment <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>word ordering</em> via the functions <ref>NCo.SetX</ref> and <ref>NCo.SetOrdering</ref>, respectively, before calling this function. The default ordering is length-lexicographic ordering ( | + | Please set ring environment <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>word ordering</em> via the functions <ref>ApCoCoA-1:NCo.SetX|NCo.SetX</ref> and <ref>ApCoCoA-1:NCo.SetOrdering|NCo.SetOrdering</ref>, respectively, before calling this function. The default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions. |
<itemize> | <itemize> | ||
| − | <item>@param <em>G:</em> a LIST of polynomials in the free monoid ring <tt>F_{2}<X></tt>. Each polynomial is represented as a LIST of words (or terms) in <tt><X></tt>. Each word is represented as a STRING. For example, <tt>xy^2x</tt> is represented as | + | <item>@param <em>G:</em> a LIST of polynomials in the free monoid ring <tt>F_{2}<X></tt>. Each polynomial is represented as a LIST of words (or terms) in <tt><X></tt>. Each word is represented as a STRING. For example, <tt>xy^2x</tt> is represented as "xyyx", and the identity is represented as the empty string "". Thus, the polynomial <tt>f=xy-y+1</tt> is represented as F:=["xy", "y", ""]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> |
<item>@return: a LIST of interreduced polynomials.</item> | <item>@return: a LIST of interreduced polynomials.</item> | ||
</itemize> | </itemize> | ||
<example> | <example> | ||
| − | NCo.SetX( | + | NCo.SetX("abc"); |
| − | NCo.SetOrdering( | + | NCo.SetOrdering("ELIM"); |
| − | Polynomials:=[[ | + | Polynomials:=[["ba","c"],["b",""], ["c"]]; |
NCo.BInterreduction(Polynomials); | NCo.BInterreduction(Polynomials); | ||
| − | [[ | + | [["a"], ["b", ""], ["c"]] |
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>NCo.SetOrdering</see> | + | <see>ApCoCoA-1:NCo.BLW|NCo.BLW</see> |
| − | <see>NCo.SetX</see> | + | <see>ApCoCoA-1:NCo.SetOrdering|NCo.SetOrdering</see> |
| − | <see>Introduction to CoCoAServer</see> | + | <see>ApCoCoA-1:NCo.SetX|NCo.SetX</see> |
| + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> | ||
</seealso> | </seealso> | ||
<types> | <types> | ||
| Line 40: | Line 42: | ||
<key>NCo.BInterreduction</key> | <key>NCo.BInterreduction</key> | ||
<key>BInterreduction</key> | <key>BInterreduction</key> | ||
| − | <wiki-category>Package_gbmr</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_gbmr</wiki-category> |
</command> | </command> | ||
Latest revision as of 13:37, 29 October 2020
| This article is about a function from ApCoCoA-1. |
NCo.BInterreduction
Interreduce a LIST of polynomials in a free monoid ring over the binary field.
Syntax
NCo.BInterreduction(G:LIST):LIST
Description
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.
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("abc");
NCo.SetOrdering("ELIM");
Polynomials:=[["ba","c"],["b",""], ["c"]];
NCo.BInterreduction(Polynomials);
[["a"], ["b", ""], ["c"]]
-------------------------------
See also
