Difference between revisions of "ApCoCoA-1:NCo.BNR"
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(New page: <command> <title>NCo.BNR</title> <short_description> The normal remainder of a polynomial with respect to a LIST of polynomials in a free monoid ring over the binary field F_{2}={0,1}. </s...) |
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<title>NCo.BNR</title> | <title>NCo.BNR</title> | ||
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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 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 the 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 the length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions. |
<itemize> | <itemize> | ||
| − | <item>@param <em>F:</em> a polynomial 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>F:</em> a polynomial 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>@param <em>G:</em> a LIST of polynomials in the free monoid ring <tt>F_{2}<X></tt>.</item> | <item>@param <em>G:</em> a LIST of polynomials in the free monoid ring <tt>F_{2}<X></tt>.</item> | ||
<item>@return: a LIST which represents the normal remainder of F with respect to G.</item> | <item>@return: a LIST which represents the normal remainder of F with respect to G.</item> | ||
</itemize> | </itemize> | ||
<example> | <example> | ||
| − | NCo.SetX( | + | NCo.SetX("xyXY"); |
| − | NCo.SetOrdering( | + | NCo.SetOrdering("LLEX"); |
| − | F1:=[ | + | F1:=["xX",""]; |
| − | F2:=[ | + | F2:=["Xx",""]; |
| − | F3:=[ | + | F3:=["yY",""]; |
| − | F4:=[ | + | F4:=["Yy",""]; |
G:=[F1,F2,F3,F4]; | G:=[F1,F2,F3,F4]; | ||
| − | F:=[ | + | F:=["xyYxxXYY"]; |
NCo.BNR(F,G); | NCo.BNR(F,G); | ||
| − | [ | + | ["xxYY"] |
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>NCo.SetOrdering</see> | + | <see>ApCoCoA-1:NCo.SetOrdering|NCo.SetOrdering</see> |
| − | <see>NCo.SetX</see> | + | <see>ApCoCoA-1:NCo.SetX|NCo.SetX</see> |
| − | <see>Introduction to CoCoAServer</see> | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> |
</seealso> | </seealso> | ||
<types> | <types> | ||
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<key>NCo.BNR</key> | <key>NCo.BNR</key> | ||
<key>BNR</key> | <key>BNR</key> | ||
| − | <wiki-category>Package_gbmr</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_gbmr</wiki-category> |
</command> | </command> | ||
Latest revision as of 13:38, 29 October 2020
| This article is about a function from ApCoCoA-1. |
NCo.BNR
The normal remainder of a polynomial with respect to a LIST of polynomials in a free monoid ring over the binary field F_{2}={0,1}.
Syntax
NCo.BNR(F:LIST, G:LIST):INT
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 the length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param F: a polynomial 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 [].
@param G: a LIST of polynomials in the free monoid ring F_{2}<X>.
@return: a LIST which represents the normal remainder of F with respect to G.
Example
NCo.SetX("xyXY");
NCo.SetOrdering("LLEX");
F1:=["xX",""];
F2:=["Xx",""];
F3:=["yY",""];
F4:=["Yy",""];
G:=[F1,F2,F3,F4];
F:=["xyYxxXYY"];
NCo.BNR(F,G);
["xxYY"]
-------------------------------
See also
