Difference between revisions of "ApCoCoA-1:NCo.BLW"
From ApCoCoAWiki
(New page: <command> <title>NCo.BLW</title> <short_description> The leading word of a non-zero polynomial in a free monoid ring over the binary field F_{2}={0,1}. </short_description> <syntax> NCo.BL...) |
m (replaced <quotes> tag by real quotes) |
||
| (5 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| + | {{Version|1}} | ||
<command> | <command> | ||
<title>NCo.BLW</title> | <title>NCo.BLW</title> | ||
<short_description> | <short_description> | ||
| − | The leading word of a non-zero polynomial in a free monoid ring over the binary field F_{2}={0,1}. | + | The leading word (or term) of a non-zero polynomial in a free monoid ring over the binary field F_{2}={0,1}. |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
NCo.BLW(F:LIST):STRING | NCo.BLW(F:LIST):STRING | ||
| + | NCo.BLT(F:LIST):STRING | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
<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 non-zero 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 non-zero 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>@return: a STRING which represents the leading word of F with respect to the current word ordering. If F=0, the function returns nothing.</item> | <item>@return: a STRING which represents the leading word of F with respect to the current word ordering. If F=0, the function returns nothing.</item> | ||
</itemize> | </itemize> | ||
<example> | <example> | ||
| − | NCo.SetX( | + | NCo.SetX("xX"); |
| − | NCo.SetOrdering( | + | NCo.SetOrdering("LLEX"); |
| − | F1:=[ | + | F1:=["xX","Xx"]; |
NCo.BLW(F1); | NCo.BLW(F1); | ||
xX | xX | ||
| Line 27: | Line 29: | ||
</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> | ||
| Line 39: | Line 41: | ||
<key>NCo.BLW</key> | <key>NCo.BLW</key> | ||
<key>BLW</key> | <key>BLW</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.BLW
The leading word (or term) of a non-zero polynomial in a free monoid ring over the binary field F_{2}={0,1}.
Syntax
NCo.BLW(F:LIST):STRING NCo.BLT(F:LIST):STRING
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 non-zero 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 [].
@return: a STRING which represents the leading word of F with respect to the current word ordering. If F=0, the function returns nothing.
Example
NCo.SetX("xX");
NCo.SetOrdering("LLEX");
F1:=["xX","Xx"];
NCo.BLW(F1);
xX
-------------------------------
NCo.BLW([]);
-------------------------------
See also
