Difference between revisions of "ApCoCoA-1:NCo.LC"
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(New page: <command> <title>NCo.LC</title> <short_description> Leading coefficient of a polynomial in a free monoid ring. </short_description> <syntax> NCo.LC(F:LIST):INT or RAT </syntax> <descriptio...) |
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<command> | <command> | ||
<title>NCo.LC</title> | <title>NCo.LC</title> | ||
<short_description> | <short_description> | ||
| − | + | The leading coefficient of a non-zero polynomial in a free monoid ring. | |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
| Line 10: | Line 11: | ||
<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>coefficient field</em> <tt>K</tt>, <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>ordering</em> via the functions <ref>NCo.SetFp</ref>, <ref>NCo.SetX</ref> and <ref>NCo.SetOrdering</ref>, respectively, before | + | Please set ring environment <em>coefficient field</em> <tt> K</tt>, <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>ordering</em> via the functions <ref>ApCoCoA-1:NCo.SetFp|NCo.SetFp</ref>, <ref>ApCoCoA-1:NCo.SetX|NCo.SetX</ref> and <ref>ApCoCoA-1:NCo.SetOrdering|NCo.SetOrdering</ref>, respectively, before using this function. The default coefficient field is <tt>Q</tt>, and 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 <tt>K<X></tt>. Each polynomial is represented as a LIST of monomials, which are | + | <item>@param <em>F</em>: a non-zero polynomial in <tt>K<X></tt>. Each polynomial is represented as a LIST of monomials, which are LISTs of the form [C, W] where W is a word in <tt><X></tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> |
| − | <item>@return: a INT or RAT which represents the leading coefficient of F | + | <item>@return: a INT or RAT, which represents the leading coefficient of F with respect to the current word ordering. If <tt>F=0</tt>, the function returns <tt>0</tt>.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
| − | NCo.SetX( | + | NCo.SetX("abc"); |
| − | F:=[[1, | + | F:=[[1,"ab"],[2,"aa"],[3,"bb"],[4,"bab"]]; |
| − | NCo.SetOrdering( | + | NCo.SetOrdering("ELIM"); |
NCo.LC(F); | NCo.LC(F); | ||
2 | 2 | ||
------------------------------- | ------------------------------- | ||
| − | NCo.SetOrdering( | + | NCo.SetOrdering("LLEX"); |
NCo.LC(F); | NCo.LC(F); | ||
4 | 4 | ||
| Line 32: | Line 33: | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>NCo.SetFp</see> | + | <see>ApCoCoA-1:NCo.SetFp|NCo.SetFp</see> |
| − | <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 45: | Line 46: | ||
<key>NCo.LC</key> | <key>NCo.LC</key> | ||
<key>LC</key> | <key>LC</key> | ||
| − | <wiki-category>Package_gbmr</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_gbmr</wiki-category> |
</command> | </command> | ||
Latest revision as of 13:40, 29 October 2020
| This article is about a function from ApCoCoA-1. |
NCo.LC
The leading coefficient of a non-zero polynomial in a free monoid ring.
Syntax
NCo.LC(F:LIST):INT or RAT
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 coefficient field K, alphabet (or set of indeterminates) X and ordering via the functions NCo.SetFp, NCo.SetX and NCo.SetOrdering, respectively, before using this function. The default coefficient field is Q, and the default ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param F: a non-zero polynomial in K<X>. Each polynomial is represented as a LIST of monomials, which are LISTs of the form [C, W] where W is a word in <X> and C is the coefficient of W. For example, the polynomial f=xy-y+1 is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. The zero polynomial 0 is represented as the empty LIST [].
@return: a INT or RAT, which represents the leading coefficient of F with respect to the current word ordering. If F=0, the function returns 0.
Example
NCo.SetX("abc");
F:=[[1,"ab"],[2,"aa"],[3,"bb"],[4,"bab"]];
NCo.SetOrdering("ELIM");
NCo.LC(F);
2
-------------------------------
NCo.SetOrdering("LLEX");
NCo.LC(F);
4
-------------------------------
NCo.LC([]); -- 0 polynomial
0
-------------------------------
See also
