Difference between revisions of "ApCoCoA-1:NC.Deg"

From ApCoCoAWiki
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<command>
 
<command>
<title>NCo.Deg</title>
+
<title>NC.Deg</title>
 
<short_description>
 
<short_description>
(Standard) degree of a polynomial in a free monoid ring.
+
The (standard) degree of a polynomial in non-commutative polynomial rings.
 
</short_description>
 
</short_description>
 
<syntax>
 
<syntax>
NCo.Deg(F:LIST):INT
+
NC.Deg(F:LIST):INT
 
</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>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 calling the function. The default coefficient field is <tt>Q</tt>. The default ordering is length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions.
+
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>NC.SetFp</ref>, <ref>NC.SetX</ref> and <ref>NC.SetOrdering</ref>, respectively, before calling the function. The default coefficient field is <tt>Q</tt>. The default ordering is length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions.
 
<itemize>
 
<itemize>
 
<item>@param <em>F</em>: a polynomial in <tt>K&lt;X&gt;</tt>. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item>
 
<item>@param <em>F</em>: a polynomial in <tt>K&lt;X&gt;</tt>. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item>
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</itemize>
 
</itemize>
 
<example>
 
<example>
NCo.SetX(<quotes>abc</quotes>);
+
NC.SetX(<quotes>abc</quotes>);
 
F:=[[1,<quotes>ab</quotes>],[2,<quotes>aa</quotes>],[3,<quotes>bb</quotes>],[4,<quotes>bab</quotes>]];
 
F:=[[1,<quotes>ab</quotes>],[2,<quotes>aa</quotes>],[3,<quotes>bb</quotes>],[4,<quotes>bab</quotes>]];
NCo.Deg(F);
+
NC.Deg(F);
 
3
 
3
 
-------------------------------
 
-------------------------------
NCo.Deg([]); -- 0 polynomial
+
NC.Deg([]); -- 0 polynomial
 
0
 
0
 
-------------------------------
 
-------------------------------
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</description>
 
</description>
 
<seealso>
 
<seealso>
<see>NCo.SetFp</see>
+
<see>NC.SetOrdering</see>
<see>NCo.SetOrdering</see>
 
<see>NCo.SetX</see>
 
 
<see>Introduction to CoCoAServer</see>
 
<see>Introduction to CoCoAServer</see>
 
</seealso>
 
</seealso>
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<type>non_commutative</type>
 
<type>non_commutative</type>
 
</types>
 
</types>
<key>gbmr.Deg</key>
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<key>ncpoly.Deg</key>
<key>NCo.Deg</key>
+
<key>NC.Deg</key>
 
<key>Deg</key>
 
<key>Deg</key>
<wiki-category>Package_gbmr</wiki-category>
+
<wiki-category>Package_ncpoly</wiki-category>
 
</command>
 
</command>

Revision as of 14:38, 25 April 2013

NC.Deg

The (standard) degree of a polynomial in non-commutative polynomial rings.

Syntax

NC.Deg(F: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 coefficient field K, alphabet (or set of indeterminates) X and ordering via the functions NC.SetFp, NC.SetX and NC.SetOrdering, respectively, before calling the function. The default coefficient field is Q. The default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

  • @param F: a polynomial in K<X>. Each polynomial is represented as a LIST of monomials, which are pairs 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: an INT which represents the (standard) degree of F. If F=0, the function returns 0.

Example

NC.SetX(<quotes>abc</quotes>);
F:=[[1,<quotes>ab</quotes>],[2,<quotes>aa</quotes>],[3,<quotes>bb</quotes>],[4,<quotes>bab</quotes>]];
NC.Deg(F);
3
-------------------------------
NC.Deg([]); -- 0 polynomial
0
-------------------------------

See also

NC.SetOrdering

Introduction to CoCoAServer