Difference between revisions of "ApCoCoA-1:NC.LC"
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<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/> | ||
| + | Before calling the function, please set ring environment coefficient field <tt>K</tt>, alphabet <tt>X</tt> and ordering through the functions <ref>NC.SetFp</ref>(Prime) (or <ref>NC.UnsetFp</ref>()), <ref>NC.SetX</ref>(X) and <ref>NC.SetOrdering</ref>(Ordering) respectively. Default coefficient field is <tt>Q</tt>. 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<X></tt>. Each polynomial in <tt>K<X></tt> is represented as a LIST of LISTs, which are pairs of form [c, w] where c is in <tt>K</tt> and w is a word in <tt>X*</tt>. Unit in <tt>X*</tt> is empty word represented as an empty STRING <quotes></quotes>. <tt>0</tt> polynomial is represented as an empty LIST []. For example, polynomial <tt>F:=xy-y+1</tt> in <tt>K<x,y></tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]].</item> | <item>@param <em>F</em>: a polynomial in <tt>K<X></tt>. Each polynomial in <tt>K<X></tt> is represented as a LIST of LISTs, which are pairs of form [c, w] where c is in <tt>K</tt> and w is a word in <tt>X*</tt>. Unit in <tt>X*</tt> is empty word represented as an empty STRING <quotes></quotes>. <tt>0</tt> polynomial is represented as an empty LIST []. For example, polynomial <tt>F:=xy-y+1</tt> in <tt>K<x,y></tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]].</item> | ||
<item>@return: an element of K which is leading term of <tt>F</tt> with respect to current ordering. If <tt>F=0</tt>, then return <tt>0</tt>. </item> | <item>@return: an element of K which is leading term of <tt>F</tt> with respect to current ordering. If <tt>F=0</tt>, then return <tt>0</tt>. </item> | ||
| Line 53: | Line 54: | ||
<see>NC.UnsetRules</see> | <see>NC.UnsetRules</see> | ||
<see>NC.UnsetX</see> | <see>NC.UnsetX</see> | ||
| − | <see> | + | <see>NC.MRAdd</see> |
| − | <see> | + | <see>NC.MRBP</see> |
| − | <see> | + | <see>NC.MRIntersection</see> |
| − | <see> | + | <see>NC.MRKernelOfHomomorphism</see> |
| − | <see> | + | <see>NC.MRMinimalPolynomials</see> |
| − | <see> | + | <see>NC.MRMultiply</see> |
| − | <see> | + | <see>NC.MRSubtract</see> |
<see>Introduction to CoCoAServer</see> | <see>Introduction to CoCoAServer</see> | ||
</seealso> | </seealso> | ||
| Line 66: | Line 67: | ||
<type>groebner</type> | <type>groebner</type> | ||
</types> | </types> | ||
| + | <key>gbmr.LC</key> | ||
<key>NC.LC</key> | <key>NC.LC</key> | ||
<key>LC</key> | <key>LC</key> | ||
<wiki-category>Package_gbmr</wiki-category> | <wiki-category>Package_gbmr</wiki-category> | ||
</command> | </command> | ||
Revision as of 10:43, 22 July 2010
NC.LC
Leading coefficient of a polynomial over a free associative K-algebra.
Syntax
NC.LC(F:LIST):K
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.
Before calling the function, please set ring environment coefficient field K, alphabet X and ordering through the functions NC.SetFp(Prime) (or NC.UnsetFp()), NC.SetX(X) and NC.SetOrdering(Ordering) respectively. Default coefficient field is Q. Default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param F: a polynomial in K<X>. Each polynomial in K<X> is represented as a LIST of LISTs, which are pairs of form [c, w] where c is in K and w is a word in X*. Unit in X* is empty word represented as an empty STRING "". 0 polynomial is represented as an empty LIST []. For example, polynomial F:=xy-y+1 in K<x,y> is represented as F:=[[1,"xy"], [-1, "y"], [1,""]].
@return: an element of K which is leading term of F with respect to current ordering. If F=0, then return 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.SetOrdering(<quotes>ELIM</quotes>); NC.LC(F); 2 ------------------------------- NC.SetOrdering(<quotes>LLEX</quotes>); NC.LC(F); 4 ------------------------------- NC.LC([]); -- 0 polynomial 0 -------------------------------
See also
