Difference between revisions of "ApCoCoA-1:NC.Interreduction"
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<title>NC.Interreduction</title> | <title>NC.Interreduction</title> | ||
<short_description> | <short_description> | ||
| − | + | Interreduction of a LIST of polynomials in a non-commutative polynomial ring. | |
<par/> | <par/> | ||
Note that, given an admissible ordering <tt>Ordering</tt>, a set of non-zero polynomial <tt>G</tt> is called <em>interreduced</em> w.r.t. <tt>Ordering</tt> if no element of <tt>Supp(g)</tt> is contained in <tt>LT(G\{g})</tt> for all <tt>g</tt> in <tt>G</tt>. | Note that, given an admissible ordering <tt>Ordering</tt>, a set of non-zero polynomial <tt>G</tt> is called <em>interreduced</em> w.r.t. <tt>Ordering</tt> if no element of <tt>Supp(g)</tt> is contained in <tt>LT(G\{g})</tt> for all <tt>g</tt> in <tt>G</tt>. | ||
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<seealso> | <seealso> | ||
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<see>NC.SetFp</see> | <see>NC.SetFp</see> | ||
<see>NC.SetOrdering</see> | <see>NC.SetOrdering</see> | ||
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<see>NC.SetX</see> | <see>NC.SetX</see> | ||
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<see>Introduction to CoCoAServer</see> | <see>Introduction to CoCoAServer</see> | ||
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<type>ideal</type> | <type>ideal</type> | ||
</types> | </types> | ||
| − | <key> | + | <key>ncpoly.Interreduction</key> |
<key>NC.Interreduction</key> | <key>NC.Interreduction</key> | ||
<key>Interreduction</key> | <key>Interreduction</key> | ||
| − | <wiki-category> | + | <wiki-category>Package_ncpoly</wiki-category> |
</command> | </command> | ||
Revision as of 15:33, 25 April 2013
NC.Interreduction
Interreduction of a LIST of polynomials in a non-commutative polynomial ring.
Note that, given an admissible ordering Ordering, a set of non-zero polynomial G is called interreduced w.r.t. Ordering if no element of Supp(g) is contained in LT(G\{g}) for all g in G.
Syntax
NC.Interreduction(G:LIST):LIST
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 G: a LIST of polynomials 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: a LIST of interreduced polynomials.
Example
NC.SetX(<quotes>abc</quotes>); NC.SetOrdering(<quotes>ELIM</quotes>); G:=[[[1,<quotes>ba</quotes>]], [[1,<quotes>b</quotes>],[1,<quotes></quotes>]], [[1,<quotes>c</quotes>]]]; NC.Interreduction(G); [[[1, <quotes>a</quotes>]], [[1, <quotes>b</quotes>], [1, <quotes></quotes>]], [[1, <quotes>c</quotes>]]] -------------------------------
See also
