Difference between revisions of "ApCoCoA-1:NC.Interreduction"
| Line 12: | Line 12: | ||
<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 | + | Please set non-commutative polynomial ring (via the command <ref>Use</ref>) and word ordering (via the function <ref>NC.SetOrdering</ref>) before calling this function. The default word ordering is the length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant commands and functions. |
<itemize> | <itemize> | ||
| − | <item>@param <em>G</em>: a LIST of polynomials | + | <item>@param <em>G</em>: a LIST of non-commutative polynomials. Each polynomial is represented as a LIST of LISTs, and each element in every inner LIST involves only one indeterminate or none (a constant). For example, the polynomial <tt>f=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5</tt> is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> |
| − | <item>@return: a LIST of | + | <item>@return: a LIST, which is an interreduced set of G.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
| Line 28: | Line 28: | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see> | + | <see>Use</see> |
<see>NC.SetOrdering</see> | <see>NC.SetOrdering</see> | ||
| − | |||
<see>Introduction to CoCoAServer</see> | <see>Introduction to CoCoAServer</see> | ||
</seealso> | </seealso> | ||
<types> | <types> | ||
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
| − | <type> | + | <type>polynomial</type> |
<type>non_commutative</type> | <type>non_commutative</type> | ||
| − | |||
</types> | </types> | ||
<key>ncpoly.Interreduction</key> | <key>ncpoly.Interreduction</key> | ||
Revision as of 12:29, 26 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 non-commutative polynomial ring (via the command Use) and word ordering (via the function NC.SetOrdering) before calling this function. The default word ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant commands and functions.
@param G: a LIST of non-commutative polynomials. Each polynomial is represented as a LIST of LISTs, and each element in every inner LIST involves only one indeterminate or none (a constant). For example, the polynomial f=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5 is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. The zero polynomial 0 is represented as the empty LIST [].
@return: a LIST, which is an interreduced set of G.
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
