Difference between revisions of "ApCoCoA-1:NC.Intersection"
(New page: <command> <title>NC.Intersection</title> <short_description> Computing Intersection of two finitely generated two-sided ideals over <tt>K<X></tt>. </short_description> <syntax> NC.In...) |
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Since the algorithm used in this function is based on Groebner basis computation, we refer users to <tt>NC.GB</tt> for information on optional parameters. | Since the algorithm used in this function is based on Groebner basis computation, we refer users to <tt>NC.GB</tt> for information on optional parameters. | ||
<example> | <example> | ||
| − | NC.SetX(<quotes> | + | NC.SetFp(); -- over F_{2} |
| − | + | NC.SetX(<quotes>xyz</quotes>); | |
| − | F1 := [[1,<quotes></quotes>], [1,<quotes> | + | F1 := [[1,<quotes>xy</quotes>], [1,<quotes>z</quotes>]]; |
| − | F2 := [[1,<quotes> | + | F2 := [[1,<quotes>yz</quotes>], [1, <quotes>x</quotes>]]; |
| − | + | F3 := [[1,<quotes>zx</quotes>], [1,<quotes>y</quotes>]]; | |
| − | + | Ideal_I := [F1, F2]; -- ideal generated by {xy+z, yz+x} | |
| − | + | Ideal_J := [F2, F3]; -- ideal generated by {yz+x, zx+y} | |
| − | + | NC.Intersection(Ideal_I, Ideal_J, 20, 25, 0); | |
------------------------------- | ------------------------------- | ||
Revision as of 13:55, 19 July 2010
NC.Intersection
Computing Intersection of two finitely generated two-sided ideals over K<X>.
Syntax
NC.Intersection(Ideal_I:LIST, Ideal_J:LIST[, DegreeBound:INT, LoopBound:INT, BFlag:BOOL]):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.
Before calling the function, please set ring environment coefficient field K and alphabet X through the functions NC.SetFp(Prime) (or NC.UnsetFp()) and NC.SetX(X) respectively. Default coefficient field is Q. For more information, please check the relevant functions.
@param Ideal_I: a LIST of polynomials generating a two-sided ideal 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,""]].
@param Ideal_J: another LIST of polynomials in K<X>.
@return: probably a Groebner basis of the intersection of Ideal_I and Ideal_J.
Since the algorithm used in this function is based on Groebner basis computation, we refer users to NC.GB for information on optional parameters.
Example
NC.SetFp(); -- over F_{2}
NC.SetX(<quotes>xyz</quotes>);
F1 := [[1,<quotes>xy</quotes>], [1,<quotes>z</quotes>]];
F2 := [[1,<quotes>yz</quotes>], [1, <quotes>x</quotes>]];
F3 := [[1,<quotes>zx</quotes>], [1,<quotes>y</quotes>]];
Ideal_I := [F1, F2]; -- ideal generated by {xy+z, yz+x}
Ideal_J := [F2, F3]; -- ideal generated by {yz+x, zx+y}
NC.Intersection(Ideal_I, Ideal_J, 20, 25, 0);
-------------------------------
See also
