Difference between revisions of "ApCoCoA-1:NC.MB"
(New page: <command> <title>NC.MB</title> <short_description> Macauley basis of <tt>K</tt>-algebra with respect to Ordering. </short_description> <syntax> NC.MB(Gb:LIST):LIST NC.MB(Gb:LIST, DegreeBou...) |
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<title>NC.MB</title> | <title>NC.MB</title> | ||
<short_description> | <short_description> | ||
| − | + | Macaulay basis of <tt>K</tt>-algebra with respect to Ordering. | |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
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<itemize> | <itemize> | ||
<item>@param <em>Gb:</em> a LIST of non-zero polynomials in <tt>K<X></tt> which is a Groebner basis of (two-sided) ideal generated by Gb. Each polynomial is represented as a LIST of LISTs, which are pairs of form [C, W] where C is a coefficient and W is a word (or term). Each term is represented as a STRING. For example, <tt>xy^2x</tt> is represented as <quotes>xyyx</quotes>, unit is represented as an empty string <quotes></quotes>. Then, polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. <tt>0</tt> polynomial is represented as an empty LIST [].</item> | <item>@param <em>Gb:</em> a LIST of non-zero polynomials in <tt>K<X></tt> which is a Groebner basis of (two-sided) ideal generated by Gb. Each polynomial is represented as a LIST of LISTs, which are pairs of form [C, W] where C is a coefficient and W is a word (or term). Each term is represented as a STRING. For example, <tt>xy^2x</tt> is represented as <quotes>xyyx</quotes>, unit is represented as an empty string <quotes></quotes>. Then, polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. <tt>0</tt> polynomial is represented as an empty LIST [].</item> | ||
| − | <item>@param <em>DegreeBound:</em> (optional) a positive integer which is a degree bound of Hilbert | + | <item>@param <em>DegreeBound:</em> (optional) a positive integer which is a degree bound of Hilbert function.</item> |
| − | <item>@return: a LIST of terms which form the | + | <item>@return: a LIST of terms which form the Macaulay basis of <tt>K<X>/(Gb)</tt> with respect to Ordering.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
Revision as of 14:59, 3 May 2011
NC.MB
Macaulay basis of K-algebra with respect to Ordering.
Syntax
NC.MB(Gb:LIST):LIST NC.MB(Gb:LIST, DegreeBound:INT):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 indeterminates) X and ordering through the functions NC.SetFp(Prime), NC.SetX(X) and NC.SetOrdering(Ordering), respectively, before calling the function. Default coefficient field is Q. Default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param Gb: a LIST of non-zero polynomials in K<X> which is a Groebner basis of (two-sided) ideal generated by Gb. Each polynomial is represented as a LIST of LISTs, which are pairs of form [C, W] where C is a coefficient and W is a word (or term). Each term is represented as a STRING. For example, xy^2x is represented as "xyyx", unit is represented as an empty string "". Then, polynomial F=xy-y+1 is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. 0 polynomial is represented as an empty LIST [].
@param DegreeBound: (optional) a positive integer which is a degree bound of Hilbert function.
@return: a LIST of terms which form the Macaulay basis of K<X>/(Gb) with respect to Ordering.
Example
NC.SetX(<quotes>xyzt</quotes>); NC.SetOrdering(<quotes>LLEX</quotes>); Gb:= [[[1, <quotes>yt</quotes>], [-1, <quotes>ty</quotes>]], [[1, <quotes>xt</quotes>], [-1, <quotes>tx</quotes>]], [[1, <quotes>xy</quotes>], [-1, <quotes>ty</quotes>]], [[1, <quotes>xx</quotes>], [-1, <quotes>yx</quotes>]], [[1, <quotes>tyy</quotes>], [-1, <quotes>tty</quotes>]], [[1, <quotes>yyx</quotes>], [-1, <quotes>tyx</quotes>]]]; NC.MB(Gb,3); [[<quotes></quotes>], [<quotes>t</quotes>, <quotes>z</quotes>, <quotes>y</quotes>, <quotes>x</quotes>], [<quotes>tt</quotes>, <quotes>tz</quotes>, <quotes>ty</quotes>, <quotes>tx</quotes>, <quotes>zt</quotes>, <quotes>zz</quotes>, <quotes>zy</quotes>, <quotes>zx</quotes>, <quotes>yz</quotes>, <quotes>yy</quotes>, <quotes>yx</quotes>, <quotes>xz</quotes>], [<quotes>ttt</quotes>, <quotes>ttz</quotes>, <quotes>tty</quotes>, <quotes>ttx</quotes>, <quotes>tzt</quotes>, <quotes>tzz</quotes>, <quotes>tzy</quotes>, <quotes>tzx</quotes>, <quotes>tyz</quotes>, <quotes>tyx</quotes>, <quotes>txz</quotes>, <quotes>ztt</quotes>, <quotes>ztz</quotes>, <quotes>zty</quotes>, <quotes>ztx</quotes>, <quotes>zzt</quotes>, <quotes>zzz</quotes>, <quotes>zzy</quotes>, <quotes>zzx</quotes>, <quotes>zyz</quotes>, <quotes>zyy</quotes>, <quotes>zyx</quotes>, <quotes>zxz</quotes>, <quotes>yzt</quotes>, <quotes>yzz</quotes>, <quotes>yzy</quotes>, <quotes>yzx</quotes>, <quotes>yyz</quotes>, <quotes>yyy</quotes>, <quotes>yxz</quotes>, <quotes>xzt</quotes>, <quotes>xzz</quotes>, <quotes>xzy</quotes>, <quotes>xzx</quotes>]] -------------------------------
See also
