TU-Berlin → Inst. f. Mathematik → Algebra und Zahlentheorie → KASH → Documentation → Reference Manual
 KASH3 Reference Manual
Documentation
IntroductionReference ManualIndex
search    

Function

IsNilpotent ( elt-rng x ) -> elt-alg^boo, elt-ord^rat

Optional Arguments

Resultselt-ord^rat1 <= Results <= 2

Description

True iff ring element x is nilpotent (i.e., x^q = 0 for some integer q); if true, returns the index of nilpotence of x, i.e., the smallest q such that x^q = 0.

Examples

x_o := MaximalOrder(X^3-X-1); IsNilpotent(Element(x_o,[1,0,1])); IsNilpotent(Zero(x_o));
x_F := NumberField(X^3-X-1); IsNilpotent(Element(x_F,[1,1,0])); IsNilpotent(Zero(x_F));
Built: Mon Nov 14 21:12:39 UTC 2005 on mack
The KANT Group