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

Function

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

Optional Arguments

Resultselt-ord^rat1 <= Results <= 2

Description

Return `TRUE' iff residue class `x' is nilpotent, i.e. if there exists an integer `q' with `x^q = 0', return `FALSE' otherwise.
If `x' is nilpotent `IsNilpotent' also returns the index of nilpotence of x, i.e. the smallest `q' such that x^q = 0.

Examples

x_r5 := pAdicQuotientRing(5,10); IsNilpotent(Element(x_r5,4)); IsNilpotent(Element(x_r5,5));
Built: Mon Nov 14 21:12:39 UTC 2005 on mack
The KANT Group