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D.12.6.2 weierstrPrep

Procedure from library weierstr.lib (see weierstr_lib).

Usage:
weierstrPrep(f,d); f=poly, d=integer

Assume:
f must be general of finite order, say b, in the last ring variable, say T; if not apply the procedure lastvarGeneral first

Purpose:
perform the Weierstrass preparation of f up to order d

Return:
- a list, say l, of two polynomials and one integer,
l[1] a unit, l[2] a Weierstrass polynomial, l[3] an integer such that l[1]*f = l[2], where l[2] is a Weierstrass polynomial, (i.e. l[2] = T^b + lower terms in T) up to (including) total degree d l[3] is the number of iterations used
- if f is not T-general, return (0,0)

Note:
the procedure works for any monomial ordering

Theory:
the proof of Grauert-Remmert (Analytische Stellenalgebren) is used for the algorithm

Example:
 


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            User manual for Singular version 3-1-6, Dec 2012, generated by texi2html.