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D.12.6.1 weierstrDiv

Procedure from library weierstr.lib (see weierstr_lib).

Usage:
weierstrDiv(g,f,d); g,f=poly, d=integer

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

Purpose:
perform the Weierstrass division of g by f up to order d

Return:
- a list, say l, of two polynomials and an integer, such that
g = l[1]*f + l[2], deg_T(l[2]) < b, up to (including) total degree d
- l[3] is the number of iterations used
- if f is not T-general, return (0,g)

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.