Singular Manual: weierstrPrep

| #### 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:
    LIB "weierstr.lib";
    ring R = 0,(x,y),ds;
    poly f = xy+y2+y4;
    list l = weierstrPrep(f,5); l; "";
    ==> [1]:
    ==>    1-x2+xy-y2+3x4-3x3y+3x2y2-2xy3+y4
    ==> [2]:
    ==>    xy+y2-x3y
    ==> [3]:
    ==>    6
    ==>
    f*l[1]-l[2];                      // = 0 up to degree 5
    ==> 3x5y+3x4y4-3x3y5+3x2y6-2xy7+y8

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