Changeset 74b737 in git


Ignore:
Timestamp:
Aug 31, 1999, 4:58:38 PM (25 years ago)
Author:
Martin Lamm <lamm@…>
Branches:
(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', 'b4f17ed1d25f93d46dbe29e4b499baecc2fd51bb')
Children:
48d74cb4e67985d6d68d25eb25c32ee983b6e927
Parents:
8632ac4fb9462c9bfd6b35849aa43a145a76fbb5
Message:
* new procedure 'further_hn_proc' listing other useful procedures


git-svn-id: file:///usr/local/Singular/svn/trunk@3571 2c84dea3-7e68-4137-9b89-c4e89433aadc
File:
1 edited

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  • Singular/LIB/hnoether.lib

    r8632ac r74b737  
    1 // $Id: hnoether.lib,v 1.16 1999-08-13 17:39:17 lamm Exp $
    2 // last change:           13.08.99
     1// $Id: hnoether.lib,v 1.17 1999-08-31 14:58:38 lamm Exp $
     2// last change:           31.08.99
    33///////////////////////////////////////////////////////////////////////////////
    44// This library is for Singular 1-3-4 or newer
    55
    6 version="$Id: hnoether.lib,v 1.16 1999-08-13 17:39:17 lamm Exp $";
     6version="$Id: hnoether.lib,v 1.17 1999-08-31 14:58:38 lamm Exp $";
    77info="
    88LIBRARY:  hnoether.lib   PROCEDURES FOR THE HAMBURGER-NOETHER DEVELOPMENT
     
    3232 squarefree(f);      returns a squarefree divisor of the poly f
    3333 allsquarefree(f,l); returns the maximal squarefree divisor of the poly f
     34 further_hn_proc();  show further procedures useful for interactive use
    3435";
    3536///////////////////////////////////////////////////////////////////////////////
    36 // newtonpoly(f);      Newton polygon of polynom f
    37 // getnm(f);           intersection points of the Newton polygon with the axes
    38 // T_Transform(f,Q,N); returns f(y,xy^Q)/y^NQ (type f(x,y): poly, Q,N: int)
    39 // T1_Transform(f,d,M); returns f(x,y+d*x^M)  (type f(x,y): poly,d:number,M:int)
    40 // T2_Transform(f,d,M,N,ref);   a composition of T1 & T
    41 // koeff(f,I,J);       gets coefficient of indicated monomial of poly f (I,J:int)
    42 // redleit(f,S,E);     restriction of monomials of f to line (S-E)
    43 // leit(f,n,m);        special case of redleit (for irred. polynomials)
     37LIB "primitiv.lib";
     38LIB "inout.lib";
     39
     40///////////////////////////////////////////////////////////////////////////////
     41
     42proc further_hn_proc()
     43"USAGE: further_hn_proc();
     44   The library `hnoether.lib' contains some more procedures which are not
     45   shown when typing @code{help hnoether.lib}. They may be useful for
     46   interactive use (e.g. if you want to do the calculation of a HNE
     47   \"by hand\" to see the intermediate results), and they can be enumerated by
     48   calling further_hn_proc. Use @code{help <procedure>;} for detailed
     49   information about each of them.
     50"
     51{
     52 "
     53 The following procedures are also part of the library `hnoether.lib':
     54
     55 newtonpoly(f);      Newton polygon of polynom f
     56 getnm(f);           intersection pts. of Newton polygon with the axes
     57 T_Transform(f,Q,N); returns f(y,xy^Q)/y^NQ (f: poly, Q,N: int)
     58 T1_Transform(f,d,M); returns f(x,y+d*x^M)  (f: poly,d:number,M:int)
     59 T2_Transform(f,d,M,N,ref);   a composition of T1 & T
     60 koeff(f,I,J);       gets coefficient of indicated monomial of poly f
     61 redleit(f,S,E);     restriction of monomials of f to line (S-E)
     62 leit(f,n,m);        special case of redleit (for irred. polynomials)
     63 testreducible(f,n,m); tests whether f is reducible
     64 charPoly(f,M,N);    characteristic polynomial of f
     65 find_in_list(L,p);  find int p in list L
     66 get_last_divisor(M,N); last divisor in Euclid's algorithm
     67 factorfirst(f,M,N); try to factor f in a trivial way without `factorize'
     68 factorlist(L);      factorize a list L of polynomials
     69 referencepoly(D);   a polynomial f s.t. D is the Newton diagram of f";
     70
     71// extrafactor(f,M,N); try to factor charPoly(f,M,N) where 'factorize' cannot
     72// (will hopefully become obsolete soon)
    4473//
    45 //           procedures (more or less) for internal use:
    46 // testreducible(f,n,m); tests whether f is reducible
     74//       static procedures not useful for interactive use:
    4775// polytest(f);        tests coefficients and exponents of poly f
    48 // charPoly(f,M,N);    characteristic polynomial of f
    49 // find_in_list(L,p);  find int p in list L
    50 // get_last_divisor(M,N); last divisor in Euclid's algorithm
    51 // factorfirst(f,M,N); try to factor f in a trivial way before using 'factorize'
    52 // factorlist(L);      factorize a list L of polynomials
    53 // extrafactor(f,M,N); try to factor charPoly(f,M,N) where 'factorize' cannot
    54 // referencepoly(D);   a polynomial f s.t. D is the Newton diagram of f
    5576// extractHNEs(H,t);   extracts output H of HN to output of reddevelop
    5677// HN(f,grenze);       recursive subroutine for reddevelop
    5778// constructHNEs(...); subroutine for HN
    58 ///////////////////////////////////////////////////////////////////////////////
    59 LIB "primitiv.lib";
    60 LIB "inout.lib";
    61 
     79}
     80example
     81{ echo=2;
     82  further_hn_proc();
     83}
    6284///////////////////////////////////////////////////////////////////////////////
    6385
     
    382404
    383405proc is_irred (poly f)
    384 "USAGE :  is_irred(f); f a squarefree bivariate polynomial
     406"USAGE:   is_irred(f); f a squarefree bivariate polynomial
    385407RETURN:  an integer:
    386408 @*      is_irred(f) @math{= 1} if f is irreducible as a formal power series
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