Changeset 96967e in git


Ignore:
Timestamp:
Dec 23, 2000, 6:11:30 PM (23 years ago)
Author:
Gert-Martin Greuel <greuel@…>
Branches:
(u'spielwiese', '4a9821a93ffdc22a6696668bd4f6b8c9de3e6c5f')
Children:
c2aa978105e99edf0b9fb6ca0fdd579277b7c665
Parents:
d1b71e049a353dc54585ba43727902aeadcd2653
Message:
* GMG: Kosmetik fuer html-Hilfe


git-svn-id: file:///usr/local/Singular/svn/trunk@4989 2c84dea3-7e68-4137-9b89-c4e89433aadc
Location:
Singular/LIB
Files:
3 edited

Legend:

Unmodified
Added
Removed

  • Singular/LIB/all.lib

    rd1b71e r96967e  
    1 // $Id: all.lib,v 1.31 2000-12-22 13:37:10 greuel Exp $
     1// $Id: all.lib,v 1.32 2000-12-23 17:08:07 greuel Exp $
    22///////////////////////////////////////////////////////////////////////////////
    3 version="$Id: all.lib,v 1.31 2000-12-22 13:37:10 greuel Exp $";
    4 category="General purpose";
     3version="$Id: all.lib,v 1.32 2000-12-23 17:08:07 greuel Exp $";
     4category = "General purpose";
    55info="
    66LIBRARY:  all.lib   Load all libraries
    77
     8@format
    89General purpose
    9   general_lib:     ELEMENTARY COMPUTATIONS OF GENERAL TYPE
    10   inout_lib:       PRINTING AND MANIPULATING IN- AND OUTPUT
    11   poly_lib:        CREATING AND MANIPULATING POLYS, IDEALS, MODULES
    12   random_lib:      CREATING RANDOM AND SPARSE MATRICES, IDEALS, POLYS
    13   ring_lib:        MANIPULATING RINGS AND MAPS
     10  general_lib:     Elementary Computations of General Type
     11  inout_lib:       Printing and Manipulating In- and Output
     12  poly_lib:        Procedures for Manipulating Polys, Ideals, Modules
     13  random_lib:      Creating Random and Sparse Matrices, Ideals, Polys
     14  ring_lib:        Manipulating Rings and Maps
    1415
    1516Linear algebra
    16   jordan_lib:      JORDAN NORMAL FORM OF A MATRIX WITH RATIONAL EIGENVALUES
    17   linalg_lib:      ALGORITHMIC LINEAR ALGEBRA
    18   matrix_lib:      ELEMENTARY MATRIX OPERATIONS
     17  jordan_lib:      Jordan Normal Form of a Matrix with rational Eigenvalues
     18  linalg_lib:      Algorithmic Linear Algebra
     19  matrix_lib:      Elementary Matrix Operations
    1920
    2021Commutative algebra
    21   algebra_lib:     COMPUTE WITH ALGBRAS AND ALGEBRA MAPS
    22   elim_lib:        ELIMINATION, SATURATION AND BLOWING UP
    23   homolog_lib:     HOMOLOGICAL ALGEBRA AND CUP PRODUCT
    24   intprog_lib:     INTEGER PROGRAMMING WITH GROEBNER BASIS METHODS
    25   mregular_lib:    CASTELNUOVO-MUMFORD REGULARITY OF CM-SCHEMES AND CURVES
    26   normal_lib:      NORMALIZATION OF AN AFFINE RING
    27   primdec_lib:     PRIMARY DECOMPOSITION AND RADICAL OF IDEALS
    28   primitiv_lib:    COMPUTING A PRIMITIVE ELEMENT
    29   reesclos_lib:    REES ALGEBRA AND INTEGRAL CLOSURE OF IDEALS
    30   toric_lib:       STANDARD BASIS OF TORIC IDEALS
     22  algebra_lib:     Compute with Algbras and Algebra Maps
     23  elim_lib:        Elimination, Saturation and Blowing up
     24  homolog_lib:     Procedures for Homological Algebra
     25  intprog_lib:     Integer Programming with Groebner Basis Methods
     26  mregular_lib:    Castelnuovo-Mumford Regularity of CM-Schemes and Curves
     27  normal_lib:      Normalization of Affine Rings
     28  primdec_lib:     Primary Decomposition and Radical of Ideals
     29  primitiv_lib:    Computing a Primitive Element
     30  reesclos_lib:    Rees Algebra and Integral Closure of Ideals
     31  toric_lib:       Standard Basis of Toric Ideals
    3132
    3233Singularities
    33   classify_lib:    ARNOLD CLASSIFIER OF SINGULARTIES
    34   deform_lib:      MINIVERSAL DEFORMATION OF SINGULARITIES AND MODULES
    35   equising_lib:    EQUISINGULARITY STRATUM OF A FAMILY OF PLANE CURVES
    36   gaussman_lib:    GAUSS-MANIN CONNECTION OF A HYPERSURFACE SINGULARITY
    37   hnoether_lib:    HAMBURGER-NOETHER (PUISEUX) DEVELOPMENT
    38   mondromy_lib:    MONODROMY OF AN ISOLATED HYPERSURFACE SINGULARITY
    39   qhmoduli.lib:    MODULI SPACES OF SEMI-QUASIHOMOGENEOUS SINGULARITIES
    40   sing_lib:        INVARIANTS OF SINGULARITIES
    41   spcurve_lib:     DEFORMATIONS AND INVARIANTS OF CM-CODIM 2 SINGULARITIES
    42   spectrum_lib:    SINGULARITY SPECTRA FOR NONDEGENERATE SINGULARITIES
     34  classify_lib:    Arnold Classifier of Singularities
     35  deform_lib:      Miniversal Deformation of Singularities and Modules
     36  equising_lib:    Equisingularity Stratum of a Family of Plane Curves
     37  gaussman_lib:    Gauss-Manin Connection of a Singularity
     38  hnoether_lib:    Hamburger-Noether (Puiseux) Development
     39  mondromy_lib:    Monodromy of an Isolated Hypersurface Singularity
     40  qhmoduli.lib:    Moduli Spaces of Semi-Quasihomogeneous Singularities
     41  sing_lib:        Invariants of Singularities
     42  spcurve_lib:     Deformations and Invariants of CM-codim 2 Singularities
     43  spectrum_lib:    Singularity Spectrum for Nondegenerate Singularities
    4344
    4445Invariant theory
    45   ainvar_lib:      INVARIANTS RINGS OF THE ADDITIVE GROUP
    46   finvar_lib:      INVARIANT RINGS OF FINITE GROUPS
    47   rinvar_lib:      INVARIANT RINGS OF REDUCTIVE GROUPS
    48   stratify_lib:    ALGORITHMIC STRATIFICATION FOR UNIPOTENT GROUP-ACTIONS
     46  ainvar_lib:      Invariant Rings of the Additive Group
     47  finvar_lib:      Invariant Rings of Finite Groups
     48  rinvar_lib:      Invariant Rings of Reductive Groups
     49  stratify_lib:    Algorithmic Stratification for Unipotent Group-Actions
    4950
    5051Symbolic-numerical solving
    51   ntsolve_lib:     REAL NEWTON SOLVING OF POLYNOMIAL SYSTEMS
    52   presolve_lib:    PRE-SOLVING OF POLYNOMIAL EQUATIONS
    53   solve_lib:       COMPLEX SOLVING OF POLYNOMIAL SYSTEMS
    54   triang_lib:      DECOMPOSE ZERO-DIMENSIONAL IDEALS INTO TRIANGULAR SETS
    55   zeroset_lib:     procedures for roots and factorization
     52  ntsolve_lib:     Real Newton Solving of Polynomial Systems
     53  presolve_lib:    Pre-Solving of Polynomial Equations
     54  solve_lib:       Complex Solving of Polynomial Systems
     55  triang_lib:      Decompose Zero-dimensional Ideals into Triangular Sets
     56  zeroset_lib:     Procedures For Roots and Factorization
    5657
    5758Visualization
    58   graphics_lib:    PROCEDURES TO USE GRAPHICS WITH MATHEMATICA
    59   latex_lib:       TYPESETTING OF SINGULAR-OBJECTS IN LATEX2E
    60   paramet_lib:     PARAMETRIZATION OF VARIETIES
    61   surf_lib:        PROCEDURES FOR GRAPHICS WITH SURF
     59  graphics_lib:    Procedures to use Graphics with Mathematica
     60  latex_lib:       Typesetting of Singular-Objects in LaTex2e
     61  paramet_lib:     Parametrization of Varieties
     62  surf_lib:        Procedures for Graphics with Surf
    6263
    6364Coding theory
    64   brnoeth_lib:     BRILL-NOETHER ALGORITHM, WEIERSTRASS-SG AND AG-CODES
     65  brnoeth_lib:     Brill-Noether Algorithm, Weierstrass-SG and AG-codes
    6566
    6667Miscellaneous
    67   makedbm_lib:     DATA BASE OF SINGULARITIES FOR THE ARNOLD-CLASSIFIER
    68   template_lib:    A TEMPLATE FOR A SINGULAR LIBRARY
     68  makedbm_lib:     Data Base of Singularities for the Arnold-Classifier
     69  template_lib:    A Template for a Singular Library
    6970
    7071Utilities
    71   tst_lib:         PROCEDURES FOR RUNNING AUTOMATIC TST TESTS
     72  tst_lib:         Procedures for running automatic tst Tests
     73
     74@end format
    7275";
    7376

  • Singular/LIB/classify.lib

    rd1b71e r96967e  
    11// KK,GMG last modified: 17.12.00
    22///////////////////////////////////////////////////////////////////////////////
    3 version  = "$Id: classify.lib,v 1.45 2000-12-22 13:39:53 greuel Exp $";
     3version  = "$Id: classify.lib,v 1.46 2000-12-23 17:10:16 greuel Exp $";
    44category="Singularities";
    55info="
    6 LIBRARY:  classify.lib  Arnold Classifier of Singularties
     6LIBRARY:  classify.lib  Arnold Classifier of Singularities
    77AUTHOR:   Kai Krueger, krueger@mathematik.uni-kl.de
    88
    … …  
    1212
    1313PROCEDURES:
    14 basicinvariants(f);  computes Milnor number, determinacy-bound and corank of f
    15 classify(f);         normal form of poly f determined with Arnold's method
    16 corank(f);           computes the corank of f (i.e. of the Hessian of f)
    17 Hcode(v);            coding of intvec v acoording to the number repetitions
    18 init_debug([n]);     print trace and debugging information depending on int n
    19 internalfunctions(); display names of internal procedures of this library
    20 milnorcode(f[,e]);   Hilbert poly of [e-th] Milnor algebra coded with Hcode
    21 morsesplit(f);       residual part of f after applying the splitting lemma
    22 quickclass(f)        normal form of f determined by invariants (milnorcode)
    23 singularity(s,[]);   normal form of singularity given by its name s and index
    24 swap (a,b);          returns b,a
    25 A_L(s/f)             shortcut for quickclass(f) or normalform(s)
    26 normalform(s);       normal form of singularity given by its name s
    27 debug_log(lev,[])    print trace and debugging information w.r.t level>@DeBug
     14basicinvariants(f); computes Milnor number, determinacy-bound and corank of
     15classify(f);        normal form of poly f determined with Arnold's method
     16 corank(f);          computes the corank of f (i.e. of the Hessian of f)
     17 Hcode(v);           coding of intvec v acoording to the number repetitions
     18 init_debug([n]);    print trace and debugging information depending on int n
     19 internalfunctions();display names of internal procedures of this library
     20 milnorcode(f[,e]);  Hilbert poly of [e-th] Milnor algebra coded with Hcode
     21 morsesplit(f);      residual part of f after applying the splitting lemma
     22 quickclass(f)       normal form of f determined by invariants (milnorcode)
     23 singularity(s,[]);  normal form of singularity given by its name s and index
     24 swap(a,b);          returns b,a
     25 A_L(s/f)            shortcut for quickclass(f) or normalform(s)
     26 normalform(s);      normal form of singularity given by its name s
     27 debug_log(lev,[])   print trace and debugging information w.r.t level>@DeBug
    2828           (parameters in square brackets [] are optional)
    2929";
    … …  
    22612261proc singularity(string typ, list #)
    22622262"USAGE:    singularity(t, l); t=string (name of singularity),
    2263           l=list of integers (index/indices of singularity)
    2264 COMPUTE:  get the Singularity named by type t from the database.
     2263          l=list of integers/polynomials (indices/parmeters of singularity)
     2264COMPUTE:  get the singularity named by type t from the database.
    22652265          list l is as follows:
    2266           l= k [,r [,s [,a [,b [,c [,d]]]]]] k,r,s=int   a,b,c,d=poly
    2267           The name of the dbm-databasefile is: NFlist.[dir,pag]
     2266          l= k [,r [,s [,a [,b [,c [,d]..]: k,r,s=int   a,b,c,d=poly.
     2267          The name of the dbm-databasefile is: NFlist.[dir,pag].
    22682268          The file is found in the current directory. If it does not
    22692269          exists, please run the script MakeDBM first.
    22702270RETURN:   Normal form and corank of the singularity named by type t and its
    2271           index (indices) l
     2271          index (indices) l.
    22722272EXAMPLE:  example singularity; shows an example"
    22732273{
    … …  
    25282528RETURN:   the corank of the Hessian matrix of f, of type int
    25292529REMARK:   corank(f) is the number of variables occuring in the residual
    2530           singulartity after applying 'morsesplit' to f
     2530          singularity after applying 'morsesplit' to f
    25312531EXAMPLE:  example corank; shows an example"
    25322532{
    … …  
    27612761///////////////////////////////////////////////////////////////////////////////
    27622762proc A_L
    2763 "USAGE:    A_L(f);         f=poly
    2764           A_L(\"name\");    type=string
    2765 COMPUTE:  the normal form in Arnold's list of the singularity given either
    2766           by a polynomial f or by its name.
    2767 RETURN:   A_L(f): compute via 'milnorcode' the class of f and
    2768           return the normal form of f found in the database.
    2769           A_L(\"name\"): Get the normal form from the database for
    2770           the singularity given by its name.
     2763"USAGE:    A_L(f);  f poly
     2764          A_L(s);  s string, the name of the singularity
     2765COMPUTE:  the normal form of f in Arnold's list of singularities in case 1,
     2766          in case 2 nothing has to be computed.
     2767RETURN:   A_L(f): compute via 'milnorcode' the class of f and return the normal
     2768          form of f found in the database.
     2769          A_L(\"name\"): get the normal form from the database for the
     2770          singularity given by its name.
    27712771EXAMPLE:  example A_L; shows an example"
    27722772{
    … …  
    28612861{ "   Internal functions for the classification using Arnold's method,";
    28622862 "   the function numbers correspond to numbers in Arnold's classifier:";
    2863  "Klassifiziere(poly f);        determine the type of the singularity f
     2863 "Klassifiziere(poly f);      //determine the type of the singularity f
    28642864  Funktion1bis (poly f, list cstn)
    28652865  Funktion3 (poly f, list cstn)
    … …  
    28862886  Isomorphie_s82_z (poly f, poly fk, int k)
    28872887  Isomorphie_s17 (poly f, poly fk, int k, int ct)
    2888   printresult (string f, string typ, int Mu, int m, int corank, int K)
     2888  printresult (string f,string typ,int Mu,int m,int corank,int K)
    28892889  ";
    28902890  "   Internal functions for the classifcation by invariants:
    28912891  Cubic (poly f)
    2892   parity (int e)               return the parity of e
     2892  parity (int e)             //return the parity of e
    28932893  HKclass (intvec i)
    28942894  HKclass3( intvec i, string SG_Typ, int cnt)
    … …  
    29012901  ";
    29022902  "   Internal functions for the Morse-splitting lemma:
    2903   Morse(poly fi, int K, int corank)          Splittinglemma itself
     2903  Morse(poly fi, int K, int corank)  //splitting lemma itself
    29042904  Coeffs (list #)
    29052905  Coeff
    … …  
    29102910  RandomPolyK
    29112911  Faktorisiere(poly f, poly g, int p, int k)   compute g = (ax+by^k)^p
    2912   Teile(poly f, poly g);                  Teilt f durch g.
     2912  Teile(poly f, poly g);             //divides f by g
    29132913  GetRf(poly f, int n);
    29142914  Show(poly f);

  • Singular/LIB/gaussman.lib

    rd1b71e r96967e  
    11///////////////////////////////////////////////////////////////////////////////
    22
    3 version="$Id: gaussman.lib,v 1.18 2000-12-21 18:06:36 mschulze Exp $";
     3version="$Id: gaussman.lib,v 1.19 2000-12-23 17:11:30 greuel Exp $";
    44category="Singularities";
    55info="
    6 LIBRARY:  gaussman.lib  GAUSS-MANIN CONNECTION OF A SINGULARITY
     6LIBRARY:  gaussman.lib  Gauss-Manin Connection of a Singularity
    77
    88AUTHOR:   Mathias Schulze, email: mschulze@mathematik.uni-kl.de
    … …  
    368368
    369369proc vfiltration(poly f,list #)
    370 "USAGE:    vfiltration(f[,mode]); poly f, int mode[=1]
     370"USAGE:    vfiltration(f[,mode]); poly f, int mode[default=1]
    371371ASSUME:   local ordering, f isolated singularity at 0
    372 RETURN:   list l :
    373           if mode=0 or mode=1 :
    374             ideal l[1] : spectral numbers in increasing order
    375             intvec l[2] :
    376               int l[2][i] : multiplicity of spectral number l[1][i]
     372RETURN:   list l:
     373          @format
     374          if mode=0 or mode=1:
     375            l[1]: ideal, spectral numbers in increasing order
     376            l[2]: intvec
     377                  l[2][i]: int, multiplicity of spectral number l[1][i]
    377378          if mode=1 :
    378             list l[3] :
    379               module l[3][i] : vector space basis of l[1][i]-th graded part
    380                                of the V-filtration on H''/H' in terms of l[4]
    381             ideal l[4] : monomial vector space basis of H''/H'
    382             ideal l[5] : standard basis of Jacobian ideal
     379            l[3]: list
     380                  l[3][i]: module, vector space basis of l[1][i]-th graded
     381                           part of the V-filtration on H''/H' in terms of l[4]
     382            l[4]: ideal, monomial vector space basis of H''/H'
     383            l[5]: ideal, standard basis of Jacobian ideal
     384          @end format
    383385NOTE:     H' and H'' denote Brieskorn lattices
    384386SEE ALSO: spectrum.lib
    … …  
    745747"USAGE:   vfiltjacalg(vfiltration(f));
    746748ASSUME:  local ordering, f isolated singularity at 0
    747 RETURN:  list l :
    748            ideal l[1] : spectral numbers of the V-filtration on the
    749                         Jacobian algebra in increasing order
    750            intvec l[2] :
    751              int l[2][i] : multiplicity of spectral number l[1][i]
    752            list l[3] :
    753              module l[3][i] : vector space basis of l[1][i]-th graded part
    754                               of the V-filtration on the Jacobian algebra
    755                               in terms of l[4]
    756            ideal l[4] : monomial vector space basis of the Jacobian algebra
    757            ideal l[5] : standard basis of Jacobian ideal
     749RETURN:  list l:
     750         @format
     751           l[1]: ideal, spectral numbers of the V-filtration on the
     752                 Jacobian algebra in increasing order
     753           l[2]: intvec
     754               l[2][i]: int, multiplicity of spectral number l[1][i]
     755           l[3]: list
     756               l[3][i]: module, vector space basis of l[1][i]-th graded part
     757                        of the V-filtration on the Jacobian algebra in terms
     758                        of l[4]
     759           l[4]: ideal, monomial vector space basis of the Jacobian algebra
     760           l[5]: ideal, standard basis of Jacobian ideal
     761           @end format
    758762EXAMPLE: example vfiltjacalg; shows an example
    759763"
Note: See TracChangeset for help on using the changeset viewer.