Changeset 61dadae in git


Ignore:
Timestamp:
Dec 4, 2000, 2:48:43 PM (23 years ago)
Author:
Mathias Schulze <mschulze@…>
Branches:
(u'spielwiese', '828514cf6e480e4bafc26df99217bf2a1ed1ef45')
Children:
b89cf5dc60a6d0fcab40ce5443e3cdb2001c8c7e
Parents:
5c8c19056d07b66b391e75ff3ed5f2a0fefb4faf
Message:
*** empty log message ***


git-svn-id: file:///usr/local/Singular/svn/trunk@4795 2c84dea3-7e68-4137-9b89-c4e89433aadc
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1 edited

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  • Singular/LIB/gaussman.lib

    r5c8c19 r61dadae  
    11///////////////////////////////////////////////////////////////////////////////
    22
    3 version="$Id: gaussman.lib,v 1.8 2000-11-10 10:29:47 mschulze Exp $";
     3version="$Id: gaussman.lib,v 1.9 2000-12-04 13:48:43 mschulze Exp $";
    44info="
    55LIBRARY:  gaussman.lib  GAUSS-MANIN CONNECTION OF A SINGULARITY
    66
    7 AUTHOR:   Mathias Schulze (mschulze@mathematik.uni-kl.de)
    8 
    9 OVERVIEW:
    10  A library to compute invariants related to the Gauss-Manin connection
    11  of an isolated hypersurface singularity
     7AUTHOR:   Mathias Schulze, email: mschulze@mathematik.uni-kl.de
    128
    139PROCEDURES:
    14  monomat  : monodromy matrix
    15  monospec : spectrum of monodromy
    16  vfilt    : V-filtration on H''/H'
    17  singspec : singularity spectrum
    18  vjacob   : V-filtration on Jacobian algebra
     10 monomat   monodromy matrix
     11 monospec  spectrum of monodromy
     12 vfilt     V-filtration on H''/H'
     13 singspec  singularity spectrum
     14 vjacob    V-filtration on Jacobian algebra
     15 gamma     Hertling's gamma invariant
     16 gamma4    Hertling's gamma4 invariant
    1917";
    2018
    … …  
    139137proc monomat(poly f,list #)
    140138"USAGE:   <matrix> M=monomat(<poly> f);
    141 ASSUME:  f defines an isolated hypersurface singularity
    142139RETURN:  exp(-2*pi*i*M) is a monodromy matrix
     140NOTE:    f isolated singularity
    143141EXAMPLE: example monomat; shows an example
    144142"
    … …  
    191189
    192190    dbprint(printlevel-voice+2,"//gaussman::monomat: compute C");
    193     C=coeffs(redNF(w,sJ,U),m);
     191    C=coeffs(redNF(w,sJ,U),m,product(maxideal(1)));
    194192    A0=A0+C*var(1)^k;
    195193
    … …  
    209207      else
    210208      {
    211         dbprint(printlevel-voice+2,"//gaussman::monomat: basis of saturation");
     209        dbprint(printlevel-voice+2,
     210          "//gaussman::monomat: compute basis of saturation");
    212211        H=minbase(H0);
    213212        int modH=maxorddif(H);
    … …  
    219218    {
    220219      N=k-modH;
    221       dbprint(printlevel-voice+2,"//gaussman::monomat: A on saturation");
     220      dbprint(printlevel-voice+2,
     221        "//gaussman::monomat: compute A on saturation");
    222222      l=division(H*var(1),A0*H+var(1)^2*diff(matrix(H),var(1)));
    223223      A=expand(l[1],l[2],N-1);
    224224      if(mide<0)
    225225      {
    226         dbprint(printlevel-voice+2,"//gaussman::monomat: eigenvalues e of A");
     226        dbprint(printlevel-voice+2,
     227          "//gaussman::monomat: compute eigenvalues e of A");
    227228        ideal e=jordan(A,-1)[1];
    228229        dbprint(printlevel-voice+2,"//gaussman::monomat: e="+string(e));
    … …  
    234235    if(k<K||sdH>0)
    235236    {
    236       dbprint(printlevel-voice+2,"//gaussman::monomat: division by J");
     237      dbprint(printlevel-voice+2,"//gaussman::monomat: divide by J");
    237238      l=division(J,ideal(matrix(w)-matrix(m)*C*U));
    238239      D=l[1];
    … …  
    346347proc monospec(poly f)
    347348"USAGE:   <matrix> M=monospec(<poly> f);
    348 ASSUME:  f defines an isolated hypersurface singularity
    349349RETURN:  the spectrum of exp(-2*pi*i*M) is the spectrum of monodromy
     350NOTE:    f isolated singularity
    350351EXAMPLE: example monospec; shows an example
    351352"
    … …  
    364365proc vfilt(poly f,list #)
    365366"USAGE:   <list> l=vfilt(<poly> f);
    366 ASSUME:  f defines an isolated hypersurface singularity
    367367RETURN:  <ideal> l[1] : spectral numbers in increasing order
    368368         <intvec> l[2] :
    … …  
    373373         <ideal> l[4] : monomial vector space basis of H''/H'
    374374         <ideal> l[5] : standard basis of Jacobian ideal
     375NOTE:    f isolated singularity
    375376EXAMPLE: example vfilt; shows an example
    376377"
    … …  
    417418
    418419    dbprint(printlevel-voice+2,"//gaussman::vfilt: compute C");
    419     C=coeffs(redNF(w,sJ,U),m);
     420    C=coeffs(redNF(w,sJ,U),m,product(maxideal(1)));
    420421    A=A+C*var(1)^k;
    421422
    … …  
    435436      else
    436437      {
    437         dbprint(printlevel-voice+2,"//gaussman::vfilt: basis of saturation");
     438        dbprint(printlevel-voice+2,
     439          "//gaussman::vfilt: compute basis of saturation");
    438440        H=minbase(H0);
    439441        int modH=maxorddif(H);
    … …  
    452454    if(k<K||sdH>0)
    453455    {
    454       dbprint(printlevel-voice+2,"//gaussman::vfilt: division by J");
     456      dbprint(printlevel-voice+2,"//gaussman::vfilt: divide by J");
    455457      l=division(J,ideal(matrix(w)-matrix(m)*C*U));
    456458      D=l[1];
    … …  
    482484  H0=expand(l[1],l[2],N-1);
    483485
    484   dbprint(printlevel-voice+2,"//gaussman::vfilt: H0 as vector space V0");
    485   dbprint(printlevel-voice+2,"//gaussman::vfilt: H1 as vector space V1");
     486  dbprint(printlevel-voice+2,
     487    "//gaussman::vfilt: compute H0 as vector space V0");
     488  dbprint(printlevel-voice+2,
     489    "//gaussman::vfilt: compute H1 as vector space V1");
    486490  poly p;
    487491  int i0,j0,i1,j1;
    … …  
    510514  }
    511515
    512   dbprint(printlevel-voice+2,"//gaussman::vfilt: A on saturation");
     516  dbprint(printlevel-voice+2,"//gaussman::vfilt: compute A on saturation");
    513517  l=division(H*var(1),A*H+var(1)^2*diff(matrix(H),var(1)));
    514518  A=expand(l[1],l[2],N-1);
    515519
    516   dbprint(printlevel-voice+2,"//gaussman::vfilt: matrix M of A");
     520  dbprint(printlevel-voice+2,"//gaussman::vfilt: compute matrix M of A");
    517521  matrix M[mu*N][mu*N];
    518522  for(i0=mu;i0>=1;i0--)
    … …  
    540544  }
    541545
    542   dbprint(printlevel-voice+2,"//gaussman::vfilt: eigenvalues eA of A");
     546  dbprint(printlevel-voice+2,"//gaussman::vfilt: compute eigenvalues eA of A");
    543547  ideal eA=jordan(A,-1)[1];
    544548  dbprint(printlevel-voice+2,"//gaussman::vfilt: eA="+string(eA));
    545549
    546   dbprint(printlevel-voice+2,"//gaussman::vfilt: eigenvalues eM of M");
     550  dbprint(printlevel-voice+2,"//gaussman::vfilt: compute eigenvalues eM of M");
    547551  ideal eM;
    548552  k=0;
    … …  
    572576  dbprint(printlevel-voice+2,"//gaussman::vfilt: eM="+string(eM));
    573577
    574   dbprint(printlevel-voice+2,"//gaussman::vfilt: V-filtration on H0/H1");
     578  dbprint(printlevel-voice+2,
     579    "//gaussman::vfilt: compute V-filtration on H0/H1");
    575580  ideal s;
    576581  k=0;
    … …  
    602607    }
    603608
    604     dbprint(printlevel-voice+2,"//gaussman::vfilt: symmetry index reached");
     609    dbprint(printlevel-voice+2,"//gaussman::vfilt: symmetry index found");
    605610    j=k;
    606611    if(number(eM[i])-1==number(n-1)/2)
    … …  
    687692    }
    688693
    689     dbprint(printlevel-voice+2,"//gaussman::vfilt: graded parts");
     694    dbprint(printlevel-voice+2,"//gaussman::vfilt: compute graded parts");
    690695    option(redSB);
    691696    for(k=1;k<size(v);k++)
    … …  
    711716proc singspec(poly f)
    712717"USAGE:   <list> l=singspec(<poly> f);
    713 ASSUME:  f defines an isolated hypersurface singularity
    714718RETURN:  <ideal> l[1] : spectral numbers in increasing order
    715719         <intvec> l[2] :
    716720           <int> l[2][i] : multiplicity of spectral number l[1][i]
     721NOTE:    f isolated singularity
    717722EXAMPLE: example singspec; shows an example
    718723"
    … …  
    731736proc gamma(list l)
    732737"USAGE:   <number> g=gamma(singspec(<poly> f));
    733 ASSUME:  f defines an isolated hypersurface singularity
    734738RETURN:  Hertling's gamma invariant
     739NOTE:    f defines an isolated singularity
    735740EXAMPLE: example gamma; shows an example
    736741"
    … …  
    761766proc gamma4(list l)
    762767"USAGE:   <number> g4=gamma4(singspec(<poly> f));
    763 ASSUME:  f defines an isolated hypersurface singularity
    764 RETURN:  Hertling's gamma(4) invariant
     768RETURN:  Hertling's gamma4 invariant
     769NOTE:    f defines an isolated singularity
    765770EXAMPLE: example gamma4; shows an example
    766771"
    … …  
    792797proc vjacob(list l)
    793798"USAGE:   <list> l=vjacob(vfilt(<poly> f));
    794 ASSUME:  f defines an isolated hypersurface singularity
    795799RETURN:  <ideal> l[1] : spectral numbers of the V-filtration on the
    796800                        Jacobian algebra in increasing order
    … …  
    803807         <ideal> l[4] : monomial vector space basis of the Jacobian algebra
    804808         <ideal> l[5] : standard basis of Jacobian ideal
     809NOTE:    f defines an isolated singularity
    805810EXAMPLE: example vjacob; shows an example
    806811"
    … …  
    819824  for(i=ncols(m);i>=1;i--)
    820825  {
    821     M[i]=lift(V,coeffs(redNF(m[i]*m,sJ),m)*V);
     826    M[i]=lift(V,coeffs(redNF(m[i]*m,sJ),m)*V,product(maxideal(1)));
    822827  }
    823828
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