Changeset 6fe3a0 in git


Ignore:
Timestamp:
Apr 25, 2005, 12:13:07 PM (19 years ago)
Author:
Hans Schönemann <hannes@…>
Branches:
(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', '4188d308699580d975efd0f6cca8dcb41c396f70')
Children:
3329dd9bcf2662f9666579abea56c33dfcb530ac
Parents:
8604751c5a5f572004bf8d35d4307e485b728435
Message:
*hannes/lossen: new libs, new tests


git-svn-id: file:///usr/local/Singular/svn/trunk@7891 2c84dea3-7e68-4137-9b89-c4e89433aadc
Files:
6 deleted
29 edited

Legend:

Unmodified
Added
Removed
  • Singular/LIB/deform.lib

    r860475 r6fe3a0  
    1 // $Id: deform.lib,v 1.30 2004-04-20 15:55:22 Singular Exp $
     1// $Id: deform.lib,v 1.31 2005-04-25 10:13:05 Singular Exp $
    22// author: Bernd Martin email: martin@math.tu-cottbus.de
    33//(bm, last modified 4/98)
    44///////////////////////////////////////////////////////////////////////////////
    5 version="$Id: deform.lib,v 1.30 2004-04-20 15:55:22 Singular Exp $";
     5version="$Id: deform.lib,v 1.31 2005-04-25 10:13:05 Singular Exp $";
    66category="Singularities";
    77info="
     
    1414 lift_kbase(N,M);          lifting N into standard kbase of M
    1515 lift_rel_kb(N,M[,kbM,p])  relative lifting N into a kbase of M
    16  kill_rings([\"prefix\"])  kills the exported rings from above
    1716";
    1817
     
    2726"USAGE:   versal(Fo[,d,any]); Fo=ideal, d=int, any=list
    2827COMPUTE: miniversal deformation of Fo up to degree d (default d=100),
    29 CREATE:  Rings (exported):
    30          'my'Px = extending the basering Po by new variables given by
    31            \"A,B,..\" (deformation parameters), returns as basering; the
    32            new variables precede the old ones, the ordering is the
    33            product between \"ls\" and \"ord(Po)\"
    34          @*'my'Qx = Px/Fo extending Qo=Po/Fo,
    35          @*'my'So = the embedding-ring of the versal base space,
    36          @*'my'Ox = Px/Js extending So/Js.   (default my=\"\")
    37 
    38       Matrices (in Px, exported):
     28RETURN: list L of 4 rings:
     29         L[1] extending the basering Po by new variables given by
     30          \"A,B,..\" (deformation parameters); the new variables precede
     31         the old ones, the ordering is the product of \"ls\" and \"ord(Po)\" @*
     32         L[2] = L[1]/Fo extending Qo=Po/Fo, @*
     33         L[3] = the embedding ring of the versal base space, @*
     34         L[4] = L[1]/Js extending L[3]/Js. @*
     35      In the ring L[1] the following matrices are stored:
    3936         @*Js  = giving the versal base space (obstructions),
    4037         @*Fs  = giving the versal family of Fo,
     
    4340      If d is defined (!=0), it computes up to degree d.
    4441      @*If 'any' is defined and any[1] is no string, interactive version.
    45       @*Otherwise 'any' gives predefined strings: \"my\",\"param\",\"order\",\"out\"
    46       (\"my\" prefix-string, \"param\" is a letter (e.g. \"A\")  for the name of
    47       first parameter or (e.g. \"A(\") for index parameter variables, \"order\"
    48       ordering string for ring extension), \"out\" name of output-file).
    49 NOTE:   printlevel < 0        no output at all,
     42      @*Otherwise 'any' is interpreted as a list of predefined strings:
     43      \"my\",\"param\",\"order\",\"out\": @*
     44      (\"my\" internal prefix, \"param\" is a letter (e.g. \"A\") for the
     45      name of the first parameter or (e.g. \"A(\") for index parameter
     46      variables, \"order\" ordering string for ring extension), \"out\" name
     47      of output file).
     48NOTE:   printlevel < 0        no additional output,
    5049        printlevel >=0,1,2,.. informs you, what is going on;
    5150        this proc uses 'execute'.
     
    104103  kill Ls;
    105104  t1' = @t1;
    106   if( @t1==0) { dbprint(p,"// rigid!"); return();}
     105  if( @t1==0) { dbprint(p,"// rigid!"); return(list());}
    107106  if( @t2==0) { @smooth=1; dbprint(p,"// smooth base space");}
    108107  dbprint(p,"// ready: T_1 and T_2");
     
    123122  }
    124123 //---- create new rings and objects ------------------------------------------
    125   get_rings(Fo,t1',1,@my,@order,@param);
    126  setring `myPx`;
     124  list list_of_rings=get_rings(Fo,t1',1,@order,@param);
     125  def `myPx`= list_of_rings[1];
     126  def `myQx`= list_of_rings[2];
     127  def `myOx`= list_of_rings[3];
     128  def `mySo`= list_of_rings[4];
     129  kill list_of_rings;
     130  setring `myPx`;
    127131  @jv=0; @jv[t1']=0; @jv=@jv+1; @jv[nvars(basering)]=0;
    128132                                               //weight-vector for calculating
     
    206210      degBound = 0;
    207211//--------------- obtain new base-ring ----------------------------------------
    208         if(system("with","Namespaces")==1) { kill Top::`myOx`; }
    209212        if(defined(`myOx`)) {kill `myOx`;}
    210213  qring `myOx` = J;
     
    268271   "// ___ Equations of miniversal base space ___",Js,
    269272   "// ___ Equations of miniversal total space ___",Fs);
    270    dbprint(p,"","// Result belongs to ring "+myPx+".",
    271    "// Equations of total space of miniversal deformation are ",
    272    "// given by Fs, equations of miniversal base space by Js.",
    273    "// Make "+myPx+" the basering and list objects defined in "
    274    +myPx+" by typing:",
    275    "   setring "+myPx+"; show("+myPx+");","   listvar(matrix);",
    276    "// NOTE: rings "+myQx+", "+myPx+", "+mySo+" are alive!",
    277    "// (use 'kill_rings(\""+@my+"\");' to remove)");
    278    return();
     273   dbprint(p,"","
     274// 'versal' returned a list, say L, of four rings. In L[1] are stored:
     275//   as matrix Fs: Equations of total space of the miniversal deformation,
     276//   as matrix Js: Equations of miniversal base space,
     277//   as matrix Rs: syzygies of Fs mod Js.
     278// To access these data, type
     279     def Px=L[1]; setring Px; print(Fs); print(Js); print(Rs);
     280");
     281   return(list(`myPx`,`myQx`,`mySo`,`myOx`));
    279282}
    280283example
     
    286289   ideal Fo       = minor(m,2);
    287290                    // cone over rational normal curve of degree 4
    288    versal(Fo);
     291   list L=versal(Fo);
     292   L;
     293   def Px=L[1];
    289294   setring Px;
    290295   // ___ Equations of miniversal base space ___:
     
    298303"USAGE:   mod_versal(Mo,I[,d,any]); I=ideal, M=module, d=int, any =list
    299304COMPUTE: miniversal deformation of coker(Mo) over Qo=Po/Io, Po=basering;
    300 CREATE:  Ringsr (exported):
    301          'my'Px  = extending the basering by new variables (deformation
    302                    parameters), the new variables precede the old ones,
    303                    the ordering is the product between \"my_ord\"
    304                    and \"ord(Po)\"
    305          @*'my'Qx  = Px/Io extending Qo (returns as basering),
    306          @*'my'Ox  = Px/(Io+Js) ring of the versal deformation of coker(Ms),
    307          @*'my'So  = embedding-ring of the versal base space.  (default 'my'=\"\")
    308 
    309       Matrices (in Qx, exported):
     305RETURN:  list L of 4 rings:
     306         L[1] extending the basering Po by new variables given by
     307          \"A,B,..\" (deformation parameters); the new variables precede
     308         the old ones, the ordering is the product of \"ls\" and \"ord(Po)\" @*
     309         L[2] = L[1]/Io extending Qo, @*
     310         L[3] = the embedding ring of the versal base space, @*
     311         L[4] = L[1]/(Io+Js) ring of the versal deformation of coker(Ms). @*
     312      In the ring L[1] the following matrices are stored:
    310313         @*Js  = giving the versal base space (obstructions),
    311          @*Ms  = giving the versal family of Mo,
    312          @*Ls  = giving the lifting of syzygies Lo=syz(Mo),
    313 
     314         @*Fs  = giving the versal family of Mo,
     315         @*Rs  = giving the lifting of syzygies Lo=syz(Mo).   
    314316      If d is defined (!=0), it computes up to degree d.
    315317      @*If 'any' is defined and any[1] is no string, interactive version.
    316       @*Otherwise 'any' gives predefined strings:\"my\",\"param\",\"order\",\"out\"
    317       (\"my\" prefix-string, \"param\" is a letter (e.g. \"A\")  for the name of
    318       first parameter or (e.g. \"A(\") for index parameter variables, \"ord\"
    319       ordering string for ring extension), \"out\" name of output-file).
    320 NOTE:   printlevel < 0        no output at all,
     318      @*Otherwise 'any' is interpreted as a list of predefined strings:
     319      \"my\",\"param\",\"order\",\"out\": @*
     320      (\"my\" internal prefix, \"param\" is a letter (e.g. \"A\") for the
     321      name of the first parameter or (e.g. \"A(\") for index parameter
     322      variables, \"order\" ordering string for ring extension), \"out\" name
     323      of output file).
     324NOTE:   printlevel < 0        no additional output,
    321325        printlevel >=0,1,2,.. informs you, what is going on,
    322326        this proc uses 'execute'.
     
    381385//-------- get new rings and objects ------------------------------------------
    382386 setring Po;
    383   get_rings(I,e1',0,@my,@order,@param);
     387  list list_of_rings=get_rings(I,e1',0,@order,@param);
     388  def `myPx`= list_of_rings[1];
     389  def `myQx`= list_of_rings[2];
     390  def `myOx`= list_of_rings[3];
     391  def `mySo`= list_of_rings[4];
     392  kill list_of_rings;
    384393 setring `myPx`;
    385394  ideal  J,m_J;
     
    454463      I_J = Io,J;                attrib(I_J,"isSB",1);
    455464//-------- obtain new base ring -----------------------------------------------
    456       if(system("with","Namespaces")) {
    457          if(defined(Top::`myOx`)) { kill Top::`myOx`; }
    458       }
    459465      if (defined(`myOx`)) {kill `myOx`;}
    460466 qring `myOx` = I_J;
     
    517523    dbprint(p-1,"// quasi-homogeneous weights of miniversal base",@degr);
    518524  }
    519   dbprint(p-1,"// Result belongs to qring "+myQx,
    520   "// Equations of total space of miniversal deformation are in Js",
    521   simplify(ideal(Js),10),
    522   "// Matrix of the deformed module is Ms and lifted syzygies are Ls.",
    523   "// Make "+myQx+" the basering and list objects defined in "+myQx+
    524   " by typing:",
    525   "   listvar(ring);setring "+myQx+"; show("+myQx+");listvar(ideal);"+
    526   "listvar(matrix);",
    527   "// NOTE: rings "+myQx+", "+myOx+", "+mySo+" are still alive!",
    528   "// (use: 'kill_rings("+@my+");' to remove them)");
     525  dbprint(p,"
     526// 'mod_versal' returned a list, say L, of four rings. In L[2] are stored:
     527//   as matrix Ms: presentation matrix of the deformed module,
     528//   as matrix Ls: lifted syzygies,
     529//   as matrix Js:  Equations of total space of miniversal deformation
     530// To access these data, type
     531     def Qx=L[2]; setring Qx; print(Ms); print(Ls); print(Js);
     532");
    529533  option(set,save_opt);
    530   return();
     534  return(list(`myPx`,`myQx`,`mySo`,`myOx`));
    531535}
    532536example
     
    537541  ideal Io = x4+y3;
    538542  matrix Mo[2][2] = x2,y,-y2,x2;
    539   mod_versal(Mo,Io);
     543  list L = mod_versal(Mo,Io);
     544  def Qx=L[2]; setring Qx;
     545  print(Ms);
     546  print(Ls);
     547  print(Js);
    540548  printlevel = p;
    541   if(system("with","Namespaces")) {
    542         kill Top::Px,Top::Qx,Top::So;
    543   }
    544549  if (defined(Px)) {kill Px,Qx,So;}
    545550}
     
    549554RETURN: nothing, but kills exported rings generated by procedures
    550555        'versal' and 'mod_versal' with optional prefix 'string'
     556NOTE: obsolete
    551557"
    552558{
     
    640646}
    641647///////////////////////////////////////////////////////////////////////////////
    642 proc get_rings(ideal Io,int e1,int switch, list #)
    643 "
    644 Sub-procedure: creating ring-extensions
     648static proc get_rings(ideal Io,int e1,int switch, list #)
     649"
     650Sub-procedure: creating ring-extensions, returned as a list of 4 rings
    645651"
    646652{
     
    649655   string my_ord = "ds";
    650656   string my_var = "A";
    651    if (size(#)>2)
     657   if (size(#)>1)
    652658   {
    653      my     = #[1];
    654      my_ord = #[2];
    655      my_var = #[3];
    656    }
    657    string my_Px = my+"Px";
    658    string my_Qx = my+"Qx";
    659    string my_Ox = my+"Ox";
    660    string my_So = my+"So";
    661    extendring(my_Px,e1,my_var,my_ord);
    662    ideal Io  = imap(Po,Io);         attrib(Io,"isSB",1);
    663    my ="qring "+my_Qx+" = Io;       export("+my_Qx+");";
    664    execute(my);
     659     my_ord = #[1];
     660     my_var = #[2];
     661   }
     662   def my_Px=extendring(e1,my_var,my_ord);
     663   setring my_Px;
     664   ideal Io  = imap(Po,Io);         
     665   attrib(Io,"isSB",1);
     666   qring my_Qx = Io;
    665667   if (switch)
    666668   {
    667      setring `my_Px`;
    668      my = "qring "+my_Ox+" = std(ideal(0));export("+my_Ox+");";
     669     setring my_Px;
     670     qring my_Ox = std(ideal(0));
    669671   }
    670672   else
    671673   {
    672      my = "def "+my_Ox+" = "+my_Qx+";export("+my_Ox+");";
    673    }
    674   execute(my);
    675   defring(my_So,charstr(Po),e1,my_var,my_ord);
    676   return();
     674     def my_Ox = my_Qx;
     675   }
     676   def my_So=defring(charstr(Po),e1,my_var,my_ord);
     677   setring my_So;
     678   list erg=list(my_Px,my_Qx,my_Ox,my_So);
     679   return(erg);
    677680}
    678681///////////////////////////////////////////////////////////////////////////////
  • Singular/LIB/equising.lib

    r860475 r6fe3a0  
    1 version="$Id: equising.lib,v 1.10 2005-04-19 15:23:39 Singular Exp $";
     1version="$Id: equising.lib,v 1.11 2005-04-25 10:13:06 Singular Exp $";
    22category="Singularities";
    33info="
     
    19571957   poly p=p3^2+x^20*p2;
    19581958   p;
    1959    versal(p);
     1959   list L=versal(p);
     1960   def Px=L[1];
    19601961   setring Px;
    19611962   poly F=Fs[1,1];
     
    19691970ring r=0,(x,y),ds;
    19701971poly f=(x-yx+y2)^2-(y+x)^31;
    1971 versal(f);
     1972list L=versal(f);
     1973def Px=L[1];
    19721974setring Px;
    19731975poly F=Fs[1,1];
     
    19831985ring r=32003,(x,y),ds;
    19841986poly f=(x4-y4)^2-x10;
    1985 versal(f);
     1987list L=versal(f);
     1988def Px=L[1];
    19861989setring Px;
    19871990poly F=Fs[1,1];
     
    20172020poly f=w2-v199;
    20182021list L=hnexpansion(f);
    2019 versal(f);
     2022List LL=versal(f);
     2023def Px=LL[1];
    20202024setring Px;
    20212025list L=imap(r,L);
     
    20432047poly f=x6y-3x4y4-x4y5+3x2y7-x4y6+2x2y8-y10+2x2y9-y11+x2y10-y12-y13;
    20442048list K=esIdeal(f);
    2045 versal(f);
     2049list L=versal(f);
     2050def Px=L[1];
    20462051setring Px;
    20472052poly F=Fs[1,1];
     
    20822087tau_es(f);        //-> 68
    20832088
    2084 versal(f);
     2089list L=versal(f);
     2090def Px=L[1];
    20852091setring Px;
    20862092poly F=Fs[1,1];
  • Singular/LIB/ring.lib

    r860475 r6fe3a0  
    1 //(GMG, last modified 03.11.95)
    2 ///////////////////////////////////////////////////////////////////////////////
    3 version="$Id: ring.lib,v 1.20 2005-04-15 13:42:55 Singular Exp $";
     1///////////////////////////////////////////////////////////////////////////////
     2version="$Id: ring.lib,v 1.21 2005-04-25 10:13:06 Singular Exp $";
    43category="General purpose";
    54info="
     
    183182///////////////////////////////////////////////////////////////////////////////
    184183
    185 proc defring (string s1, string s2, int n, string s3, string s4)
    186 "USAGE:   defring(s1,s2,n,s3,s4);  s1..s4=strings, n=integer
    187 CREATE:  Define a ring with name 's1', characteristic 's2', ordering 's4' and
    188          n variables with names derived from s3 and make it the basering.
    189          If s3 is a single letter, say s3=\"a\", and if n<=26 then a and the
    190          following n-1 letters from the alphabeth (cyclic order) are taken as
    191          variables. If n>26 or if s3 is a single letter followed by (, say
    192          s3=\"T(\", the variables are T(1),...,T(n).
    193 RETURN:  No return value
     184proc defring (string s2, int n, string s3, string s4)
     185"USAGE:   defring(ch,n,va,or);  ch,va,or=strings, n=integer
     186RETURN:  ring R with characteristic 'ch', ordering 'or' and n variables with
     187         names derived from va.
     188         If va is a single letter, say va=\"a\", and if n<=26 then a and the
     189         following n-1 letters from the alphabet (cyclic order) are taken as
     190         variables. If n>26 or if va is a single letter followed by a bracket,
     191         say va=\"T(\", the variables are T(1),...,T(n).
    194192NOTE:    This proc is useful for defining a ring in a procedure.
    195193         This proc uses 'execute' or calls a procedure using 'execute'.
    196          If you use it in your own proc, let the local names of your proc
    197          start with @.
     194         If you use it in your own proc, it may be advisable to let the local
     195         names of your proc start with a @.
    198196EXAMPLE: example defring; shows an example
    199197"
    200198{
    201    string @newring = "ring "+s1+"=("+s2+"),(";
     199   string @newring = "ring newring =("+s2+"),(";
    202200   if( n>26 or s3[2]=="(" ) { string @v = s3[1]+"(1.."+string(n)+")"; }
    203201   else { string @v = A_Z(s3,n); }
    204202   @newring=@newring+@v+"),("+s4+");";
    205203   execute(@newring);
    206    export(basering);
    207    keepring(`s1`);
    208    if (voice==2) { "// basering is now:",s1; }
    209    return();
     204   return(newring);
    210205}
    211206example
    212207{ "EXAMPLE:"; echo = 2;
    213    defring("r","0",5,"u","ls"); r; "";
    214    defring("R","2,A",10,"x(","dp(3),ws(1,2,3),ds"); R;
    215    if(system("with","Namespaces")) { kill Top::R,Top::r; }
    216    if (defined(R)) {kill R,r;}
     208   def r=defring("0",5,"u","ls"); r; setring r;"";
     209   def R=defring("2,A",10,"x(","dp(3),ws(1,2,3),ds"); R; setring R;
     210   kill R,r;
    217211}
    218212///////////////////////////////////////////////////////////////////////////////
     
    287281///////////////////////////////////////////////////////////////////////////////
    288282
    289 proc extendring (string na, int n, string va, string o, list #)
    290 "USAGE:   extendring(na,n,va,o[iv,i,r]);  na,va,o=strings,
    291          n,i=integers, r=ring, iv=intvec of positive integers or iv=0
    292 CREATE:  Define a ring with name `na` which extends the ring r by adding n new
    293          variables in front of [after, if i!=0] the old variables and make it
    294          the basering [default: (i,r)=(0,basering)].
     283proc extendring (int n, string va, string o, list #)
     284"USAGE:   extendring(n,va,o[iv,i,r]);  va,o=strings, n,i=integers, r=ring,
     285          iv=intvec of positive integers or iv=0
     286RETURN:  ring R, which extends the ring r by adding n new variables in front
     287         of (resp. after, if i!=0) the old variables.
     288         [default: (i,r)=(0,basering)].
    295289@*       -- The characteristic is the characteristic of r.
    296290@*       -- The new vars are derived from va. If va is a single letter, say
    297291            va=\"T\", and if n<=26 then T and the following n-1 letters from
    298292            T..Z..T (resp. T(1..n) if n>26) are taken as additional variables.
    299             If va is a single letter followed by (, say va=\"x(\", the new
    300             variables are x(1),...,x(n).
    301 @*       -- The ordering is the product ordering between the ordering of r and
    302             an ordering derived from `o` [and iv].
    303 @*        -  If o contains a 'c' or a 'C' in front resp. at the end this is
    304             taken for the whole ordering in front resp. at the end. If o does
     293            If va is a single letter followed by a bracket, say va=\"x(\",
     294            the new variables are x(1),...,x(n).
     295@*       -- The ordering is the product ordering of the ordering of r and of an
     296            ordering derived from `o` [and iv].
     297@*        -  If o contains a 'c' or a 'C' in front resp. at the end, this is
     298            taken for the whole ordering in front, resp. at the end. If o does
    305299            not contain a 'c' or a 'C' the same rule applies to ordstr(r).
    306300@*        -  If no intvec iv is given, or if iv=0, o may be any allowed ordstr,
     
    319313            e.g. o=\"dp,ws,Dp,ds\", iv=3,2,3,4,2,5 creates the ordering
    320314            dp(2),ws(2,3,4),Dp(5),ds
    321 RETURN:  No return value
    322315NOTE:    This proc is useful for adding deformation parameters.
    323316         This proc uses 'execute' or calls a procedure using 'execute'.
    324          If you use it in your own proc, let the local names of your proc
    325          start with @ (see the file HelpForProc)
     317         If you use it in your own proc, it may be advisable to let the local
     318         names of your proc start with a @ (see the file HelpForProc)
    326319EXAMPLE: example extendring; shows an example
    327320"
     
    391384   }
    392385//------------------------ prepare string of new ring -------------------------
    393    @newring = "ring "+na+"=("+charstr(@r)+"),(";
     386   @newring = "ring na =("+charstr(@r)+"),(";
    394387   if( n>26 or va[2]=="(" ) { @v = va[1]+"(1.."+string(n)+")"; }
    395388   else                     { @v = A_Z(va,n); }
     
    407400//---------------------------- execute and export -----------------------------
    408401   execute(@newring);
    409    export(basering);
    410    keepring(`na`);
    411    if (voice==2) { "// basering is now",na; }
    412    return();
     402   dbprint(printlevel-voice+2,"
     403// 'extendring' created a new ring.
     404// To see the ring, type (if the name 'R' was assigned to the return value):
     405     show(R);
     406");
     407
     408   return(na);
    413409}
    414410example
     
    416412   ring r=0,(x,y,z),ds;
    417413   show(r);"";
    418    //blocksize is derived from no of vars:
     414   // blocksize is derived from no of vars:
    419415   int t=5;
    420    extendring("R1",t,"a","dp");         //t global: "dp" -> "dp(5)"
    421    show(R1); "";
    422    extendring("R2",4,"T(","c,dp",1,r);    //"dp" -> "c,..,dp(4)"
    423    show(R2);"";
    424 
    425    //no intvec given, blocksize given: given blocksize is used:
    426    extendring("R3",4,"T(","dp(2)",0,r);   // "dp(2)" -> "dp(2)"
    427    show(R3);"";
    428 
    429    //intvec given: weights and blocksize is derived from given intvec
    430    //(no specification of a blocksize in the given ordstr is allowed!)
    431    //if intvec does not cover all given blocks, the last block is used
    432    //for the remaining variables, if intvec has too many components,
    433    //the last ones are ignored
     416   def R1=extendring(t,"a","dp");         //t global: "dp" -> "dp(5)"
     417   show(R1); setring R1; "";
     418   def R2=extendring(4,"T(","c,dp",1,r);    //"dp" -> "c,..,dp(4)"
     419   show(R2); setring R2; "";
     420
     421   // no intvec given, blocksize given: given blocksize is used:
     422   def R3=extendring(4,"T(","dp(2)",0,r);   // "dp(2)" -> "dp(2)"
     423   show(R3); setring R3; "";
     424
     425   // intvec given: weights and blocksize is derived from given intvec
     426   // (no specification of a blocksize in the given ordstr is allowed!)
     427   // if intvec does not cover all given blocks, the last block is used
     428   // for the remaining variables, if intvec has too many components,
     429   // the last ones are ignored
    434430   intvec v=3,2,3,4,1,3;
    435    extendring("R4",10,"A","ds,ws,Dp,dp",v,0,r);
    436          //v covers 3 blocks: v[1] (=3) : no of components of ws
    437          //next v[1] values (=v[2..4]) give weights
    438          //remaining components of v are used for the remaining blocks
     431   def R4=extendring(10,"A","ds,ws,Dp,dp",v,0,r);
     432   // v covers 3 blocks: v[1] (=3) : no of components of ws
     433   // next v[1] values (=v[2..4]) give weights
     434   // remaining components of v are used for the remaining blocks
    439435   show(R4);
    440    if(system("with","Namespaces")){kill Top::r,Top::R1,Top::R2,Top::R3,Top::R4;}
    441    if (defined(r)) { kill r,R1,R2,R3,R4; }
     436   kill r,R1,R2,R3,R4;
    442437}
    443438///////////////////////////////////////////////////////////////////////////////
  • Singular/LIB/rinvar.lib

    r860475 r6fe3a0  
    11// Last change 10.12.2000 (TB)
    22///////////////////////////////////////////////////////////////////////////////
    3 version="$Id: rinvar.lib,v 1.8 2002-02-19 12:30:16 Singular Exp $";
     3version="$Id: rinvar.lib,v 1.9 2005-04-25 10:13:07 Singular Exp $";
    44category="Invariant theory";
    55info="
     
    9797
    9898  dbPrt = printlevel-voice+2;
    99   dbprint(dbPrt, "Image Group of " + string(Grp) + ", action =  " + string(Gaction));
     99  dbprint(dbPrt, "Image Group of " + string(Grp) + ", action =  "
     100                                   + string(Gaction));
    100101  def RIGB = basering;
    101102  mPoly = minpoly;
     
    104105
    105106  // compute the representation of G induced by Gaction, i.e., a matrix
    106   // of size(Gaction) x size(Gaction) and polynomials in s(1),...,s(r) as entries
     107  // of size(Gaction) x size(Gaction) and polynomials in s(1),...,s(r) as
     108  // entries
    107109  // the matrix is represented as the list 'matrixEntries' where
    108110  // the entries which are always 0 are omittet.
     
    127129
    128130  order = "(dp(" + string(nvars(basering)) + "), dp);";
    129   ringSTR1 = "ring RIGR = (" + charstr(basering) + "), (" + varstr(basering) + ", z(1.." + string(newVars) + "))," + order;
     131  ringSTR1 = "ring RIGR = (" + charstr(basering) + "), (" + varstr(basering)
     132                             + ", z(1.." + string(newVars) + "))," + order;
    130133  execute(ringSTR1);
    131134  minpoly = number(imap(RIGB, mPoly));
     
    138141  // and compute the new action of the image on K^m
    139142
    140   for(i = 1; i <= size(mEntries); i++) { I1[i] = var(i + nvars(RIGB)) - mEntries[i]; }
     143  for(i=1;i<=size(mEntries);i++){ I1[i] = var(i + nvars(RIGB))-mEntries[i]; }
    141144  I1 = std(I1);
    142145
     
    151154  // Gn (contians only z(1..newVars)) to this ring
    152155
    153   ringSTR2 = "ring RIGS = (" + charstr(basering) + "), (s(1.." + string(newVars) + "), t(1.." + string(nrt) + ")), lp;";
     156  ringSTR2 = "ring RIGS = (" + charstr(basering) + "), (s(1.."
     157                     + string(newVars) + "), t(1.." + string(nrt) + ")), lp;";
    154158  execute(ringSTR2);
    155159  minpoly = number(imap(RIGB, mPoly));
     
    159163  // construct the map F : RIGB -> RIGS
    160164
    161   for(i = 1; i <= nvars(RIGB) - nrt; i++) { mapIdeal[i] = 0;}      // s(i) -> 0
     165  for(i=1;i<=nvars(RIGB)-nrt;i++) { mapIdeal[i] = 0;}            // s(i)-> 0
    162166  offset = nvars(RIGB) - nrt;
    163   for(i = 1; i <= nrt; i++) { mapIdeal[i + offset] = var(newVars + i);}    // t(i) -> t(i)
     167  for(i=1;i<=nrt;i++) { mapIdeal[i+offset] = var(newVars + i);}  // t(i)->t(i)
    164168  offset = offset + nrt;
    165   for(i = 1; i <= newVars; i++) { mapIdeal[i + offset] = var(i);}      // z(i) -> s(i)
     169  for(i=1;i<=newVars;i++) { mapIdeal[i + offset] = var(i);}      // z(i)->s(i)
    166170
    167171  // map Gn and newGaction to RIGS
     
    170174  groupid = F(Gn);
    171175  actionid = F(newGaction);
    172   export(groupid);
    173   export(actionid);
    174   dbprint(dbPrt, "
     176  export groupid, actionid;
     177  dbprint(dbPrt+1, "
    175178// 'ImageGroup' created a new ring.
    176 // To see the ring, type (if the name of the ring is R):
     179// To see the ring, type (if the name 'R' was assigned to the return value):
    177180     show(R);
    178 // To access the ideal of the image-group Gn of the group G w.r.t. 'action'
    179 // and the new action of Gn, type
    180      def R = ImageGroup(G, action); setring R;  groupid; actionid;
    181 // 'groupid' is the ideal defining the image of the group G w.r.t. 'action'
    182 // and 'actionid' is the new action of 'groupid'.
     181// To access the ideal of the image of the input group and to access the new
     182// action of the group, type
     183     setring R;  groupid; actionid;
    183184");
     185  setring RIGB;
    184186  return(RIGS);
    185187}
     
    334336  ideal imageid = imap(RAR1, J2);
    335337  export(imageid);
    336      dbprint(dbPrt, "
     338     dbprint(dbPrt+1, "
    337339// 'ImageVariety' created a new ring.
    338 // To see the ring, type (if the name of the ring is R):
     340// To see the ring, type (if the name 'R' was assigned to the return value):
    339341     show(R);
    340 // To access the ideal of the image F(X), where F is a map and X is a variety
    341 // with ideal I,type
    342      def R = ImageVariety(I, F); setring R;  imageid;
    343 // 'imageid' is the ideal of the Zariski closure of F(X).
     342// To access the ideal of the image variety, type
     343     setring R;  imageid;
    344344");
     345  setring RARB;
    345346  return(RAR2);
    346347}
     
    363364ASSUME:  G contains only variables var(1..r) (r = nrs)
    364365basering = K[s(1..r),t(1..m)], K = Q or K = Q(a) and minpoly != 0.
    365 RETURN:  polynomial ring contianing the ideals 'actionid', 'embedid', 'groupid'
     366RETURN:  polynomial ring containing the ideals 'actionid', 'embedid', 'groupid'
    366367         - 'actionid' is the ideal defining the linearized action of G
    367368         - 'embedid' is a parameterization of an equivariant embedding (closed)
     
    371372"
    372373{
     374  def altring = basering;
    373375  int i, j, k, ok, loop, nrt, sizeOfDecomp, dbPrt;
    374376  intvec wt;
     
    404406
    405407    // compute the minimal decomposition of action[i]
    406     // action[i] = decompMx[1,1]*decompMx[2,1] + ... + decompMx[1,k]*decompMx[2,k]
     408    // action[i]=decompMx[1,1]*decompMx[2,1]+ ... +decompMx[1,k]*decompMx[2,k]
    407409    // decompMx[1,j] contains variables var(1)...var(nrs)
    408410    // decompMx[2,j] contains variables var(nrs + 1)...var(nvars(basering))
    409411
    410     dbprint(dbPrt, "  " + string(action[i]) + " is not linear, a minimal decomposition is :");
     412    dbprint(dbPrt, "  " + string(action[i])
     413                   + " is not linear, a minimal decomposition is :");
    411414    decompMx = MinimalDecomposition(action[i], nrs, nrt);
    412415    sizeOfDecomp = ncols(decompMx);
    413416    dbprint(dbPrt, decompMx);
    414417
    415     for(j = 1; j <= sizeOfDecomp; j++) {   // check if decompMx[2,j] is a linear combination of basis elements
     418    for(j = 1; j <= sizeOfDecomp; j++) {   
     419      // check if decompMx[2,j] is a linear combination of basis elements
    416420      actCoeff = decompMx[2, j];
    417421      ok = LinearCombinationQ(basis, actCoeff, nrt + nrs);
     
    420424        // nonlinear element, compute new component of the action
    421425
    422         dbprint(dbPrt, "  the polynomial " + string(actCoeff) + " is not a linear combination of the elements of basis");
     426        dbprint(dbPrt, "  the polynomial " + string(actCoeff)
     427                   + " is not a linear combination of the elements of basis");
    423428        nrt++;
    424         str = charstr(basering) + ", (" + varstr(basering) + ",t(" + string(nrt) + ")),";
     429        str = charstr(basering) + ", (" + varstr(basering)
     430                   + ",t(" + string(nrt) + ")),";
    425431        if(defined(RLAB)) { kill(RLAB);}
    426432        def RLAB = basering;
     
    451457        dbprint(dbPrt, "  extend basering by " + string(var(nrs + nrt)));
    452458        dbprint(dbPrt, "  new basis = " + string(basis));
    453         dbprint(dbPrt, "  action of G on new basis element = " + string(actCoeff));
    454         dbprint(dbPrt, "  decomp : " + string(decompMx[2, j]) + " -> " + string(var(nrs + nrt)));
     459        dbprint(dbPrt, "  action of G on new basis element = "
     460                    + string(actCoeff));
     461        dbprint(dbPrt, "  decomp : " + string(decompMx[2, j]) + " -> "
     462                    + string(var(nrs + nrt)));
    455463      } // end if
    456464      else {
    457         dbprint(dbPrt, "  the polynomial " + string(actCoeff) + " is a linear combination of the elements of basis");
     465        dbprint(dbPrt, "  the polynomial " + string(actCoeff)
     466                    + " is a linear combination of the elements of basis");
    458467      }
    459468    } // end for
     
    464473    else {loop = 0;}
    465474  } // end while
    466   if(defined(actionid)) { kill(actionid); }
     475  if(defined(actionid)) { kill actionid; }
    467476  ideal actionid, embedid, groupid;
    468477  actionid = action;
    469478  embedid = basis;
    470479  groupid = G;
    471   export(actionid);
    472   export(embedid);
    473   export(groupid);
    474 dbprint(dbPrt, "
     480  export actionid, embedid, groupid;
     481dbprint(dbPrt+1, "
    475482// 'LinearizeAction' created a new ring.
    476 // To see the ring, type (if the name of the ring is R):
     483// To see the ring, type (if the name 'R' was assigned to the return value):
    477484     show(R);
    478 // To access the new action and the equivariant embedding, where G and 'action'
    479 // are the original group and group-action contained in K[s(1..ns)] and
    480 // K[s(1..ns),t(1..nt)] respectively, type
    481      def R = LinearizeAction(G, action, ns, nt); setring R; actionid; embedid; groupid
    482 // 'actionid' is the ideal of the linearized action, 'embedid' is the ideal
    483 // defining the equivariant embedding and 'grouid' is the ideal G.
     485// To access the new action and the equivariant embedding, type
     486     setring R; actionid; embedid; groupid
    484487");
     488  setring altring;
    485489  return(RLAR);
    486490}
     
    503507
    504508proc LinearActionQ(Gaction, int nrs)
    505 "USAGE:   LinearActionQ(action,nrs,nrt); ideal action, int nrs
     509"USAGE:   LinearActionQ(action,nrs); ideal action, int nrs
    506510PURPOSE: check if the action defined by 'action' is linear w.r.t. the variables
    507511         var(nrs + 1...nvars(basering)).
     
    533537{"EXAMPLE:";  echo = 2;
    534538  ring R   = 0,(s(1..5), t(1..3)),dp;
    535   ideal G =  s(3)-s(4), s(2)-s(5), s(4)*s(5), s(1)^2*s(4)+s(1)^2*s(5)-1, s(1)^2*s(5)^2-s(5), s(4)^4-s(5)^4+s(1)^2, s(1)^4+s(4)^3-s(5)^3, s(5)^5-s(1)^2*s(5);
    536   ideal Gaction = -s(4)*t(1)+s(5)*t(1), -s(4)^2*t(2)+2*s(4)^2*t(3)^2+s(5)^2*t(2), s(4)*t(3)+s(5)*t(3);
    537   LinearActionQ(Gaction, 5, 3);
     539  ideal G =  s(3)-s(4), s(2)-s(5), s(4)*s(5), s(1)^2*s(4)+s(1)^2*s(5)-1,
     540             s(1)^2*s(5)^2-s(5), s(4)^4-s(5)^4+s(1)^2, s(1)^4+s(4)^3-s(5)^3,
     541             s(5)^5-s(1)^2*s(5);
     542  ideal Gaction = -s(4)*t(1)+s(5)*t(1),
     543                  -s(4)^2*t(2)+2*s(4)^2*t(3)^2+s(5)^2*t(2),
     544                   s(4)*t(3)+s(5)*t(3);
     545  LinearActionQ(Gaction, 5);
     546  LinearActionQ(Gaction, 8);
    538547}
    539548
     
    586595PURPOSE: compute generators of the invariant ring of G w.r.t. the action 'Gact'
    587596ASSUME:  G is a finite group and 'Gact' is a linear action.
    588 RETURN:  polynomial ring over a simple extension of the groundfield of the
    589          basering (the extension might be trivial), containing the ideals
    590          'invars' and 'groupid' and the poly 'newA'
    591          - 'invars' contains the algebra-generators of the invariant ring
     597RETURN:  ring R; this ring comes with the ideals 'invars' and 'groupid' and
     598         with the poly 'newA':
     599         - 'invars' contains the algebra generators of the invariant ring
    592600         - 'groupid' is the ideal of G in the new ring
    593          - 'newA' if the minpoly changes this is the new representation of the
    594            algebraic number, otherwise it is set to 'a'.
    595 NOTE:    the delivered ring might have a different minimal polynomial
     601         - 'newA' is the new representation of the primitive root of the
     602           minimal polynomial of the ring which was active when calling the
     603           procedure (if the minpoly did not change, 'newA' is set to 'a').
     604NOTE:    the minimal polynomial of the output ring depends on some random
     605         choices
    596606EXAMPLE: example InvariantRing; shows an example
    597607"
     
    613623  // compute the nullcone of G by means of Derksen's algorithm
    614624
    615   invarsGens = NullCone(groupid, action);    // compute the nullcone of the linear action
     625  invarsGens = NullCone(groupid, action);  // compute nullcone of linear action
    616626  dbprint(dbPrt, " generators of zero-fibre ideal are " + string(invarsGens));
    617627
    618628  // make all generators of the nullcone invariant
    619629  // if necessary, compute the Reynolds Operator, i.e., find all elements
    620   // of the variety defined by G. It might be necessary to extend the groundfield.
     630  // of the variety defined by G. It might be necessary to extend the
     631  // ground field.
    621632
    622633  def IRB = basering;
     
    624635  def RIRR = basering;
    625636  setring RIRR;
    626   export(RIRR);
    627   export(invarsGens);
     637//  export(RIRR);
     638//  export(invarsGens);
    628639  noReynolds = 1;
    629640  dbprint(dbPrt, " nullcone is generated by " + string(size(invarsGens)));
    630641   dbprint(dbPrt, " degrees = " + string(maxdeg(invarsGens)));
    631642  for(i = 1; i <= ncols(invarsGens); i++){
    632     ok =  InvariantQ(invarsGens[i], groupid, action);
    633     if(ok) { dbprint(dbPrt, string(i) + ": poly " + string(invarsGens[i]) + " is invariant");}
     643    ok = InvariantQ(invarsGens[i], groupid, action);
     644    if(ok) { dbprint(dbPrt, string(i) + ": poly " + string(invarsGens[i])
     645                                      + " is invariant");}
    634646    else {
    635647      if(noReynolds) {
    636648
    637649        // compute the Reynolds operator and change the ring !
    638 
     650        noReynolds = 0;
    639651        def RORN = ReynoldsOperator(groupid, action, primaryDec);
    640         noReynolds = 0;
    641652        setring RORN;
    642         export(RORN);
    643653        ideal groupid = std(id);
    644654        attrib(groupid, "isSB", 1);
    645655        ideal action = actionid;
    646         ideal invarsGens = TransferIdeal(RIRR, "invarsGens", newA);
    647         export(invarsGens);
    648         kill(RIRR);
     656//        ideal invarsGens = TransferIdeal(RIRR, "invarsGens", newA);
     657//        export(invarsGens);
     658// lossen: ersetzt durch
     659        setring RIRR;
     660        string parName, minPoly;
     661        if(npars(basering) == 0) {
     662          parName = "a";
     663          minPoly = "0";
     664        }
     665        else {
     666          parName = parstr(basering);
     667          minPoly = string(minpoly);
     668        }
     669        execute("ring RA1=0,(" + varstr(basering) + "," + parName + "), lp;");
     670        if (minPoly!="0") { execute("ideal mpoly = std(" + minPoly + ");"); }
     671        ideal I = imap(RIRR,invarsGens);
     672        setring RORN;
     673        map Phi = RA1, maxideal(1);
     674        Phi[nvars(RORN) + 1] = newA;
     675        ideal invarsGens = Phi(I);
     676        kill Phi,RA1,RIRR;
     677// end of ersetzt durch     
    649678
    650679      }
    651       dbprint(dbPrt, string(i) + ": poly " + string(invarsGens[i]) + " is NOT invariant");
     680      dbprint(dbPrt, string(i) + ": poly " + string(invarsGens[i])
     681                               + " is NOT invariant");
    652682      invarsGens[i] = ReynoldsImage(ROelements, invarsGens[i]);
    653683      dbprint(dbPrt, " --> " + string(invarsGens[i]));
     
    656686  for(i = 1; i <= ncols(invarsGens); i++){
    657687    ok =  InvariantQ(invarsGens[i], groupid, action);
    658     if(ok) { dbprint(dbPrt, string(i) + ": poly " + string(invarsGens[i]) + " is invariant"); }
     688    if(ok) { dbprint(dbPrt, string(i) + ": poly " + string(invarsGens[i])
     689                                      + " is invariant"); }
    659690    else { print(string(i) + ": Fatal Error with Reynolds ");}
    660691  }
    661   kill(IRB);
    662692  if(noReynolds == 0) {
    663693    def RIRS = RORN;
    664     setring(RIRS);
    665     kill(RORN);export(groupid);
     694    setring RIRS;
     695    kill RORN;
     696    export groupid;
    666697  }
    667698  else {
    668699    def RIRS = RIRR;
    669     kill(RIRR);
    670     setring(RIRS);
    671                 export(groupid);
     700    kill RIRR;
     701    setring RIRS;
     702    export groupid;
    672703  }
    673704  ideal invars = invarsGens;
    674   kill(invarsGens);
    675   export(invars);
    676   // export(groupid);
    677 dbprint(dbPrt, "
     705  kill invarsGens;
     706  if (defined(ROelements)) { kill ROelements,actionid,zeroset,id; }
     707  export invars;
     708  dbprint(dbPrt+1, "
    678709// 'InvariantRing' created a new ring.
    679 // To see the ring, type (if the name of the ring is R):
     710// To see the ring, type (if the name 'R' was assigned to the return value):
    680711     show(R);
    681 // To access the generators of the invariant ring of G w.r.t. the linear
    682 // group-action 'action' of G, where G is contained in K[s(1..ns)] and
    683 // 'action' in K[s(1..ns),t(1..nt)], type
    684      def R = InvariantRing(G, action); setring R; invars;
    685 // 'invars' contains generator of the invariant ring.
    686 // Note that G is containd in R as the ideal 'groupid', to see it, type
     712// To access the generators of the invariant ring type
     713     setring R; invars;
     714// Note that the input group G is stored in R as the ideal 'groupid'; to
     715// see it, type
    687716    groupid;
    688717// Note that 'InvariantRing' might change the minimal polynomial
    689718// The representation of the algebraic number is given by 'newA'
    690719");
     720  setring IRB;
    691721  return(RIRS);
    692722}
     
    715745         1 if f is invariant
    716746NOTE:    G need not be finite
    717 EXAMPLE: example InvariantQ; shows an example
    718 "
    719 {
     747"
     748{
     749  def altring=basering;
    720750  map F;
    721 
    722751  if(deg(f) == 0) { return(1); }
    723752  for(int i = 1; i <= size(action); i++) {
     
    850879  order = "(dp(" + string(nvars(basering) - nt) + "), dp);";
    851880  vars = "(s(1.." + string(nvars(basering) - nt);
    852   vars = vars + "), t(1.." + string(nt) + "), Y(1.." + string(nt) + "))," + order;
    853   ringSTR = "ring RNCR = (" + charstr(basering) +  "),"  + vars; // ring for the computation
     881  vars = vars +"),t(1.."+string(nt) + "), Y(1.." + string(nt) + "))," + order;
     882  ringSTR = "ring RNCR = (" + charstr(basering) +  "),"  + vars;
     883  // ring for the computation
    854884
    855885  minPoly = minpoly;
    856886  offset =  size(G) + nt;
    857887  execute(ringSTR);
    858   minpoly = number(imap(RNCB, minPoly));
     888  def aaa=imap(RNCB, minPoly);
     889  if (aaa!=0) { minpoly = number(aaa); }
    859890  ideal action, G, I, J, N, generators;
    860891  map F;
     
    880911
    881912  // substitute
    882 
    883913  for(i = 1; i <= nvars(basering); i = i + 1) { F[i] = 0; }
    884914  for(i = groupVars + 1; i <= offset; i = i + 1) { F[i] = var(i); }
    885915
    886916  generators = mstd(F(N))[2];
    887         setring(RNCB);
     917  setring RNCB;
    888918  return(fetch(RNCR, generators));
    889919}
     
    901931
    902932proc ReynoldsOperator(ideal Grp, ideal Gaction, list #)
    903 "USAGE:   ReynoldsOperator(G, action [, opt); ideal G, action; int opt
     933"USAGE:   ReynoldsOperator(G, action [, opt]); ideal G, action; int opt
    904934PURPOSE: compute the Reynolds operator of the group G which act via 'action'
    905935RETURN:  polynomial ring R over a simple extension of the groundfield of the
     
    907937         'ROelements', the ideals 'id', 'actionid' and the polynomial 'newA'.
    908938         R = K(a)[s(1..r),t(1..n)].
    909          - 'ROelements'  is a list of ideal, each ideal represents a
     939         - 'ROelements'  is a list of ideals, each ideal represents a
    910940           substitution map F : R -> R according to the zero-set of G
    911941         - 'id' is the ideal of G in the new ring
     
    915945         G is the ideal of a finite group in K[s(1..r)], 'action' is a linear
    916946         group action of G
    917 EXAMPLE: example ReynoldsOperator; shows an example
    918 "
    919 {
     947"
     948{
     949  def ROBR = basering;
    920950  int i, j, n, ns, primaryDec;
    921951  ideal G1 = Grp;
     
    925955  if(size(#) > 0) { primaryDec = #[1]; }
    926956  else { primaryDec = 0; }
     957  kill #;
    927958
    928959  n = nvars(basering);
     
    930961  for(i = ns + 1; i <= n; i++) { G1 = G1, var(i);}
    931962
    932   def ROBR = basering;
    933   export(Grp);
    934   export(Gaction);
    935   def RORN = ZeroSet(G1, primaryDec);
    936   setring RORN;
    937   id = TransferIdeal(ROBR, "Grp", newA);  // defined in ZeroSet ...
    938   ideal actionid = TransferIdeal(ROBR, "Gaction", newA);
     963  def RORR = ZeroSet(G1, primaryDec);
     964//  setring RORR;
     965//  id = TransferIdeal(ROBR, "Grp", newA);  // defined in ZeroSet ...
     966//  ideal actionid = TransferIdeal(ROBR, "Gaction", newA);
     967// lossen: ersetzt durch
     968  setring ROBR;
     969  string parName, minPoly;
     970  if(npars(basering) == 0) {
     971    parName = "a";
     972    minPoly = "0";
     973  }
     974  else {
     975    parName = parstr(basering);
     976    minPoly = string(minpoly);
     977  }
     978  execute("ring RA1=0,(" + varstr(basering) + "," + parName + "), lp;");
     979  if (minPoly!="0") { execute("ideal mpoly = std(" + minPoly + ");"); }
     980  ideal Grp = imap(ROBR,Grp);
     981  ideal Gaction = imap(ROBR,Gaction);
     982  setring RORR;
     983  map Phi = RA1, maxideal(1);
     984  Phi[nvars(RORR) + 1] = newA;
     985  ideal id = Phi(Grp);
     986  ideal actionid = Phi(Gaction);
     987  kill parName,minPoly,Phi,RA1;
     988// end of ersetzt durch   
    939989  list ROelements;
    940990  ideal Rf;
     
    944994  for(i = 1; i <= size(zeroset); i++) {
    945995    groupElem = zeroset[i];    // element of G
    946     for(j = ns + 1; j <= n; j++) { groupElem[j] = var(j); } // do not change t's
     996    for(j = ns + 1; j<=n; j++) { groupElem[j] = var(j); } //do not change t's
    947997    for(j = 1; j <= n - ns; j++) {
    948998      h1 = actionid[j];
     
    9521002    ROelements[i] = Rf;
    9531003  }
    954   export(actionid);
    955   export(ROelements);
    956   return(RORN);
     1004  export actionid, ROelements;
     1005  setring ROBR;
     1006  return(RORR);
    9571007}
    9581008
     
    9661016"
    9671017{
     1018  def RIBR=basering;
    9681019  map F;
    9691020  poly h = 0;
    9701021
    9711022  for(int i = 1; i <= size(reynoldsOp); i++) {
    972     F = basering, reynoldsOp[i];
     1023    F = RIBR, reynoldsOp[i];
    9731024    h = h + F(f);
    9741025  }
     
    10631114///////////////////////////////////////////////////////////////////////////////
    10641115
    1065 static proc TransferIdeal(R, string name, poly newA)
    1066 " USAGE:  TransferIdeal(R, name, newA); ring R, string name, poly newA
    1067 PURPOSE: Maps an ideal with name 'name' in R to the basering, s.t. all
    1068          variables are fixed but par(1) is replaced by 'newA'.
    1069 RETURN:  ideal
    1070 NOTE:    this is used to transfor an ideal if the minimal polynomial has changed
    1071 "
    1072 {
    1073   def RAB = basering;
    1074   def RA1 = TransferRing(R);
    1075 
    1076   setring RA1;
    1077   execute("ideal I = imap(R, " + name + ");");
    1078   setring RAB;
    1079   map F = RA1, maxideal(1);
    1080   F[nvars(RAB) + 1] = newA;
    1081   return(F(I));
    1082 }
    1083 
    1084 ///////////////////////////////////////////////////////////////////////////////
    1085 
    10861116static proc RingVarProduct(index)
    10871117// list of indices
  • Singular/LIB/zeroset.lib

    r860475 r6fe3a0  
    1 // changed 12.02.2001 (Eric Westenberger)
    2 // last change 29.10.2004 (Bayer Thomas, Quotient, QuotientMain)
    3 ///////////////////////////////////////////////////////////////////////////////
    4 version="$Id: zeroset.lib,v 1.10 2005-04-19 15:23:42 Singular Exp $";
     1// Last change 12.02.2001 (Eric Westenberger)
     2///////////////////////////////////////////////////////////////////////////////
     3version="$Id: zeroset.lib,v 1.11 2005-04-25 10:13:07 Singular Exp $";
    54category="Symbolic-numerical solving";
    65info="
    76LIBRARY:  zeroset.lib      Procedures For Roots and Factorization
    8 AUTHOR:   Thomas Bayer,    email: bayert@web.de
    9           http://www14.informatik.tu-muenchen.de/personen/bayert/
     7AUTHOR:   Thomas Bayer,    email: tbayer@mathematik.uni-kl.de
     8          http://wwwmayr.informatik.tu-muenchen.de/personen/bayert/
    109          Current Adress: Institut fuer Informatik, TU Muenchen
    1110
     
    1514 where a is an algebraic number. Written in the frame of the
    1615 diploma thesis (advisor: Prof. Gert-Martin Greuel) 'Computations of moduli
    17  spaces of semiquasihomogeneous singularities and an implementation in
    18  Singular'.
     16 spaces of semiquasihomogeneous singularities and an implementation in Singular'.
    1917 This library is meant as a preliminary extension of the functionality
    2018 of Singular for univariate factorization of polynomials over simple algebraic
     
    2523
    2624PROCEDURES:
    27  EGCD(f, g)      gcd over an algebraic extension field of Q
    28  Factor(f)       factorization of f over an algebraic extension field
    29  Quotient(f, g)  quotient q  of f w.r.t. g (in f = q*g + remainder)
    30  Remainder(f,g)  remainder of the division of f by g
    31  Roots(f)        computes all roots of f in an extension field of Q
    32  SQFRNorm(f)     norm of f (f must be squarefree)
    33  ZeroSet(I)      zero-set of the 0-dim. ideal I
     25 EGCD(f, g)    gcd over an algebraic extension field of Q
     26 Factor(f)    factorization of f over an algebraic extension field
     27 Quotient(f, g)    quotient q  of f w.r.t. g (in f = q*g + remainder)
     28 Remainder(f,g)    remainder of the division of f by g
     29 Roots(f)    computes all roots of f in an extension field of Q
     30 SQFRNorm(f)    norm of f (f must be squarefree)
     31 ZeroSet(I)    zero-set of the 0-dim. ideal I
    3432
    3533AUXILIARY PROCEDURES:
    36  EGCDMain(f, g)       gcd over an algebraic extension field of Q
    37  FactorMain(f)        factorization of f over an algebraic extension field
     34 EGCDMain(f, g)    gcd over an algebraic extension field of Q
     35 FactorMain(f)    factorization of f over an algebraic extension field
    3836 InvertNumberMain(c)  inverts an element of an algebraic extension field
    39  QuotientMain(f, g)   quotient of f w.r.t. g
    40  RemainderMain(f,g)   remainder of the division of f by g
    41  RootsMain(f)         computes all roots of f, might extend the ground field
    42  SQFRNormMain(f)      norm of f (f must be squarefree)
     37 QuotientMain(f, g)  quotient of f w.r.t. g
     38 RemainderMain(f,g)  remainder of the division of f by g
     39 RootsMain(f)    computes all roots of f, might extend the ground field
     40 SQFRNormMain(f)  norm of f (f must be squarefree)
    4341 ContainedQ(data, f)  f in data ?
    44  SameQ(a, b)          a == b (list a,b)
     42 SameQ(a, b)    a == b (list a,b)
    4543";
    4644
     
    4947
    5048// note : return a ring : ring need not be exported !!!
    51 // Arithmetic in Q(a)[x] without built-in procedures
     49
     50// Artihmetic in Q(a)[x] without built-in procedures
    5251// assume basering = Q[x,a] and minpoly is represented by mpoly(a).
    53 // The algorithms are taken from "Polynomial Algorithms in Computer Algebra",
     52// the algorithms are taken from "Polynomial Algorithms in Computer Algebra",
    5453// F. Winkler, Springer Verlag Wien, 1996.
    5554
     
    6968// extension field is represented as Q[x...,a] together with the ideal
    7069// 'mpoly' (attribute "isSB"). The arithmetic in the extension field is
    71 // implemented in the procedures 'MultPolys' (multiplication)
     70// implemented in the procedures in the procedures 'MultPolys' (multiplication)
    7271// and 'InvertNumber' (inversion). After addition and substraction one should
    7372// apply 'SimplifyPoly' to the result to reduce the result w.r.t. 'mpoly'.
     
    106105  def ROR = TransferRing(basering);
    107106  setring ROR;
     107  export(ROR);
    108108
    109109  // get the polynomial f and find the roots
     
    173173"
    174174{
    175   def altring=basering;
    176175  int i, linFactors, nlinFactors, dbPrt;
    177176  intvec wt = 1,0;    // deg(a) = 0
     
    333332  else { primaryDecQ = 0; }
    334333
    335   // create a new ring 'ZSR' with one additional variable instead of the parameter
    336   // if the basering does not contain a parameter then 'a' is used as the additional variable.
     334  // create a new ring 'ZSR' with one additional variable instead of the
     335  // parameter
     336  // if the basering does not contain a parameter then 'a' is used as the
     337  // additional variable.
    337338
    338339  def RZSB = basering;
    339   def ZSR = TransferRing(basering);
     340  def ZSR = TransferRing(RZSB);
    340341  setring ZSR;
    341342
     
    343344
    344345  ideal id = std(imap(RZSB, I));
    345         print(dim(id));
    346         if(dim(id) > 1) {       // new variable adjoined to ZSR
    347                 ERROR(" ideal not zerodimensional ");
    348         }
     346//  print(dim(id));
     347  if(dim(id) > 1) {       // new variable adjoined to ZSR
     348    ERROR(" ideal not zerodimensional ");
     349  }
    349350
    350351  list result = ZeroSetMain(id, primaryDecQ);
     
    356357  poly minPoly = result[3][1];
    357358
    358   // transform the generators of the ideal I w.r.t. the new representation of 'a'
     359  // transform the generators of the ideal I w.r.t. the new representation
     360  // of 'a'
    359361
    360362  map F = basering, maxideal(1);
     
    382384   def R = ZeroSet(I); setring R; zeroset; newA; id;
    383385");
     386  setring RZSB;
    384387  return(RZBN);
    385388}
     
    467470
    468471proc Quotient(poly f, poly g)
    469 "USAGE:   Quotient(f, g); poly f, g;
    470 PUROPSE: compute the quotient q and remainder r s.t. f = g*q + r, deg(r) < g
     472"USAGE:   Quotient(f, g); where f,g are polynomials;
     473PURPOSE: compute the quotient q and remainder r s.t. f = g*q + r, deg(r) < deg(g)
    471474RETURN:  list of polynomials
    472          _[1] = quotient  q
    473          _[2] = remainder r
     475  @format
     476  _[1] = quotient  q
     477  _[2] = remainder r
     478  @end format
    474479ASSUME:  basering = Q[x] or Q(a)[x]
    475480EXAMPLE: example  Quotient; shows an example
    476481"
    477482{
    478         def QUOB = basering;
    479         def QUOR = TransferRing(basering);      // new ring with parameter 'a' replaced by a variable
    480         setring QUOR;
    481         poly f = imap(QUOB, f);
    482         poly g = imap(QUOB, g);
    483         list result = QuotientMain(f, g);
    484 
    485         setring(QUOB);
    486         list result = imap(QUOR, result);
    487         kill(QUOR);
    488         return(result);
    489 }
    490 
     483  def QUOB = basering;
     484  def QUOR = TransferRing(basering);  // new ring with parameter 'a' replaced by a variable
     485  setring QUOR;
     486  export(QUOR);
     487  poly f = imap(QUOB, f);
     488  poly g = imap(QUOB, g);
     489  list result = QuotientMain(f, g);
     490
     491  setring(QUOB);
     492  list result = imap(QUOR, result);
     493  kill(QUOR);
     494  return(result);
     495}
    491496example
    492497{"EXAMPLE:";  echo = 2;
     
    501506
    502507proc QuotientMain(poly f, poly g)
    503 "USAGE:   QuotientMain(f, g); poly f, g
    504 PUROPSE: compute the quotient q and remainder r s.t. f = g*q + r, deg(r) < g
     508"USAGE:   QuotientMain(f, g); where f,g are polynomials
     509PURPOSE: compute the quotient q and remainder r s.t. f = g*q + r, deg(r) < deg(g)
    505510RETURN:  list of polynomials
    506          _[1] = quotient  q
    507          _[2] = remainder r
    508 ASSUME:  basering = Q[x,a] and ideal 'mpoly' is defined (it might be 0),
    509          this represents the ring Q(a)[x] together with 'minpoly'.
     511  @format
     512  _[1] = quotient  q
     513  _[2] = remainder r
     514  @end format
     515ASSUME:  basering = Q[x,a] and ideal mpoly is defined (it might be 0),
     516         this represents the ring Q(a)[x] together with its minimal polynomial.
    510517EXAMPLE: example  Quotient; shows an example
    511518"
    512519{
    513         def altring=basering;
    514         int dg;
    515         intvec wt = 1,0;
    516         list ltList;
    517         poly fn, q, p, lcgInv, lmonog;
    518 
    519         if(g == 0) { ERROR("Division by zero !");}
    520 
    521         ltList = LeadTerm(g, 1);
    522         dg = deg(ltList[2]);
    523         if(dg == 0) {                   // g is a constant
    524                 result[1] = MultPolys(f, InvertNumberMain(g));
    525                 result[2] = 0;
    526                 return(result);
    527         }
    528         fn = f;
    529         q = 0;
    530         lcgInv = InvertNumberMain(ltList[3]);   // inverse of leading coef of g
    531         lmonog = ltList[2];                     // leading monomial of g
    532 
    533         while(deg(fn, wt) >= dg) {              // degree of fn > degree of g
    534                 p = MultPolys(LeadTerm(fn, 1)[1]/lmonog, lcgInv);
    535                 q = SimplifyPoly(q + p);
    536                 fn = SimplifyPoly(fn - MultPolys(p, g));
    537         }
    538         return(list(q, fn));
     520  if(g == 0) { ERROR("Division by zero !");}
     521
     522  def QMB = basering;
     523  def QMR = NewBaseRing();
     524  setring QMR;
     525  poly f, g, h;
     526  h = imap(QMB, f) / imap(QMB, g);
     527  setring QMB;
     528  return(list(imap(QMR, h), 0));
    539529}
    540530
     
    552542  def REMR = TransferRing(basering);  // new ring with parameter 'a' replaced by a variable
    553543  setring(REMR);
     544  export(REMR);
    554545  poly f = imap(REMB, f);
    555546  poly g = imap(REMB, g);
     
    578569"
    579570{
    580   def altring=basering;
    581571  int dg;
    582572  intvec wt = 1,0;;
     
    605595  def GCDR = TransferRing(basering);  // new ring with parameter 'a' replaced by a variable
    606596  setring GCDR;
     597  export(GCDR);
    607598  poly f = imap(GCDB, f);
    608599  poly g = imap(GCDB, g);
     
    674665  execute("poly @f = " + @sf + ";");
    675666  execute("poly @g = " + @sg + ";");
     667  export(@RGCD);
    676668  poly @h = EGCD(@f, @g);
    677669  setring(@RGCDB);
     
    698690{
    699691  def SNB = basering;
    700   def SNR = TransferRing(basering);  // new ring with parameter 'a' replaced by a variable
     692  def SNR = TransferRing(SNB);  // new ring with parameter 'a'
     693                                // replaced by a variable
    701694  setring SNR;
    702695  poly f = imap(SNB, f);
    703696  list result = SQFRNormMain(f);  // squarefree norm of f
    704697
    705   setring(SNB);
     698  setring SNB;
    706699  list result = imap(SNR, result);
    707   kill(SNR);
     700  kill SNR;
    708701  return(result);
    709702}
     
    731724"
    732725{
    733   def altring=basering;
     726  def SNRMB = basering;
    734727  int s = 0;
    735728  intvec wt = 1,0;
     
    741734  mapId[1] = var(1) - var(2);    // linear transformation
    742735  mapId[2] = var(2);
    743   map Fs = basering, mapId;
     736  map Fs = SNRMB, mapId;
    744737
    745738  N = resultant(f, mpoly[1], var(2));  // norm of f
     
    748741
    749742  ringSTR = "ring SNRM1 = 0, " + string(var(1)) + ", dp;";  // univariate ring
    750   def SNRMB = basering;
    751743  execute(ringSTR);
    752744  poly N, N1, h;        // N, N1 do not contain 'a', use built-in gcd
     
    786778  def FRR = TransferRing(basering);  // new ring with parameter 'a' replaced by a variable
    787779  setring FRR;
     780  export(FRR);
    788781  poly f = imap(FRB, f);
    789782  list result = FactorMain(f);  // squarefree norm of f
     
    891884  // transformed according to 'newA', i.e., only bookeeping is done.
    892885
     886  def altring=basering;
    893887  int i, j, n, noMP, dbPrt;
    894888  intvec w;
     
    968962"
    969963{
     964  def altring=basering;
    970965  int i, j, k, nrSols, n, noMP;
    971966  ideal I, generators, gens, solid, partsolid;
     
    10771072"
    10781073{
     1074  def altring=basering;
    10791075  int i, ok, n, found, nrSols;
    10801076  ideal generators, newGens;
     
    11401136
    11411137  def NLZR = basering;
     1138  export(NLZR);
    11421139
    11431140  n = nvars(basering) - 1;
     
    11681165      list roots;
    11691166      poly f = imap(NLZR, f);
     1167      export(RIS1);
    11701168      export(mpoly);
    11711169      roots = RootsMain(f);
     1170
    11721171      // get "old" basering with new minpoly
    11731172
     
    14241423"
    14251424{
     1425  def altring=basering;
    14261426  int n;
    14271427  poly f;
     
    14511451"
    14521452{
     1453  def altring=basering;
    14531454  string ringSTR, parName, minPoly;
    14541455
     
    14681469  execute("ideal mpoly = std(" + minPoly + ");");
    14691470  export(mpoly);
     1471  setring altring;
    14701472  return(TR);
    14711473}
     
    15041506  execute(ringSTR);
    15051507  if(MP) { minpoly = number(imap(BR, mpoly)[1]); }
     1508  setring BR;
    15061509  return(TR);
    15071510}
  • Tst/Long/deform_l.res.gz.uu

    r860475 r6fe3a0  
    11begin 640 deform_l.res.gz
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    80 #/```
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    8196`
    8297end
  • Tst/Long/deform_l.stat

    r860475 r6fe3a0  
    1 1 >> tst_memory_0 :: 1068715858:2003111219:2-0-5:ix86-Linux:nepomuck:411348
    2 1 >> tst_memory_1 :: 1068715858:2003111219:2-0-5:ix86-Linux:nepomuck:1890296
    3 1 >> tst_memory_2 :: 1068715858:2003111219:2-0-5:ix86-Linux:nepomuck:8312824
    4 1 >> tst_timer_1 :: 1068715858:2003111219:2-0-5:ix86-Linux:nepomuck:2640
     11 >> tst_memory_0 :: 1114421867:2005042510:2-1-99:ix86-Linux:nepomuck:23818368
     21 >> tst_memory_1 :: 1114421867:2005042510:2-1-99:ix86-Linux:nepomuck:25373516
     31 >> tst_memory_2 :: 1114421867:2005042510:2-1-99:ix86-Linux:nepomuck:29973324
     41 >> tst_timer_1 :: 1114421867:2005042510:2-1-99:ix86-Linux:nepomuck:2160
  • Tst/Long/deform_l.tst

    r860475 r6fe3a0  
    88ring  r0  = 0,(x,y,z),ls;
    99 ideal i2 = y4-xy,yz-xz,z4-xz;   
    10  versal(i2);kill_rings();
    11 //------------------------------------------------------------------------------
     10 list L=versal(i2);
     11kill L;
     12//-----------------------------------------------------------------------------
    1213ring  r1  = 0,(x,y,z,u),dp;
    1314 ideal i5 = x3-y2,xz,xu,yz,yu,z3-u2;
    14  versal(i5);kill_rings();
     15 list L=versal(i5);
    1516 ideal i6 = z2-xz,zu-xu,u2-yu,yz-xu;
    16  versal(i6);kill_rings();
     17 L=versal(i6); kill L;
    1718//------- cone over rational normal curve ofe degree d -------------------------
    1819 int    d = 4;
     
    2223       i7 = minor(m,2);
    2324       i7 = minbase(i7);
    24  versal(i7);kill_rings();
    25 //------- L_d_d: d generic lines in A^d ________________________________________
     25 list L=versal(i7);
     26 def Px=L[1]; setring Px; Fs; print(Js); print(Rs);
     27 kill L,Px;
     28//------- L_d_d: d generic lines in A^d ---------------------------------------
    2629        d = 4;
    2730ring r3=0,(x(1..d)),ls;
     
    3134 }
    3235        i8 = simplify(i8,10);
    33  versal(i8,3,"myring");kill_rings("myring");
    34 //------- two elliptic singularity  (t1=7 and 13,t2=3) ---------------------------
     36 list L=versal(i8,3,"myring");
     37 def Px=L[1]; setring Px; Fs;
     38 kill L,Px;
     39//------- two elliptic singularity  (t1=7 and 13,t2=3) ------------------------
    3540ring r6   = 0,(x,y,z,u,v,w),ds;
    3641 ideal i9 = uv-zw,u2-yw,zu-yv,yu-xw,xu+v2-uw,yz-xv,y2+v2-uw,xy+zv-yw,x2+z2-yu;
    37  versal(i9);kill_rings();
     42 list L=versal(i9);
     43 def Px=L[1]; setring Px; Fs;
     44 kill L,Px;
    3845ring r7   = 0,(x,y,z,u,v),dp;
    3946 ideal I1 = xy,xz,xu,xv,yz,yu,yv,zu,zv,uv;   
    40  versal(I1);kill_rings();
     47 list L=versal(I1);
     48 def Px=L[1]; setring Px; Fs;
     49 kill L,Px;
     50
    4151ring r8   = 0,(w(1..9)),dp;
    4252 ideal I3 = w(8)^2-w(6)*w(9),
     
    6474            w(2)*w(6)^2-w(3)^2*w(8),
    6575            w(1)*w(6)^2-w(2)*w(3)*w(8);
    66  versal(I3);kill_rings();
    67 kill r0,r1,r2,r3,r6,r7,r8;
     76list L= versal(I3);
     77def Px=L[1]; setring Px; Fs;
     78kill L,Px;
     79kill r0,r1,r2,r3,r6,r7,r8,m,n,d;
    6880//////////////////////////////////////////////////////////////////////////////////
    6981ring   Po = 0,(x,y),dp;
     
    8597{
    8698  Mo=m(i');
    87   mod_versal(Mo,Io);
    88   kill_rings();
     99  list L=mod_versal(Mo,Io);
     100  def Qx=L[2];
     101  print(Ms);
     102  print(Ls);
     103  print(Js);
     104  kill L,Qx;
    89105}
    90 mod_versal(m(2),Io,4,"qq","W","dp","oo");
     106list L=mod_versal(m(2),Io,4,"qq","W","dp","oo");
     107def Px=L[1]; def Qx=L[2]; def So=L[3]; def Ox=L[4];
    91108listvar(ring);
    92 qqQx;
     109show(Qx);
    93110tst_status(1);$
  • Tst/Long/mre.res.gz.uu

    r860475 r6fe3a0  
    11begin 640 mre.res.gz
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    52475239`
    52485240end
  • Tst/Long/mre.stat

    r860475 r6fe3a0  
    1 1 >> tst_memory_0 :: 998562788:2001082217:2-0-2:ix86-Linux-libc5:monty.mathematik.uni-kl.de:181112
    2 1 >> tst_memory_1 :: 998562788:2001082217:2-0-2:ix86-Linux-libc5:monty.mathematik.uni-kl.de:3491876
    3 1 >> tst_memory_2 :: 998562788:2001082217:2-0-2:ix86-Linux-libc5:monty.mathematik.uni-kl.de:9316388
    4 1 >> tst_timer_1 :: 998562788:2001082217:2-0-2:ix86-Linux-libc5:monty.mathematik.uni-kl.de:10564
     11 >> tst_memory_0 :: 1114422339:2005042510:2-1-99:ix86-Linux:nepomuck:3327096
     21 >> tst_memory_1 :: 1114422339:2005042510:2-1-99:ix86-Linux:nepomuck:5077836
     31 >> tst_memory_2 :: 1114422339:2005042510:2-1-99:ix86-Linux:nepomuck:9349964
     41 >> tst_timer_1 :: 1114422339:2005042510:2-1-99:ix86-Linux:nepomuck:3541
  • Tst/Long/mre.tst

    r860475 r6fe3a0  
    180180I;
    181181kill r;
    182 LIB "tst.lib";tst_status(1);$;
     182tst_status(1);$;
  • Tst/Long/mre_nonhom.res.gz.uu

    r860475 r6fe3a0  
    11begin 640 mre_nonhom.res.gz
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    16231615`
    16241616end
  • Tst/Long/mre_nonhom.stat

    r860475 r6fe3a0  
    1 1 >> tst_memory_0 :: 982765924:2001022113:2-0-0:ix86-Linux:nepomuck:149960
    2 1 >> tst_memory_1 :: 982765924:2001022113:2-0-0:ix86-Linux:nepomuck:791772
    3 1 >> tst_memory_2 :: 982765924:2001022113:2-0-0:ix86-Linux:nepomuck:6583516
    4 1 >> tst_timer_1 :: 982765924:2001022113:2-0-0:ix86-Linux:nepomuck:2707
     11 >> tst_memory_0 :: 1114423311:2005042510:2-1-99:ix86-Linux:nepomuck:963528
     21 >> tst_memory_1 :: 1114423311:2005042510:2-1-99:ix86-Linux:nepomuck:2366284
     31 >> tst_memory_2 :: 1114423311:2005042510:2-1-99:ix86-Linux:nepomuck:6585164
     41 >> tst_timer_1 :: 1114423311:2005042510:2-1-99:ix86-Linux:nepomuck:2601
  • Tst/Long/mre_nonhom.tst

    r860475 r6fe3a0  
    5656I;
    5757kill cyc5;
    58 LIB "tst.lib";tst_status(1);$;
     58tst_status(1);$;
  • Tst/Long/ok_l.lst

    r860475 r6fe3a0  
    3434mre
    3535mre_nonhom
    36 Mregular
    3736pAdd0L_l
    3837pAdd0_l
  • Tst/Long/rinvar.tst

    r860475 r6fe3a0  
    88// email : bayert@in.tum.de
    99//
    10 // Last change 10.12.2000
    11 //
    12 // written in the frame of the diploma thesis (advisor: Prof. Gert-Martin Greuel)
    13 // "Computations of moduli spaces of semiquasihomogenous singularities and an
    14 //  implementation in Singular"
    15 // Arbeitsgruppe Algebraische Geometrie, Fachbereich Mathematik,
    16 // Universitaet Kaiserslautern
     10// Last change 10.12.2000
    1711///////////////////////////////////////////////////////////////////////////////
    1812
     
    2115
    2216tst_init();
    23 tst_ignore("CVS ID $Id: rinvar.tst,v 1.1 2000-12-11 16:07:30 Singular Exp $");
     17tst_ignore("CVS ID $Id: rinvar.tst,v 1.2 2005-04-25 10:11:18 Singular Exp $");
    2418 
    2519
  • Tst/Long/zeroset1.res.gz.uu

    r860475 r6fe3a0  
    11begin 640 zeroset1.res.gz
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