Changeset 2a4328 in git


Ignore:
Timestamp:
Mar 19, 2004, 4:52:30 PM (20 years ago)
Author:
Viktor Levandovskyy <levandov@…>
Branches:
(u'spielwiese', 'e7cc1ebecb61be8b9ca6c18016352af89940b21a')
Children:
72391bbb1d0acd8a82fe089b6bb86b8c7e773a73
Parents:
b3082aecde5b2bf7ac5652c2bd96123ae61d04a9
Message:
*levandov: lieA renamed to ncalg


git-svn-id: file:///usr/local/Singular/svn/trunk@7099 2c84dea3-7e68-4137-9b89-c4e89433aadc
File:
1 moved

Legend:

Unmodified
Added
Removed

  • Singular/LIB/ncalg.lib

    • Property mode changed from 100755 to 100644
    rb3082ae r2a4328  
    11///////////////////////////////////////////////////////////////////////////////
    2 version="$Id: lieA.lib,v 1.6 2004-03-18 21:34:54 levandov Exp $";
    3 category="Plural: Lie Theory";
     2version="$Id: ncalg.lib,v 1.1 2004-03-19 15:52:29 levandov Exp $";
     3category="Noncommutative";
    44info="
    55LIBRARY:  lieA.lib      definitions of important G-algebras
    66AUTHORS:  Viktor Levandovskyy,     levandov@mathematik.uni-kl.de,
    7 @*        Oleksandr Khomenko,      Oleksandr.Khomenko@math.uni-freiburg.de,
    8 @*        Oleksandr Motsak,        motsak@mathematik.uni-kl.de
    9 
     7          Oleksandr Khomenko,      Oleksandr.Khomenko@math.uni-freiburg.de,
     8          Oleksandr Motsak,        motsak@mathematik.uni-kl.de
    109
    1110PROCEDURES:
    12  A (n[,p]);               returns U(A(n))=U(sl_{n+1}) in char p, if an integer p is given,
    13  sl(n[,p]);               returns U(sl_n) in char p, if an integer p is given,
    14  sl2([ p]);               returns U(sl_2) in the {e,f,h} presentation; in char p, if an integer p is given,
    15  g2 ([ p]);               returns U(g_2) in the {x(i),y(i),Ha,Hb} presentation; in char p, if an integer p is given,
    16  gl3([ p]);               returns U(gl_3) in the {e_ij (1<i,j<3)} presentation; in char p, if an integer p is given,
     11sl(n[,p]);   returns U(sl_n) in char p, if an integer p is given,
     12sl2([p]);    returns U(sl_2) in the (e,f,h) presentation; in char p, if an integer p is given,
     13g2([p]);     returns U(g_2) in the (x(i),y(i),Ha,Hb) presentation; in char p, if an integer p is given,
     14gl3([p]);    returns U(gl_3) in the (e_ij (1<i,j<3)) presentation; in char p, if an integer p is given,
     15Qso3([n]);   returns U_q(so_3) in the presentation of Klimyk, if integer n is given, the quantum parameter will be specialized at the n-th root of unity,
     16Qsl3([n]);   returns ring, corresponding to the U_q(sl_3) as the factor algebra of V_q(sl3), if integer n is given, the quantum parameter q will be specialized at the n-th root of unity,
     17
     18ALIAS PROCEDURES:
     19A(n[,p]);   returns U(A(n))=U(sl_(n+1)) in char p, if an integer p is given.
    1720";
    1821
    19 
     22LIB "nctools.lib";
    2023///////////////////////////////////////////////////////////////////////////////
    2124
    … …  
    2831  {
    2932    kill @@@_RING_NAME;
    30   };
     33  }
    3134 
    3235  if (string(#) != "0")
    3336  {
    3437    string @@@_RING_NAME = @baseName + "_" + string(#);
    35   } else
     38  }
     39  else
    3640  {
    3741    string @@@_RING_NAME = @baseName;
    38   };
     42  }
    3943  export(@@@_RING_NAME);
    4044 
    … …  
    4246  {
    4347    kill @@@_RING;
    44   };
     48  }
    4549 
    4650  string @@@_RING = "" + @baseName +"(" + string(#) + ")";
    … …  
    5054  {
    5155    kill @@@_CHAR;
    52   };
     56  }
    5357 
    5458  int @@@_CHAR = char(basering);
    … …  
    6266  {
    6367    return( @@@_RING );
    64   };
    65  
     68  }
    6669  return( "No lieA.lib ring defined" );
    6770}
    … …  
    7376  {
    7477    return( @@@_RING_NAME );
    75   };
     78  }
    7679 
    7780  return( "No lieA.lib ring defined" );
    … …  
    8487  {
    8588    return( @@@_CHAR );
    86   };
     89  }
    8790 
    8891  return( char(basering) );
    … …  
    135138"USAGE:   sl(n,[p]); n an integer, n>1; p an optional integer (field characteristic)
    136139RETURN:  a ring, describing U(sl_n)
    137 NOTE:    You have to activate this ring with the "setring" command.
    138          The presentation of U(sl_n) is derived from the
    139          standard representation of sl_n, positive
    140          resp. negative roots are denoted by x(i) resp. y(i),
    141          the Cartan elements are denoted by h(i).
    142 SEE ALSO: sl2
     140NOTE:    You have to activate this ring with the "setring" command. The presentation of U(sl_n) is derived from the standard representation of sl_n, positive resp. negative roots are denoted by x(i) resp. y(i); Cartan elements are denoted by h(i).
     141SEE ALSO: sl2, g2, gl3, Qsl3, Qso3
    143142EXAMPLE: example sl; shows examples
    144143"{
    … …  
    177176    }
    178177  }
    179  
    180178  for(k=1; k<=n-1; k++)
    181179  {
    … …  
    204202            D[k,l]=D[k,l]+leadcoef(TMP[i,j])*x(buf);
    205203          }
    206          
    207204          if (TMP[j,i]!=0)
    208205          {         
    … …  
    210207          }
    211208        }
    212       } 
     209      }
    213210      i=1;
    214       while ((TMP[i,i]==0)&&(i<n)) {i++;}
     211      while ( (TMP[i,i]==0) && (i<n) ) { i++; }
    215212      for(j=i; j<=n-1; j++)
    216213      {
    … …  
    221218        TMP[j+1,j+1]=TMP[j+1,j+1]+p;
    222219      }
    223      
    224220    }
    225221  }
    226222  ncalgebra(1,D);
    227   mySetRing("sl", n, #); 
     223  mySetRing("sl", n, #);
    228224  return(@@@rr);
    229225}
    … …  
    238234
    239235proc A(int n, list #)
    240 "USAGE:   A(n,[p]); n an integer, n>1; , p an optional integer (field characteristic)
     236"USAGE:   A(n,[p]); n an integer, n>1, p an optional integer (field characteristic)
    241237RETURN:  a ring, describing U(A(n))
    242 NOTE:    You have to activate this ring with the setring command.
    243          The presentation of U(A(n)) is derived from the
    244          standard representation of sl(n+1), positive
    245          resp. negative roots are denoted by x(i) resp. y(i),
    246          the Cartan elements are denoted by h(i).
    247 SEE ALSO: sl2, g2, gl3
     238NOTE:    You have to activate this ring with the setring command. The presentation of U(A(n)) is derived from the standard representation of sl(n+1), positive resp. negative roots are denoted by x(i) resp. y(i), the Cartan elements are denoted by h(i).
     239SEE ALSO: sl2, g2, gl3, Qsl3, Qso3
    248240EXAMPLE: example A; shows examples
    249241"{
    … …  
    254246  }
    255247  def @@@a=sl(n+1, #);
    256   mySetRing("A", n, #);
    257248  return(@@@a);
    258249}
    259250example
    260251{ "EXAMPLE:"; echo = 2;
    261  def a2=A(2);
     252   def a2 = A(2);
    262253   setring a2;
    263254   a2;
    … …  
    267258
    268259proc g2(list #)
    269 
    270 "USAGE:   g2([p]), p an optional integer (field characteristic)
     260"USAGE:  g2([p]), p an optional integer (field characteristic)
    271261RETURN:  ring, corresponding to the U(g_2) in (x(i),y(i),Ha,Hb) presentation
    272262NOTE:    you have to activate this ring with the "setring" command
    … …  
    394384proc Qso3(list #)
    395385"USAGE:   Qso3([n]), n an optional integer
    396 RETURN:  ring, corresponding to the U'_q(so_3) in the presentation of Klimyk;
    397 if n is specified, the quantum parameter Q will be specialized at the (2*n)-th root of unity
     386RETURN:  ring, corresponding to the U_q(so_3) in the presentation of Klimyk; if n is specified, the quantum parameter Q will be specialized at the (2*n)-th root of unity
    398387NOTE:    you have to activate this ring with the "setring" command
    399 SEE ALSO: sl, Qsl3, g2, gl3
     388SEE ALSO: sl, g2, gl3, Qsl3
    400389EXAMPLE: example Qso3; shows examples
    401 "
    402 {
    403   int @p = myInt(#);   
     390"{
     391  int @p = myInt(#);
     392  @p = 2*@p;
    404393  ring @@@r=(0,Q),(x,y,z),dp;
    405   minpoly = RootOfUnity(2*p);
     394  minpoly = RootOfUnity(@p);
    406395  matrix C[3][3];
    407   matrix D[3][3];
    408  
    409396  C[1,2]=Q2;
    410397  C[1,3]=1/Q2;
    411398  C[2,3]=Q2;
    412  
     399  matrix D[3][3];
    413400  D[1,2]=-Q*z;
    414401  D[1,3]=1/Q*y;
    415402  D[2,3]=-Q*x;
    416  
    417403  ncalgebra(C,D);
    418404  mySetRing("Qso3", #);
    419405  return(@@@r);
    420406}
     407example
     408{ "EXAMPLE:"; echo = 2;
     409   def K = Qso3(3);
     410   setring K;
     411   K;
     412}
    421413       
    422414///////////////////////////////////////////////////////////////////////////////
    … …  
    424416proc Qsl3(list #)
    425417"USAGE:   Qsl3([n]), n an optional integer
    426 RETURN:  ring, corresponding to the U_q(sl_3) as the factor algebra of
    427 V_q(sl3); if n is specified, the quantum parameter q will be specialized at the n-th root of unity
     418RETURN:  ring, corresponding to the U_q(sl_3) as the factor algebra of V_q(sl3); if n is specified, the quantum parameter q will be specialized at the n-th root of unity
    428419NOTE:    you have to activate this ring with the "setring" command
    429420SEE ALSO: sl, Qso3, g2, gl3
    430421EXAMPLE: example Qso3; shows examples
    431 "
    432 {
     422"{
    433423  int @p = myInt(#);
    434424  //   ring @@@rrr=(@p, q), (f12, f13, f23, k1, k2, l1, l2, e12, e13, e23), wp(7, 10, 11, 1, 1, 1, 1, 7, 10, 11);
    … …  
    517507  return(@@qr);
    518508}
    519 
    520 ///////////////////////////////////////////////////////////////////////////////
     509example
     510{ "EXAMPLE:"; echo = 2;
     511   def L = Qsl3(3);
     512   setring L;
     513   L;
     514}
     515
     516///////////////////////////////////////////////////////////////////////////////
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