Changeset 5bc4ee3 in git


Ignore:
Timestamp:
Apr 27, 2005, 9:32:14 PM (18 years ago)
Author:
Viktor Levandovskyy <levandov@…>
Branches:
(u'jengelh-datetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', 'a800fe4b3e9d37a38c5a10cc0ae9dfa0c15a4ee6')
Children:
8647dd78e27cd22cb1d534128af44420765ce382
Parents:
06d5e10cda81b8b254f3c4e329dd70a92415fcd6
Message:
*levandov: better documentation and examples


git-svn-id: file:///usr/local/Singular/svn/trunk@7918 2c84dea3-7e68-4137-9b89-c4e89433aadc
Location:
Singular/LIB
Files:
2 edited

Legend:

Unmodified
Added
Removed

  • Singular/LIB/gkdim.lib

    r06d5e10 r5bc4ee3  
    11///////////////////////////////////////////////////////////////////////////////
    2 version="$Id: gkdim.lib,v 1.6 2005-02-23 18:10:45 levandov Exp $";
     2version="$Id: gkdim.lib,v 1.7 2005-04-27 19:32:14 levandov Exp $";
    33category="Noncommutative";
    44info="
    … …  
    4747proc GKdim(list L)
    4848"USAGE:   GKdim(L);   L is a left ideal/module/matrix
    49 RETURN:  int, the Gelfand-Kirillov dimension of the factor-module, whose presentation is given by L
     49PURPOSE: compute the Gelfand-Kirillov dimension of the factor-module, whose presentation is given by L
     50RETURN:  int
    5051NOTE:  if the factor-module is zero, -1 is returned
    5152EXAMPLE: example GKdim; shows examples

  • Singular/LIB/involut.lib

    r06d5e10 r5bc4ee3  
    1 version="$Id: involut.lib,v 1.2 2005-02-23 18:10:45 levandov Exp $";
     1version="$Id: involut.lib,v 1.3 2005-04-27 19:32:14 levandov Exp $";
    22category="Noncommutative";
    33info="
    … …  
    1717find_invo_diag();     describes a variety of homothetic (diagonal) involutions on a basering;
    1818find_auto();          describes a variety of linear automorphisms of a basering;
    19 ncdetection(ring r);  computes an ideal, presenting an involution map on some classical noncommutative algebras;
    20 involution(m, map theta);  applies the involution, presented by theta, to the object m =
     19ncdetection(ring r);  computes an ideal, presenting an involution map on some particular noncommutative algebras;
     20involution(m, map theta);  applies the involution to an object.
    2121";
    2222
    … …  
    2727proc ncdetection(def r)
    2828"USAGE:  ncdetection(r), r a ring
    29 RETURN:  ideal, presenting an involution map on a noncommutative algebra r
    30 NOTE:    returns optimized involutions for some classical noncomm algebras,
    31 arising in the Control Theory, namely algebras with
    32 differential, shift or advance operators
     29PURPOSE: compute optimized involutions for some particular noncommutative algebras
     30RETURN:  ideal (presenting an involution map)
     31NOTE:    the procedure is aimed at noncommutative algebras with differential, shift or advance operators arising in the Control Theory
    3332EXAMPLE: example ncdetection; shows an example
    34 "
    35 {
     33"{
    3634// in this procedure an involution map is generated from the NCRelations
    3735// that will be used in the function involution
    … …  
    272270RETURN:  object of the same type as m
    273271EXAMPLE: example involution; shows an example
    274 "
    275 {
     272"{
    276273  // applies the involution map theta to m,
    277274  // where m= vector, polynomial, module, matrix, ideal
    … …  
    411408RETURN: a ring together with a list of pairs L, where
    412409@*        L[i][1]  =  Groebner Basis of an i-th associated prime,
    413 @*        L[i][2]  =  multiplication matrix, reduced wrt L[i][1]
    414 NOTE: for convenience, the full ideal of relations 'idJ'
    415 and the matrix with indeterminates 'matD' are exported in the output ring.
    416 "
    417 {
     410@*        L[i][2]  =  matrix, defining a linear map, with entries, reduced with respect to L[i][1]
     411NOTE: for convenience, the full ideal of relations @code{idJ}
     412and the initial matrix with indeterminates @code{matD} are exported in the output ring.
     413"{
    418414  def @B    = basering; //save the name of basering
    419415  int NVars = nvars(@B); //number of variables in basering
    … …  
    503499  matrix IM = @@D;     // involution map
    504500  list L    = list();  // the answer
    505   list TL;
     501  list TL;
     502  ideal tmp = 0;
    506503  for (i=1; i<=sL; i++) // compute GBs of components
    507504  {
    508505    TL    = list();
    509506    TL[1] = std(mL[i]);
    510     TL[2] = NF( ideal(IM), TL[1] );
     507    tmp   = NF( ideal(IM), TL[1] );
     508    TL[2] = matrix(tmp, NVars,NVars);
    511509    L[i]  = TL;
    512510  }
    … …  
    521519{ "EXAMPLE:"; echo = 2;
    522520 def a = CreateWeyl(1);
    523  setring a;
     521 setring a; // this algebra is a first Weyl algebra
    524522 def X = find_invo();
    525  setring X;
     523 setring X; // ring with new variables, corresponding to unknown coefficients
    526524 L;
     525 print(L[1][2]);  // L[i][2] is a matrix in new variables, defining the linear involution
     526 L[1][1];  // where new variables obey these relations
    527527}
    528528///////////////////////////////////////////////////////////////////////////
    … …  
    532532RETURN: a ring together with a list of pairs L, where
    533533@*        L[i][1]  =  Groebner Basis of an i-th associated prime,
    534 @*        L[i][2]  =  multiplication matrix, reduced wrt L[i][1]
    535 NOTE: for convenience, the full ideal of relations 'idJ'
    536 and the matrix with indeterminates 'matD' are exported in the output ring.
    537 "
    538 {
     534@*        L[i][2]  =  matrix, defining a linear map, with entries, reduced with respect to L[i][1]
     535NOTE: for convenience, the full ideal of relations @code{idJ}
     536and the initial matrix with indeterminates @code{matD} are exported in the output ring.
     537"{
    539538  def @B    = basering; //save the name of basering
    540539  int NVars = nvars(@B); //number of variables in basering
    … …  
    626625  list L = list(); // the answer
    627626  list TL;
    628   for (i=1; i<=sL; i++)// compute GBs of components
     627  ideal tmp = 0;
     628  for (i=1; i<=sL; i++) // compute GBs of components
    629629  {
    630630    TL    = list();
    631631    TL[1] = std(mL[i]);
    632     TL[2] = NF( ideal(IM), TL[1] );
     632    tmp   = NF( ideal(IM), TL[1] );
     633    TL[2] = matrix(tmp, NVars,NVars);
    633634    L[i]  = TL;
    634   } 
     635  }
    635636  export(L);
    636637  ideal idJ = J; // debug-comfortable exports
    … …  
    643644{ "EXAMPLE:"; echo = 2;
    644645 def a = CreateWeyl(1);
    645  setring a;
     646 setring a; // this algebra is a first Weyl algebra
    646647 def X = find_invo_diag();
    647  setring X;
    648  L;
     648 setring X; // ring with new variables, corresponding to unknown coefficients
     649 print(L[1][2]);  // a first matrix, defining the linear involution: we see it is constant
     650 print(L[2][2]);  // and a second possible matrix; it is constant too
     651 L; // let us take a look on the whole list
    649652}
    650653/////////////////////////////////////////////////////////////////////
    … …  
    653656PURPOSE: describes a variety of linear automorphisms of a basering
    654657RETURN: a ring together with a list of pairs L, where
    655 @*           L[i][1]  =  Groebner Basis of an i-th associated prime,
    656 @*           L[i][2] = multiplication matrix, reduced wrt L[i][1]
    657 NOTE: for convenience, the full ideal of relations 'idJ'
    658 and the matrix with indeterminates 'matD' are exported in the output ring.
    659 "
    660 {
     658@*        L[i][1]  =  Groebner Basis of an i-th associated prime,
     659@*        L[i][2]  =  matrix, defining a linear map, with entries, reduced with respect to L[i][1]
     660NOTE: for convenience, the full ideal of relations @code{idJ}
     661and the initial matrix with indeterminates @code{matD} are exported in the output ring.
     662"{
    661663  def @B    = basering; //save the name of basering
    662664  int NVars = nvars(@B); //number of variables in basering
    … …  
    747749  list L = list(); // the answer
    748750  list TL;
     751  ideal tmp = 0;
    749752  for (i=1; i<=sL; i++)// compute GBs of components
    750753  {
    751754    TL    = list();
    752755    TL[1] = std(mL[i]);
    753     TL[2] = NF( ideal(IM), TL[1] );
     756    tmp   = NF( ideal(IM), TL[1] );
     757    TL[2] = matrix(tmp,NVars, NVars);
    754758    L[i]  = TL;
    755759  }
    … …  
    764768{ "EXAMPLE:"; echo = 2;
    765769 def a = CreateWeyl(1);
    766  setring a;
     770 setring a; // this algebra is a first Weyl algebra
    767771 def X = find_auto();
    768  setring X;
    769  L;
    770 }
     772 setring X; // ring with new variables, corresponding to unknown coefficients
     773 print(L[1][2]);  // a first matrix, defining the linear automorphism : we see it is constant
     774 print(L[2][2]);  // and a second possible matrix; it is constant too
     775 L; // let us take a look on the whole list
     776}
Note: See TracChangeset for help on using the changeset viewer.