Changeset 816868 in git for Singular/LIB/qmatrix.lib


Ignore:
Timestamp:
May 9, 2005, 12:31:30 PM (19 years ago)
Author:
Viktor Levandovskyy <levandov@…>
Branches:
(u'spielwiese', '4a9821a93ffdc22a6696668bd4f6b8c9de3e6c5f')
Children:
f6c9006209a9d3dd56eda544c0153792c2522afd
Parents:
eb716b0a6899ddce95c849b7761d45f58580c170
Message:
*levandov: corrected and update documentation for Plural libs


git-svn-id: file:///usr/local/Singular/svn/trunk@8105 2c84dea3-7e68-4137-9b89-c4e89433aadc
File:
1 edited

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  • Singular/LIB/qmatrix.lib

    reb716b0 r816868  
    1 version="$Id: qmatrix.lib,v 1.10 2005-05-06 14:39:06 hannes Exp $";
     1version="$Id: qmatrix.lib,v 1.11 2005-05-09 10:31:30 levandov Exp $";
    22category="Noncommutative";
    33info="
    44LIBRARY: qmatrix.lib     Quantum matrices, quantum minors and symmetric groups
    55AUTHORS: Lobillo, F.J.,  jlobillo@ugr.es
    6 @*         Rabelo, C.,     crabelo@ugr.es
     6@*       Rabelo, C.,     crabelo@ugr.es
    77
    88SUPPORT: 'Metodos algebraicos y efectivos en grupos cuanticos', BFM2001-3141, MCYT, Jose Gomez-Torrecillas (Main researcher).
    99
    1010MAIN PROCEDURES:
    11 quant(n, [p]);                generates the quantum matrix ring of order n;
     11quantMat(n, [p]);          generates the quantum matrix ring of order n;
    1212qminor(u, v, nr);          calculate a quantum minor of a quantum matrix
    1313
    1414AUXILIARY PROCEDURES:
    15 SymGroup(n);                  generates an intmat containing S(n), each row is an element of S(n)
     15SymGroup(n);                generates an intmat containing S(n), each row is an element of S(n)
    1616LengthSymElement(v);        calculates the length of the element v of S(n)
    17 LengthSym(M);                calculates the length of each element of M, being M a subset of S(n)
     17LengthSym(M);               calculates the length of each element of M, being M a subset of S(n)
    1818";
    1919
    … …  
    2323
    2424proc SymGroup(int n)
    25 "USAGE:   SymGroup(n); n an integer, n>0
    26 PURPOSE: present the symmetric group S(n) via integer vectors
     25"USAGE:   SymGroup(n); n an integer (positive)
    2726RETURN:  intmat
     27PURPOSE: represent the symmetric group S(n) via integer vectors (permutations)
    2828NOTE:    each row of the output integer matrix is an element of S(n)
    29 SEE ALSO: LengthSym, LengthSymElement;
     29SEE ALSO: LengthSym, LengthSymElement
    3030EXAMPLE: example SymGroup; shows examples
    3131"{
    … …  
    7979
    8080proc LengthSymElement(intvec v)
    81 "USAGE:   LengthSymElement(v); v an intvec representing an element of S(n)
     81"USAGE:  LengthSymElement(v); v intvec
     82RETURN:  int
    8283PURPOSE: determine the length of v
    83 RETURN:  int
    84 NOTE:    if v doesn't represent an element of S(n), the output may have no sense
     84ASSUME:  v represents an element of S(n); otherwise the output may have no sense
    8585SEE ALSO: SymGroup, LengthSym
    8686EXAMPLE: example LengthSymElement; shows examples
    … …  
    108108
    109109proc LengthSym(intmat M)
    110 "USAGE:   LengthSym(M); M an intmat representing a subset of S(n) (each row must be an element of S(n))
    111 PURPOSE: determine a vector, which i-th element is the length of the i-th row of M
     110"USAGE:   LengthSym(M); M an intmat
    112111RETURN:  intvec
    113 NOTE:    If M is not a subset of S(n), the output may not have meaning
     112PURPOSE: determine a vector, where the i-th element is the length of the i-th row of M
     113ASSUME: M represents a subset of S(n) (each row must be an element of S(n)); otherwise, the output may have no sense
    114114SEE ALSO: SymGroup, LengthSymElement
    115115EXAMPLE: example LengthSym; shows examples
    … …  
    129129{
    130130  "EXAMPLE:";echo=2;
    131   def M=SymGroup(3);
    132   M;
     131  def M = SymGroup(3); M;
    133132  LengthSym(M);
    134133}
    … …  
    136135///////////////////////////////////////////////////////////////////////////////
    137136
    138 proc quant(int n, list #)
    139 "USAGE:   quant(n [, p]); n integer (n>1), p an optional integer
    140 PURPOSE: compute the quantum matrix ring of order n;
     137proc quantMat(int n, list #)
     138"USAGE:   quantMat(n [, p]); n integer (n>1), p an optional integer
    141139RETURN:  ring (of quantum matrices). If p is specified, the quantum parameter q
    142 @*       will be specialized at p-th root of unity
    143 NOTE:    You have to activate this ring with the 'setring' command.
     140@*       will be specialized at the p-th root of unity
     141PURPOSE: compute the quantum matrix ring of order n
     142NOTE:    activate this ring with the 'setring' command.
    144143@*       The usual representation of the variables in this quantum
    145 @*         algebra is not used because double indexes are not allowed
    146 @*         in the variables. Instead the variables are listed reading
    147 @*         the rows of the usual matrix representation.
     144@*       algebra is not used because double indexes are not allowed
     145@*       in the variables. Instead the variables are listed by reading
     146@*       the rows of the usual matrix representation.
    148147SEE ALSO: qminor
    149 EXAMPLE: example quant; shows examples
     148EXAMPLE: example quantMat; shows examples
    150149"{
    151150  if (n>1)
    … …  
    207206{
    208207  "EXAMPLE:"; echo=2;
    209   def r=quant(2); // generate O_q(M_2) at q generic
     208  def r = quantMat(2); // generate O_q(M_2) at q generic
    210209  setring r;   r;
    211210  kill r;
    212   def r=quant(2,5); // generate O_q(M_2) at q^5=1
     211  def r = quantMat(2,5); // generate O_q(M_2) at q^5=1
    213212  setring r;   r;
    214213}
    … …  
    217216
    218217proc qminor(intvec I, intvec J, int nr)
    219 "USAGE:        qminor(I,J,nr); where
    220 @*      I is the ordered list of the rows to consider in the minor,
    221 @*      J is the ordered list of the columns to consider in the minor and
    222 @*      nr is the order of the quantum matrix algebra you are working with (quant(nr)).
    223 RETURN: poly, the quantum minor.
    224 NOTE:    I and J must have the same number of elements.
    225 SEE ALSO: quant
     218"USAGE:        qminor(I,J,n); I,J intvec, n int
     219RETURN: poly, the quantum minor
     220ASSUME: I is the ordered list of the rows to consider in the minor,
     221@*      J is the ordered list of the columns to consider in the minor,
     222@*      I and J must have the same number of elements,
     223@*      n is the order of the quantum matrix algebra you are working with (quantMat(n)).
     224SEE ALSO: quantMat
    226225EXAMPLE: example qminor; shows examples
    227226"{
    … …  
    255254example
    256255{
    257   "EXAMPLE: Let r be the quantum matrix of order 3."; echo=2;
    258   def r=quant(3); setring r;
    259   intvec u=1,2;
    260   intvec v=2,3;
    261   intvec w=1,2,3;
     256  "EXAMPLE:";
     257  echo=2;
     258  def r = quantMat(3); // let r be a quantum matrix of order 3
     259  setring r;
     260  intvec u = 1,2;
     261  intvec v = 2,3;
     262  intvec w = 1,2,3;
    262263  qminor(w,w,3);
    263264  qminor(u,v,3);
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