FUNCTION:  partitions[agcrank] - The Andrews-Garvan crank of a partition
 
CALLING SEQUENCE:  agcrank(ptn)
 
PARAMETERS:    ptn -  partition (list of integers)
                   -  
SYNOPSIS:  
   agcrank(ptn) returns the Andrews-Garvan crank of the partition ptn
                    
EXAMPLES:  
                    
> with(combinat):
> with(partitions):
> ptn6:=partition(6):
> interface(rtablesize=11):
> PMAT:=Matrix(11,3):
> for j from 1 to 11 do ptn:=ptn6[j]:
> PMAT[j,1]:=ptn:
> PMAT[j,2]:=agcrank(ptn):
> PMAT[j,3]:=modp(agcrank(ptn),11):
> od:
> print(PMAT);
                        [[1, 1, 1, 1, 1, 1]    -6     5]
                        [                              ]
                        [ [1, 1, 1, 1, 2]      -4     7]
                        [                              ]
                        [   [1, 1, 2, 2]       -2     9]
                        [                              ]
                        [    [2, 2, 2]          2     2]
                        [                              ]
                        [   [1, 1, 1, 3]       -3     8]
                        [                              ]
                        [    [1, 2, 3]          1     1]
                        [                              ]
                        [      [3, 3]           3     3]
                        [                              ]
                        [    [1, 1, 4]         -1    10]
                        [                              ]
                        [      [2, 4]           4     4]
                        [                              ]
                        [      [1, 5]           0     0]
                        [                              ]
                        [       [6]             6     6]

DISCUSSION:  
   We compute the crank and crank mod 11 of each partition of 6
   Observe there is exactly one partition for each reside of
   the crank mod 11
                    
SEE ALSO:  drank