share/matrix/pfaff.mac

   1 ttyoff:true$
   2 pfaffian(integ,list):=block([sgn:-1,ans:0,pdum,ldum],
   3   if not (listp(list)
   4           and integerp(integ)
   5           and integ>0
   6           and length(list)=integ*(integ+1)/2)
   7   then error((errexp:[integ,list],"invalid arg to pfaffian.merrexp holds the offending expression.")),
   8   if integ =1 then return(first(list)),
   9   if evenp(integ)
  10   then return(0),
  11   if integ = 3
  12   then return(list[1]*list[6]-list[2]*list[5]+list[3]*list[4])
  13   else for kzero thru integ do
  14         ans:ans+
  15             inpart(list,kzero)*(sgn:-sgn)*
  16                 pfaffian(integ-2,
  17                          rest(inpart(list,
  18                                      apply('allbut,
  19                                            if listp(pdum:pfaffm[integ,kzero])
  20                                            then pdum
  21                                            else pfaffm[integ,kzero]:(ldum:(kzero+1)*(2*integ-kzero)/2,
  22                                                                      pdum:[],
  23                                                                      if kzero#1 then for mdum:2 thru kzero do
  24                                                                        pdum:endcons(kzero+(mdum-1)*(2*integ-mdum)/2,pdum),
  25                                                                      for mdum:kzero*(2*integ-kzero+1)/2+1 thru ldum do
  26                                                                        pdum:endcons(mdum,pdum),
  27                                                                      pdum))),integ)),
  28   ans)$
  29 ttyoff:false$