Dear Forum, dear Mathieu, Great! It seems to work excellent!
Mathieu: What are my right for using this? Is this code going to be included in some GAP package? Can I include it (also) in my package PL (which is still in its "pre-alpha" stage, but the work will hopefully go faster soon when a graduate student of mine grows a bit more mature :) ), with a proper indication who its author is? Igor 31.08.2011, 20:02, "Mathieu Dutour" <mathieu.dut...@ens.fr>: > Right now, no as far as I know. > > But meanwhile, there is a way to compute polynomially by some > analog of the row column operations for the determinant. > > See below some code: > # operation Li <--> Lj and Ci <--> Cj if ThePerm=(i,j) > PermutationRowColumn:=function(TheMat, ThePerm) > local NewMat, i; > NewMat:=[]; > for i in [1..Length(TheMat)] > do > Add(NewMat, Permuted(TheMat[i], ThePerm)); > od; > return Permuted(NewMat, ThePerm); > end; > > # operations, Lj <- alpha*Lj and Cj<-alpha*Cj > RowColumnMultiplication:=function(TheMat, j, alpha) > local NewMat, i; > NewMat:=[]; > for i in [1..Length(TheMat)] > do > if i<>j then > Add(NewMat, TheMat[i]); > else > Add(NewMat, alpha*TheMat[i]); > fi; > od; > for i in [1..Length(TheMat)] > do > NewMat[i][j]:=alpha*NewMat[i][j]; > od; > return NewMat; > end; > > # operations, Li<- Li+alpha Lj > # operations, Ci<- Ci+alpha Ci > AdditionRowColumn:=function(TheMat, i, j, alpha) > local NewMat, k; > NewMat:=[]; > for k in [1..Length(TheMat)] > do > if k=i then > Add(NewMat, TheMat[i]+alpha*TheMat[j]); > else > Add(NewMat, TheMat[k]); > fi; > od; > for k in [1..Length(NewMat)] > do > NewMat[k][i]:=NewMat[k][i]+alpha*NewMat[k][j]; > od; > return NewMat; > end; > > Pfaffian:=function(MatInput) > local i, m, p, piv, zero, pfaff, j, k, sgn, row, row2, mult, mult2, result, > AntiSymMat; > AntiSymMat:=StructuralCopy(MatInput); > m:=Length(AntiSymMat); > if m mod 2=1 then > return 0; > fi; > p:=m/2; > zero:=Zero(AntiSymMat[1][1]); > pfaff:=1; > sgn:=1; > for k in [1..p] > do > j:=2*k; > while j<=m and AntiSymMat[2*k-1][j]=zero > do > j:=j+1; > od; > if j>m then > return zero; > fi; > if j<> 2*k then > AntiSymMat:=PermutationRowColumn(AntiSymMat, (j,2*k)); > sgn:=-sgn; > fi; > row:=AntiSymMat[2*k]; > piv:=row[2*k-1]; > for j in [2*k+1..m] > do > row2:=AntiSymMat[j]; > mult:=-row2[2*k-1]; > # > AntiSymMat:=RowColumnMultiplication(AntiSymMat, j, piv); > # > AntiSymMat:=AdditionRowColumn(AntiSymMat, j, 2*k, mult); > # > row2:=AntiSymMat[j]; > mult2:=row2[2*k]/piv; > AntiSymMat:=AdditionRowColumn(AntiSymMat, j, 2*k-1, mult2); > # > AntiSymMat:=RowColumnMultiplication(AntiSymMat, j, Inverse(pfaff)); > od; > pfaff:=-piv; > od; > result:=pfaff; > for k in [1..p-1] > do > result:=result/AntiSymMat[2*k-1][2*k]; > od; > return sgn*result; > end; > > On Wed, Aug 31, 2011 at 06:24:12PM +0400, Igor Korepanov wrote: > >> Dear Forum, >> >> does GAP calculate a Pfaffian? And with the right sign? And for a big >> antisymmetric matrix with indeterminates? >> >> I will be grateful for any advice. >> >> Currently, I found the letter >> http://mail.gap-system.org/pipermail/forum/2006/001324.html >> from Mathieu Dutour Sikiric whom I am sending a personal copy of this >> letter. >> >> Igor _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
