Determinant function in Mathematica

*To*: mathgroup <mathgroup at yoda.physics.unc.edu>*Subject*: Determinant function in Mathematica*From*: HAY at leicester.ac.uk*Date*: Sat, 18 APR 92 11:35:30 GMT

Here's a speed up of my earlier code; obtained by exploiting Transpose better. The moral seems to be to work globally on large list constructions- Think big I guess. NewDet2[M_] := Plus@@Times@@( Append[Transpose[Transpose[M[[#]]&/@#,{1,2,2}]],Signature/@#]&@ Permutations[Range[Length[M]]] ) The timings on my MacIIfx are a[n_] := Table[ StringJoin["a",ToString[i],ToString[j]], {i,1,n},{j,1,n}] Do[ Print[ First[ Timing[ NewDet2[ a[t]]]]], {t,1,7}] 0.0666667 Second 0.0833333 Second 0.133333 Second 0.283333 Second 0.933333 Second 5.13333 Second 38.1833 Second The timings for the previous form (NewDet) were Do[ Print[ First[ Timing[ NewDet[ a[t]]]]], {t,1,7}] 0.25 Second 0.0833333 Second 0.15 Second 0.3 Second 1.06667 Second 5.91667 Second 43.9333 Second From Allan Hayes Department of Mathematics The University Leicester LE1 7RH U.K. hay at leicester.ac.uk