Re: Determinant function in Mathematica

*To*: mathgroup <mathgroup at yoda.physics.unc.edu>*Subject*: Re: Determinant function in Mathematica*From*: HAY at leicester.ac.uk*Date*: Thu, 16 APR 92 19:08:25 GMT

Here's some quicker V2.0 code (though it is still looks to less than 2/3 the speed of Det in Version 1.2 - I don't have a copy of V1.2 to hand to check this }. NewDet[M_] := Plus@@Times@@( Append[Transpose[Transpose[M[[#]],{1,1}]&/@#],Signature/@#]&@ Permutations[Range[Length[M]]] ) Transpose[M,{1,1}] is very quick at extracting the diagonal of M. Here are the timimgs on a Mac IIfx using Oliver Gloor's tests a[n_] := Table[ StringJoin["a",ToString[i],ToString[j]], {i,1,n},{j,1,n}] 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 Using the system Det I get Do[ Print[ First[ Timing[ Det[ a[t]]]]], {t,1,7}] 0.2 Second 0.633333 Second 0.883333 Second 2.01667 Second 13.5 Second 199.317 Second $Aborted For a DEC Risc larry reported the following timings for Det. 0.0166667 Second 0.0666667 Second 0.266667 Second 1. Second 5.76667 Second 70.65 Second Interrupt> a [Sorry, I couldn't afford the 45 minutes!] BUT on the same machine with Version 1.2 he gets much shorter times 0. 0.0166667 Second 0.0166667 Second 0.0666667 Second 0.216667 Second 1.25 Second 9.78333 Second From Allan Hayes Department of Mathematics The University Leicester LE1 7RH U.K. hay at leicester.ac.uk