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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