#############################################################################
##
#W  determinant.tst                                           Robert F. Morse
##  
##
#H  $Id: determinant.tst,v 1.4 2001/11/23 13:32:50 unialg Exp $ 
##
##  
##
gap> START_TEST("$Id: determinant.tst,v 1.4 2001/11/23 13:32:50 unialg Exp $");
gap> ########################################################################
gap> ## Test strategy: 
gap> ##   Fix a commutative ring, 
gap> ##   create (randomly) a Vandermonde matrix over that ring,
gap> ##   compute the determinant analytically and then via the 
gap> ##   fraction or division-free method and compare results.
gap> ##
gap> ## Integers
gap> ##
gap> n:=5;;
gap> r := Integers;
Integers
gap> ## Vandermonde Matrix
gap>  _X := List([1..n],z->Random(r));; 
gap> M := List(_X,x->List([0..n-1],y->x^y));;
gap> VD := Product(List(Filtered(Cartesian([1..n],[1..n]), x->x[1]<x[2]), x->_X[x[2]]-_X[x[1]]));;
gap> D := DeterminantMatDivFree(M);;
gap> VD=D;
true
gap> ## GaussianIntegers
gap> ##
gap> r := GaussianIntegers;
GaussianIntegers
gap> ## Vandermonde Matrix
gap> _X := List([1..n],z->Random(r));; 
gap> M := List(_X,x->List([0..n-1],y->x^y));;
gap> VD := Product(List(Filtered(Cartesian([1..n],[1..n]), x->x[1]<x[2]), x->_X[x[2]]-_X[x[1]]));;
gap> D := DeterminantMatDivFree(M);;
gap> VD=D;
true
gap> ##
gap> ## Group ring
gap> ##
gap> r := GroupRing(Integers,CyclicGroup(10));;
gap> _X := List([1..n],z->Random(r));; 
gap> M := List(_X,x->List([0..n-1],y->x^y));;
gap> VD := Product(List(Filtered(Cartesian([1..n],[1..n]), x->x[1]<x[2]), x->_X[x[2]]-_X[x[1]]));;
gap> D := DeterminantMatDivFree(M);;
gap> VD=D;
true
gap> ##
gap> ## polynomial ring
gap> ##
gap> r := PolynomialRing(Integers);;
gap> x := IndeterminatesOfPolynomialRing(r)[1];;
gap> _X := List([1..n],z->Random(Integers)*x^Random(Integers));;
gap> M := List(_X,x->List([0..n-1],y->x^y));;
gap> VD := Product(List(Filtered(Cartesian([1..n],[1..n]), x->x[1]<x[2]), x->_X[x[2]]-_X[x[1]]));;
gap> D := DeterminantMatDivFree(M);;
gap> VD=D;
true
gap> STOP_TEST( "determinant.tst", 1000000000 );

#############################################################################
##
#E  determinant.tst . . . . . . . . . . . . . . . . . . . . . . . . ends here