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# 4. The algorithm

Here we give the "pseudo"-code of the algorithm.

INPUT: (A,A') - a pair of representation matrices of modules M,M'
OUTPUT: (X0,Y0) - a pair of transformation matrices if M,M' are isomorphic and FALSE otherwise

A := minimize(A)
A' := minimize(A')
IF (size(A)size(A')) THEN return FALSE END
M := transformation(A,A')
Mc := constant_part(M)
F := det_of_linear_combination(Mc)
IF (F==0) THEN return FALSE END
P := point_outside_surface(F)
IF ( ) THEN return FALSE END
(X0,Y0) := linear_comb(M,P)
return (X0,Y0)

The procedure computes the vector space of all constant transformations depending on the ordering as described above. Note, that in case a point P exists whenever whereas in this must not be true. It follows the code of the main subprocedure - the other are selfevident.

INPUT: as above
OUTPUT: M - the module of all solutions of XA-A'Y=0, where every column is of dimension m2+n2 and represents a pair of matrices (X,Y)

:= kontra_hom(A)
:= ko_hom(A')
C := concat( )
M := syz(C)
return M

Next: Bibliography Up: An algorithm for constructing Previous: 3.2 The global homogeneous
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