qpa-version-1.30/lib/moduledecomp.gi

101     local map, semi, simp, cents, prims, i;
109         simp := FLMLORByGenerators( LeftActingDomain(a), BasisVectors(Basis(semi*i)));
110         SetParent(simp, a);
111         SetOne(simp, i);
112         SetMultiplicativeNeutralElement(simp, i);
113         SetFilterObj(simp, IsAlgebraWithOne);
114         prims := Concatenation(prims,PrimitiveIdempotents(simp));
126 ##  such that  <M>  is isomorphic to the direct sum of the modules on
157 ##  such that  <M>  is isomorphic to the direct sum of the images of the
187 ##  This function is an extension of above version of DecomposeModule
242 ##  if  M_i  is isomorphic to M_1 for  i in [2..t], removing those
245 ##  rest, and continue as above until rest is empty.
307 ##  <f>  is nilpotent, this function returns an idempotent  e  in the
341 …Error("entered map is not a IsAlgebraGeneralMapping or the entered element is not in the range of …
352 ##  the range of  <f>, such that the kernel of  <f>  is nilpotent and
355 ##  that  \{v, e\}  is a pair of orthogonal idempotents in the source of
393 ##  where each  Im e_i  is isomorphic to  X_i^{n_i}  for some
432 ##  where each  M_i  is isomorphic to  X_i^{n_i}  for some
449 ##  that is, if  <M> \simeq M_1^{n_1} \oplus \cdots \oplus M_t^{n_t}
450 ##  where  M_i  is indecomposable, then  M_1\oplus \cdots \oplus M_t
451 ##  is returned. At present, this function only work at best for
453 ##  field. If  <M>  is zero, then  <M> is returned.
480 ##  does this as long as it finds such elements.  The output is not
482 ##  sum is isomorphic to the entered module  M. This was constructed as
485 ##  This is an experimental function, so use with caution.
499         Error( "The entered module is not over a finite field.\n" );