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Controlling inverses of functions


I've got some functions (Tensor's actually) which aren't trivially
inverted and I want to either control their inverse form, or prevent
mathematica from inverting them altogether, so that I can use Solve
in safety on expressions containing them.  Is there anyway of doing
that?

For example:

    In: F[a] == F[b] F[c]
    In: Solve[%, F[b]]
    Out: {F[b] -> F[a] / F[c]}

This is incorrect because 1 / F[c] is an invalid statement (as the
inverse isn't defined).  The "correct" answer is that an answer can't be
derived.

Any help on this would be wonderful.

Thanks,
Joe
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