mpz_invert behavior -addendum

[Benjamin Eltzner]

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>> * The return value of mpz_invert is wrongly different from 0,
>> when the inverse cannot be calculated (cf. documentation, section
>> 5.9). In the example, the modulus by 1 yields 0, which cannot be
>> inverted. Thus, the result should be 0 but is 1.
> 
> https://gmplib.org/gmp6.0.html
> 
> First item of the changes in 6.0.0:
> 
> * The function mpz_invert now considers any number invertible in
> Z/1Z.
> 
> (because 0 * x == 1 modulo 1 whatever x)

To make my discomfort clearer: note that all of the following are "true"

a) for all n: 0 * n = 0 mod 1    (rop = indef, return = 0)
b) for all n: 0 * n = 1 mod 1    (rop = 0, return != 0)
c) for all n: 1 * n = 0 mod 1    (rop = indef, return = 0)
d) for all n: 1 * n = 1 mod 1    (rop = 1, return != 0)

I would consider a) conventional and a) and d) self-consistent in that
the single element of the zero ring is cast in a consistent role in
the whole expression. Your current implementation goes with b) which
chooses the single element of the zero ring once in its "zero-role"
and once in its "one-role".

I can imagine there has been a lot of discussion around this and you
are probably tired of the issue, so I would just like to ask you to
please update your documentation. (However, should you choose to
reconsider, I would be very glad if you reverted the behavior to case a).)

Best regards,
Benjamin
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