[GiNaC-list] matrix::solve()-related problems

[Vitaly Magerya]

On 01/18/2018 03:19 PM, Vladimir V. Kisil wrote:
>     From time to time I am asking myself either .is_zero() needs to call
>   .normal() first and then make the test. This would look more natural
>   in my opinion.

It will, but usually if you've called normal() on something you don't
want to throw the result away, you want to store it. This is because
normal() is slow (GCDs and stuff). Auto-normal()ing in is_zero() and
throwing away the result is a waste, and can be a major performance hit
for some applications.

On a related note: when testing for zero you don't really need the full
normal() calculation, which involves canceling common divisors of
numerator and denominator -- you can keep those in; if you have any in
the final result, then the expression is not a zero anyway. Basically,
there's a place for normal() equivalent which never calls gcd().

On another related note: there's a flag that tells you if an expression
is expanded (status_flag::expanded), which presumably exists so that
expand() repeated twice would be a quick no-op. There's no such flag for
normal() though, and I'd argue it's much more needed there than in
expand(). With such a flag you could pretty much put normal() all over
the place without fearing for wasted computation: performance-minded
code would have already normal()ized whatever it's passing into
is_zero() and the like, so no performance penalty there, and more
careless code would get the benefit of always obtaining correct results
even when it forgot to normal()ize it's expressions.