On Sunday, June 3, 2018 at 9:56:01 PM UTC+10, Simon King wrote:
>
> On 2018-06-03, Simon King <simon...@uni-jena.de <javascript:>> wrote:
> > Hi Travis,
> >
> > On 2018-06-03, Travis Scrimshaw <tsc...@ucdavis.edu <javascript:>>
> wrote:
> >> I am also generally in favor of having == being a (generally) fast
> check.
> >> However, the symbolics code takes the opposite approach: it has the
> method
> >> is_trivial_equal() for quick checks but == fires up the proof engine.
> >
> > No, that's not correct.
> >
> > For symbolics, "==" only does trivial checks
>
> That's not correct either. "==" apparently always returns an equation,
> not a bool.
>
>
Sorry, I was thinking of in the context of evaluating a boolean statement
(such as "if x == y"). However, when checking the truth value of an
expression, it does fire up the full engine:
sage: x = var('x')
sage: f = sin(x)^2 + cos(x)^2
sage: f
cos(x)^2 + sin(x)^2
sage: %timeit bool(f == 1)
10 loops, best of 3: 22.2 ms per loop
sage: %timeit f.is_trivially_equal(1)
The slowest run took 11394.28 times longer than the fastest. This could
mean that an intermediate result is being cached.
1000000 loops, best of 3: 1.67 µs per loop
sage: bool(f == 1)
True
sage: f.is_trivially_equal(1)
False
If it was doing something trivial, both outputs would be the same and there
would be far less time taken to evaluate the bool.
Best,
Travis
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