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• core

  • is_neq now takes assumptions (#21203 by @JSS95)

  • Eq and Ne can be refined by predicates such as Q.positive, Q.zero, etc. (#21203 by @JSS95)

This will be added to https://github.com/sympy/sympy/wiki/Release-Notes-for-1.9.

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#### Brief description of what is fixed or changed

Fix handler for `Q.extended_real`
Allow `is_neq` to take assumptions.
Apply the change from #21235 to `Q.eq` and `Q.neq`.

In the future, facts will modified so that assuming binary predicates such as `x != y` or `x > y` can return the appropriate result.

#### Other comments

#### Release Notes

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  * Added a new solver for logarithmic equations.

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<!-- BEGIN RELEASE NOTES -->
* core
  * `is_neq` now takes assumptions
  * `Eq` and `Ne` can be refined by predicates such as `Q.positive`, `Q.zero`, etc.
<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

@oscarbenjamin

Inspired by your comment in #21055, I came up with the design to implement refine logic without having duplicate code. The idea is to pass different getter functions as parameter. In obj.__new__, getter function which uses old assumption system (e.g. x.is_zero) is passed for faster evaluation. In ask() and refine(), getter function which uses new assumption system is passed in order to take local assumptions into account.

I tried with that approach here to let ask(Q.eq(x,0), Q.zero(x)) return True. Please review this PR. If this looks OK, I think other refine logic can be changed in this way to remove the duplication.

I have thought about something like this. We do need to be clear about whether it does slow some things down though e.g.:

In [12]: x = S.Zero

In [13]: getter = lambda obj, key: getattr(obj, 'is_%s' % key)

In [14]: %timeit x.is_zero
86.7 ns ± 0.865 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)

In [15]: %timeit getter(x, 'zero')
785 ns ± 60.3 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)

Also the approach here requires putting getter everywhere in the logic which makes the code messy.

Another approach I thought about was to make a wrapper class that wraps an object with assumptions and then presents the interface of the old assumptions e.g.:

def func(obj, assumptions=None):
    objq = AssumptionsWrapper(obj, assumptions):
    if objq.is_positive:
        ...

The idea here is that if assumptions are not given then AssumptionsWrapper can just return the object unmodified so that is_positive is exactly as fast as it would be otherwise. If assumptions are given then an AssumptionsWrapper instance is returned with methods like:

def _eval_is_positive(self):
    return ask(Q.positive(self.obj), self.assumptions)

That is an interesting idea. I will open a discussion i mailing list.

@oscarbenjamin
Please check the discussion I opened : https://groups.google.com/u/3/g/sympy/c/0NStDt45U-s

This PR is an improvement of what was introduced in #21235. I will wait for a few days for review and merge this.