Better inequalities with integer variables #23771

oscargus · 2022-07-13T13:01:03Z

References to other Issues or PRs

Inspired by #22066 (comment)

Brief description of what is fixed or changed

Inequalities where at least one side is integer are now simplified in a better way. E.g. x < pi is turned into x <= 3.

Other comments

Release Notes

core
- Inequalities with integer variables are better simplified.

sympy-bot · 2022-07-13T13:01:12Z

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- Inequalities with integer variables are better simplified. (#23771 by @oscargus)

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Inspired by https://github.com/sympy/sympy/issues/22066#issuecomment-1166413191

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

Inequalities where at least one side is integer are now simplified in a better way. E.g. x < pi is turned into x <= 3.


#### Other comments


#### Release Notes

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   * Inequalities with integer variables are better simplified.
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oscargus · 2022-07-13T15:23:17Z

This needs more thinking. Currently:

n = Symbol('n', integer=True)
(Eq(n, 2) | (n>= 3)).simplify()

gives

(Eq(n, 2) | Eq(n, 3) | (n>= 4))

Which breaks a test.

smichr · 2022-07-14T16:21:10Z

Could you do the following with Or having a mix of equalities and inequalities?

create a Union of Intervals with Eq(x, i) -> Interval.open(i-1,i+1), Gt(x, i) -> Interval(i+1,oo), etc...
convert result back to relational Union(Interval(2,3),Interval(5,oo)).as_relational(i) and do whatever canonicalization you wish knowing that contiguous ints are now combined

asmeurer · 2022-07-16T20:48:16Z

sympy/core/relational.py

+        r = self.reversed._eval_simplify(**kwargs)
+        r = r.canonical
+        measure = kwargs['measure']
+        if measure(r) < kwargs['ratio'] * measure(self):


Doesn't the recursive _eval_simplify already do this?

If I do not include this, the last test here will fail:

sympy/sympy/core/tests/test_relational.py

Lines 732 to 736 in 68bd362

# canonical operations are not the same as simplification,

# so if there is no simplification, canonicalization will

# be done unless the measure forbids it

assert simplify(r) == r.canonical

assert simplify(r, ratio=0) != r.canonical

But I agree that it is a bit of a mess to include it everywhere...

asmeurer · 2022-07-16T20:51:37Z

sympy/core/relational.py

@@ -1130,6 +1130,34 @@ def _eval_fuzzy_relation(cls, lhs, rhs):
    def strict(self):
        return Gt(*self.args)

+    def _eval_simplify(self, **kwargs):
+        # standard simplify
+        eorg = e = super()._eval_simplify(**kwargs)


Is this really necessary? What is the superclass _eval_simplify in this case?

I went with the similar approach as in Equality. I'd expect Relational to be the superclass.

I didn't notice that method existed. Any reason this logic shouldn't go there?

asmeurer · 2022-07-16T20:52:14Z

sympy/core/relational.py

+        lhs_is_int = e.lhs.is_integer
+        rhs_is_int = e.rhs.is_integer
+        r = e
+        if lhs_is_int is True:


Are all the cases here represented in the tests?

I think so.

asmeurer · 2022-07-16T20:52:53Z

sympy/core/relational.py

+        if lhs_is_int is True:
+            if rhs_is_int is True:
+                if e.lhs.is_number:
+                    r = Ge(e.lhs - 1, e.rhs)


I guess it's subjective, but I wonder if it would be better to put use e.rhs <= e.lhs - 1 so that the number is on the right-hand side.

The reason is that this is a Ge to start with, so returns it like that. Then, there is a canonical call anyway further down.

asmeurer · 2022-07-16T20:54:23Z

This seems to have let to a test failure

________________________________________________________________________________
__________ sympy/concrete/tests/test_sums_products.py:test_issue_2787 __________
Traceback (most recent call last):
  File "/home/runner/work/sympy/sympy/sympy/concrete/tests/test_sums_products.py", line 980, in test_issue_2787
    assert res == ans.subs(x, p/Abs(p - 1) <= 1)
AssertionError

asmeurer · 2022-07-16T20:56:06Z

I'm not a fan of the _eval_simplify method (see #19281 and #23609), but the changes here use it as well as they can. The simplifications themselves look fine, although I also wonder how well code like this would scale given other types of simplifications that we might want to do. A more general method will be needed for simplifying inequalities at some point.

oscargus · 2022-07-19T14:05:33Z

A more general method will be needed for simplifying inequalities at some point.

Indeed. I see this primarily as "bounds tightening", which can be beneficial for a more general method as well.

oscargus added simplify core.relational labels Jul 13, 2022

Better relational with integer variables

ce083bf

oscargus force-pushed the integerrelationals branch from 3c5f97f to ce083bf Compare July 13, 2022 13:16

oscargus modified the milestone: SymPy 1.11 Jul 13, 2022

asmeurer reviewed Jul 16, 2022

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oscargus marked this pull request as draft July 19, 2022 14:02

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Better inequalities with integer variables #23771

Better inequalities with integer variables #23771

oscargus commented Jul 13, 2022

sympy-bot commented Jul 13, 2022

oscargus commented Jul 13, 2022

smichr commented Jul 14, 2022

asmeurer Jul 16, 2022

oscargus Jul 19, 2022

oscargus Jul 19, 2022

asmeurer Jul 16, 2022

oscargus Jul 19, 2022

asmeurer Jul 19, 2022

asmeurer Jul 16, 2022

oscargus Jul 19, 2022

asmeurer Jul 16, 2022

oscargus Jul 19, 2022

asmeurer commented Jul 16, 2022

asmeurer commented Jul 16, 2022 •

edited

oscargus commented Jul 19, 2022

	# canonical operations are not the same as simplification,
	# so if there is no simplification, canonicalization will
	# be done unless the measure forbids it
	assert simplify(r) == r.canonical
	assert simplify(r, ratio=0) != r.canonical

Better inequalities with integer variables #23771

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Better inequalities with integer variables #23771

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oscargus commented Jul 13, 2022

References to other Issues or PRs

Brief description of what is fixed or changed

Other comments

Release Notes

sympy-bot commented Jul 13, 2022

oscargus commented Jul 13, 2022

smichr commented Jul 14, 2022

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asmeurer commented Jul 16, 2022

asmeurer commented Jul 16, 2022 • edited

oscargus commented Jul 19, 2022

asmeurer commented Jul 16, 2022 •

edited