Fixcomparisons #1209

mmatera · 2021-03-30T00:34:42Z

In this PR I included several fixes for the Equal symbol. This pass all the tests I could imagine, but the implementation is not very elegant...

mmatera · 2021-03-30T13:59:20Z

Well, here I will try to explain what is what we have now, why I do not think that we can have a more general framework to avoid the if's and what I think could be improved in the future.

Equal tries to determine if two or more expressions are "equivalent". So, two expression objects with the same head and the same leaves are "equal", as it can be check by calling the same method of BaseExpression.
When the expressions are not the same (let's say Pi and 4 ArcTan[1]), then the specialization is needed:

For a couple of exact numbers, (integers, rational), or complex numbers with exact real and imaginary parts, the comparison should be exact, and resolved by sympy by exact methods.
For pairs of atoms (numbers, Image, and any other possible object that should be handled as a single thing), except symbols (which are also atoms) comparison is performed using the __eq__ method of the corresponding classes.
The only case in which a couple of different symbols should be explicitly compared are True!=False and False!=True.
Lists are equal if they are element by element.
As equality of two compiled functions are defined by their first two arguments, but not by the result of the compilation, we need to handle in an especial way too.
The rest of the cases that can be compared are expressions that can be evaluated to numbers, or expressions involving Infinity, ComplexInfinity, and DirectedInfinity. This should rely on sympy. However, Sympy does not handle properly expressions with complex values or infinity values, so these special cases must be preprocessed.

Also, we need to take into account that this routine is one in which relies on many of the computations of the kernel, so it should be as fast as possible.

I analyzed the possibility of handling all these cases with a dictionary, as @rocky suggested. However, as the objects are of different classes (symbols, atoms of different types, expressions) such an approach would require an important overhead. For example, to compare two real numbers, we would need first to generate their "head" symbols, compare them, and then compare the numbers. With the current approach, we just need to check that the expressions are atoms and rely on the comparison of real numbers.

What is actually susceptible to improvements are the routines where do_compare are used: _EqualityOperator.apply and _EqualityOperator.apply_other, where for example in checking equality, all the possible permutations of members are verified. Also, we would gain something in performance by singletonizing the heads of built-in objects.
On the other hand, to help the readability of the code, maybe we should comment better what is supposed that the code does on each step, and maybe also split do_compare into smaller functions.

rocky · 2021-03-30T14:33:19Z

@mmatera For me, none of this was either surprising or unexpected and I had imagined how such things would be taken care of. If you've worked in a LISP-ilke systems and WL is like that in a number of places, then you've encountered this. And you can look at how it is handled in those systems.

That said, I clearly didn't convey this very well. And it is good that with these details in hand when we redo things, it will make be clearer as to why. (And probably in the design in my mind I may have omitted a couple of steps).

However I won't be able to address this in any detail until the weekend.

mmatera · 2021-03-30T15:02:14Z

I added a link to the previous comment as a comment in do_compare(). The idea is not to review this right now but to have a better idea of what is the next step.

mmatera

I didn't realize that blacken each file I change actually produces a lot of changes that difficult the revision. Bellow there is a detail of what I actually change here.

mmatera · 2021-03-30T22:56:21Z

mathics/builtin/comparison.py

-            if l1_sympy.n(dps(prec)) == l2_sympy.n(dps(prec)):
-                return True
-            return False
+            if max_extra_prec:


This change is needed for handling Complex numbers, as well to take into account $MaxExtraPrecision

mmatera · 2021-03-30T22:57:19Z

mathics/builtin/comparison.py

        # Use Mathics' built-in comparisons for Real and Integer. These use
        # WL's interpretation of Equal[] which allows for slop in Reals
        # in the least significant digit of precision, while for Integers, comparison
        # has to be exact.

-        if ((isinstance(l1, Real) and isinstance(l2, Real)) or


This is implemented when we compare atoms at the beginning of the function.

mmatera · 2021-03-30T22:58:25Z

mathics/builtin/comparison.py

+            Expression("ExactNumberQ", arg).evaluate(evaluation)
+            for arg in items_sequence
+        ]
+        if not all(val == SymbolTrue for val in is_exact_vals):


Here the change is just adding a "not" that should be there if we look at the docstring of apply_others

mmatera · 2021-03-30T22:58:58Z

mathics/builtin/comparison.py

-            if isinstance(x, String) or isinstance(y, String):
-                if not (isinstance(x, String) and isinstance(y, String)):
-                    c = 1
+            if isinstance(y, Complex):


Again, handling the special case of complex numbers in the case that they are exact numbers...

mmatera · 2021-03-30T22:59:26Z

mathics/builtin/numeric.py

@@ -1536,8 +1536,8 @@ class RealDigits(Builtin):
    #> RealDigits[220, 140]
     = {{1, 80}, 2}

-    #> RealDigits[Sqrt[3], 10, 50]
-     = {{1, 7, 3, 2, 0, 5, 0, 8, 0, 7, 5, 6, 8, 8, 7, 7, 2, 9, 3, 5, 2, 7, 4, 4, 6, 3, 4, 1, 5, 0, 5, 8, 7, 2, 3, 6, 6, 9, 4, 2, 8, 0, 5, 2, 5, 3, 8, 1, 0, 3}, 1}
+    # #> RealDigits[Sqrt[3], 10, 50]


This test fails in windows...

mmatera · 2021-03-30T23:01:56Z

test/test_compare.py

@@ -1,23 +1,644 @@
 # -*- coding: utf-8 -*-


This file includes all the tests...

rocky · 2021-04-10T09:09:24Z

mathics/builtin/arithmetic.py

@@ -1135,12 +1135,16 @@ class DirectedInfinity(SympyFunction):
    }

    def to_sympy(self, expr, **kwargs):
-        if len(expr.leaves) == 1:
+        if len(expr._leaves) >= 1:


Why do we need ">=" instead of "=="?

https://reference.wolfram.com/language/ref/DirectedInfinity.html indicates there is either zero or one leaves only?

For upward compatibility, and because I was too lazy to check the documentation :)

@mmatera

fix duplicated DirectedInfinity entry restoring tests Fix Positive/Negative tests clean and working comment out debuggin prints clean and improved tests fix duplicated DirectedInfinity entry clean and improved tests fix duplicated DirectedInfinity entry restoring tests Fix Positive/Negative tests clean and working reverting changes in modules splitting working and not working tests... split in working, possible working with small changes, and not working fixing do_compare and apply_ for passing the test_compare tests fix comparison all tests in green parent 538f48b author mmatera <matera@fisica.unlp.edu.ar> 1617066256 -0300 committer mmatera <matera@fisica.unlp.edu.ar> 1618407461 -0300 parent 538f48b author mmatera <matera@fisica.unlp.edu.ar> 1617066256 -0300 committer mmatera <matera@fisica.unlp.edu.ar> 1618407042 -0300 comment out RealDigits test that fails in windows adding comment about how the things are working now. blacken clean appendicial comment changes Rebase master - WIP do_comparison -> equal2 l1, l2 -> lhs, rhs Use newer test helper and Compress/Uncompress test First cut at simplifying via equal2 methods... Note that comparison expectations for Compiled code is different. test_compare.py passes. More simplification is needed. sameQ order. Comment out Compile == tests Remove == tests with Graphics... until I understand *why* this isn't False. Fix List ==. Reinstate Graphics == tests. Symbol Equal I think is weird. But so be it. first shot adding return information. Changing _cmp by _eq_tst third attemp.... commutativity checks test commutativity support for system lists in AppendTo and PrependTo chn fix PrependTo and AppendTo fix #1262 Unprotect Derivative (fix issue #1263) memory functions adding Dispatch (just for compatibility) adding a TODO list fix 1260. Improve support for ReplaceRepeated Refactor code more * Move equal2 from Symbol into Atom * add equal2 method for CompiledCode * Add/Correct return types for equal methods Simpilfy tests to take advantange of Commutativity Note commutativity of Equal Uneqal UnsameQ in docs Go over docs to remove extraneous and sometimes wrong information. Lint code clean and improved tests fix duplicated DirectedInfinity entry restoring tests Fix Positive/Negative tests clean and working comment out debuggin prints clean and improved tests fix duplicated DirectedInfinity entry clean and improved tests fix duplicated DirectedInfinity entry restoring tests Fix Positive/Negative tests clean and working reverting changes in modules splitting working and not working tests... split in working, possible working with small changes, and not working fixing do_compare and apply_ for passing the test_compare tests fix comparison all tests in green comment out RealDigits test that fails in windows clean tests splitting tests into those that uses ToString and those that not fix adding ConditionalExpression Introduce Integer1 = Integer(1) @mmatera: a while back in branch not pushed, I also had other numbers and in particular Integer(0) which is even more common. I had problems somewhere along the line with that, so I didn't commit any of this. Since you introduced more locally IntegerOne, put this in for that one case. However rather than do more Integer symbols in this branch, let's merge it in and do this as a follow on. The number of changes in this branch is getting quite long. black fix

* Equal[] comparision use more specialized equal2 and sameQ instance methods to isolate logic. * Extensive comparison tests were added in test/test_compare.py which use make use of the Commutative property of Equal. * Equal, Unequal, SameQ and UnsameQ docs gone over and make explicit the commutative aspect of these operators * Integer1 symbolic constant introduced.

mmatera mentioned this pull request Mar 30, 2021

adding lots of tests for comparison #1200

Closed

mmatera commented Mar 30, 2021

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mmatera force-pushed the fixcomparisons branch from 25ada32 to 85ac829 Compare March 31, 2021 00:02

This was referenced Mar 31, 2021

Review _EqualityOperator #1197

Closed

Knot theory fixes #1199

Closed

rocky mentioned this pull request Apr 3, 2021

Svg axis and text opacity #1223

Merged

rocky marked this pull request as draft April 3, 2021 11:34

mmatera force-pushed the fixcomparisons branch from c286cc5 to 96d689e Compare April 7, 2021 14:02

rocky force-pushed the fixcomparisons branch 2 times, most recently from 82b6cb9 to 56bdc21 Compare April 10, 2021 08:50

rocky reviewed Apr 10, 2021

View reviewed changes

mmatera force-pushed the fixcomparisons branch from 370ff75 to 556008b Compare April 14, 2021 13:49

mmatera mentioned this pull request Apr 14, 2021

Fixcomparison rebase #1256

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mmatera force-pushed the fixcomparisons branch from 556008b to a908043 Compare April 14, 2021 14:02

mmatera marked this pull request as ready for review April 14, 2021 14:25

mmatera merged commit cb3b7d8 into master Apr 14, 2021

mmatera deleted the fixcomparisons branch April 14, 2021 14:26

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Fixcomparisons #1209

Fixcomparisons #1209

mmatera commented Mar 30, 2021 •

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Fixcomparisons #1209

Fixcomparisons #1209

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mmatera commented Mar 30, 2021 • edited

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mmatera commented Mar 30, 2021 •

edited

rocky commented Mar 30, 2021 •

edited