Invalid syntax result from Integrate command.

[nasser1]

Using 4.0 on Linux, I get the following

mathics

Mathics 4.0.0
on CPython 3.10.4 (main, Apr  2 2022, 09:04:19) [GCC 11.2.0]
using SymPy 1.10.1, mpmath 1.2.1, numpy 1.22.4

Copyright (C) 2011-2021 The Mathics Team.
This program comes with ABSOLUTELY NO WARRANTY.
This is free software, and you are welcome to redistribute it
under certain conditions.
See the documentation for the full license.

Quit by evaluating Quit[] or by pressing CONTROL-D.

In[1]:= Integrate[(1 - x^3)^(2/3)/x,x]
Out[1]= --1 ^ (2 / 3) x ^ 2 Gamma[-2 / 3] hyper[{-2 / 3, -2 / 3}, {1 / 3}, 1 / x ^ 3] / (3 Gamma[1 / 3])

Notice the --1 output. This is an error. Mathematica says

PreDecrement::rvalue: 1 is not a variable with a value, so its value cannot be changed.

Btw, as a side issue, what is hyper[ function above? There is no such function in Mathematica.

But the main problem is generating --1

[rocky]

Btw, as a side issue, what is hyper[ function above?

It probably is SymPy's hyper() and probably appears because Mathics doesn't know of a Mathematica equivalent - perhaps there isn't one.

So this is a translation from SymPy results into the Wolfram Language. In that regard to your other bug mathics/Mathics#1591 which is also related to conversion from SymPy into the Wolfram Language.

Personally, I don't think I will be looking at this for a while. However if you are interested in digging deeper you might check to see what would happen if you wrote this in SymPy and then compare the results.

[DUOLabs333]

This is because Mathics doesn't add parentheses around the leading -1. Here is what sympy returns: -(-1)**(2/3)*x**2*gamma(-2/3)*hyper((-2/3, -2/3), (1/3,), x**(-3))/(3*gamma(1/3)).

[nasser1]

removes the parentheses from the result

Thanks for finding this. Removing parentheses from result is not good thing to do. Hopefully someone familiar with Mathics code could fix this.

[DUOLabs333]

You can get the same thing with -Power[-1,b]. However, -Power[-a,b] is done correctly.

[rocky]

Thanks for finding this. Removing parentheses from result is not good thing to do. Hopefully someone familiar with Mathics code could fix this.

No one is born being familiar with Mathics code. Mathics is an open source project. That means anyone who is interested enough in solving a problem in the code, can do so.

There are a number of long-standing problems in Mathics that, personally, I want to address before this kind of thing.
When an issue is opened, there is a section for describing why this bug should have priority, or why it would be important for this problem to get solved. Since there was no mention, this like the other issue have low priority.

Basically where one would start to look is in how sympy expressions are converted to Mathics expressions. git grep -n "def from_sympy(" will list the the places where this is done. And that other issue where there was a traceback, that function should also be replaced with a call to from_sympy() as well.

I don't doubt that these bugs will get fixed. But in the scheme of things, unless there is good reason otherwise, for me it is going to be a while before I look at such things.

[DUOLabs333]

Basically where one would start to look is in how sympy expressions are converted to Mathics expressions. git grep -n from_sympy will list the the places where this is done. And that other issue where there was a traceback, that function should also be replaced with a call to from_sympy() as well.

Thanks --- I was looking through the codebase to solve this. Why would that be the culprit --- I was thinking that it had something to do with the implementation of Power, as the bug doesn't occur with negative variables.

[rocky]

Thanks --- I was looking through the codebase to solve this. Why would that be the culprit --- I was thinking that it had something to do with the implementation of Power, as the bug doesn't occur with negative variables.

Note the corrected grep: git grep -n "def from_sympy(" which shows where the function is defined. The other grep works as well, but it shows all uses which here is too much.

[DUOLabs333]

Where does Mathics determine how to format Power?

[mmatera]

Something that we could start to do is to create a module to handle hypergeometic functions. You can mimic the code from the exptrig module.

[mmatera]

Regarding the format of "power" it is defined in the mathics.builtin.arithfns.basic module

[DUOLabs333]

What decides if something is wrapped in parentheses? I see parenthesize in inout.py. Is that it?

[DUOLabs333]

I go something that works, I just need to deal with the fact that integers don't have precision.

[DUOLabs333]

Here's my preliminary diff:

diff --git a/mathics/builtin/inout.py b/mathics/builtin/inout.py
index 2d241338..0f740ac4 100644
--- a/mathics/builtin/inout.py
+++ b/mathics/builtin/inout.py
@@ -212,8 +212,15 @@ def parenthesize(precedence, leaf, leaf_boxes, when_equal):
         leaf_prec = leaf.leaves[1].get_int_value()
     else:
         leaf_prec = builtins_precedence.get(leaf.get_head_name())
+    
+    #Give integer precision of Infinity
+    if isinstance(leaf,Integer):
+        leaf_prec=float("inf")
+    
+    #Check if leaf is an integer
+    is_negative = True if isinstance(leaf,Integer) and int(leaf.to_python())<0 else False
     if precedence is not None and leaf_prec is not None:
-        if precedence > leaf_prec or (precedence == leaf_prec and when_equal):
+        if precedence > leaf_prec or (precedence == leaf_prec and when_equal) or is_negative:
             return Expression(
                 SymbolRowBox,
                 Expression(SymbolList, String("("), leaf_boxes, String(")")),

Anything I should change before submitting a PR?

[rocky]

Does this pass all of the existing tests and doctests? And a test should be added that catches this particular problem.

A quick look and this doesn't feel right. builtins_precendence .get() should be returning the right value so there shouldn't be this test or possibly there is some larger problem.

[DUOLabs333]

In builtins_precedence, System`Integer isn't defined.

[rocky]

What I see is a bit different than just a missing parenthesis. The -1 should be used in a Rational[-1, 3]:

$ mathics 

Mathics 4.0.1.dev0
on CPython 3.8.12 (default, Oct 21 2021, 14:26:19) 
using SymPy 1.8, mpmath 1.2.1, numpy 1.21.3, cython 0.29.28

Copyright (C) 2011-2021 The Mathics Team.
This program comes with ABSOLUTELY NO WARRANTY.
This is free software, and you are welcome to redistribute it
under certain conditions.
See the documentation for the full license.

Quit by evaluating Quit[] or by pressing CONTROL-D.

In[1]:= Integrate[(1 - x^3)^(2/3)/x,x] // FullForm
Out[1]= Times[Rational[-1, 3], Power[-1, Rational[2, 3]], Power[x, 2], Gamma[Rational[-2, 3]], Power[Gamma[Rational[1, 3]], -1], hyper[List[Rational[-2, 3], Rational[-2, 3]], List[Rational[1, 3]], Power[x, -3]]]

Given that the above shows something a bit different from the OutputForm output, I'd say that the problem is not (just) in from_sympy() but also in a OutputForm formatting routine, possibly as a result of the untranslated symbol.

And the bug with Power is also a bug is the same and not related to from_sympy.

[DUOLabs333]

What do you mean?

[rocky]

I mean you may have made a mistake in your sympy translation. Paste the exact sympy session like I did above and the poster of the original issue did.

I thought we went over before the basics of reporting all input given and output shown.

I am sorry, but I do not have the time right now to be able to answer all of your questions.

Also, when I ask questions or ask for something, please answer them, before going off on more questions.

[mmatera]

Here there is a simpler example:
-1/3*(-1)^(3/4)

The FullForm of this expression is

Times[Rational[-1, 3], Power[-1, Rational[3, 4]]]

but in StandardForm, we get
--1 ^ (3 / 4) / 3

@rocky, I am going to try fixing this before the release.

[mmatera]

Fixed in #460