Include SymPy's Rubi integrator as integration method

[rwst]

More info about it:

The rule-based integrator Rubi by Albert D. Rich consists of about 10,000 pattern-matching rules and "dramatically out-performs Maple and Mathematica" see

• http://www.apmaths.uwo.ca/~arich/

The rules are available as of 2017 only as Mathematica code. There were efforts by the SymPy community to either translate them manually or on the fly to Python:

• Implement rule-based integrator (Rubi)  sympy/sympy#7749

Rubi was proposed as a GSoC project for Sage:

• https://groups.google.com/d/msg/sage-devel/t-fYDsiFvxw/HA9YxMToAAAJ

Proof of concept of rule translation into Sage:

• https://groups.google.com/d/msg/sage-devel/t-fYDsiFvxw/mGnnyl3FAgAJ

CC: @miguelmarco @slel

Component: calculus

Issue created by migration from https://trac.sagemath.org/ticket/22410

[kcrisman]

comment:1

Huh, I never heard of this! Very interesting. If this could be "integrated" into Pynac or Sage that would be impressive - many have proposed a Risch or other algorithm implementation in Sage (including one person who claimed their student had one, but then never followed up).

Interesting comment in the Sympy thread:

I talked with Albert Rich, the author of Rubi, and he told me that the next version will not use pattern matching, but rather just use a decision tree.

[rwst]

comment:2

I think SymPy now has the lead on this, and we just want to include that code with Sage. I'm changing the ticket description accordingly.

This depends on a SymPy upgrade ticket.

[rwst]

Description changed:

--- 
+++ 
@@ -1,4 +1,6 @@
-This is more of an ideas/info page about the subject at the moment. The rule-based integrator Rubi by Albert D. Rich consists of about 10,000 pattern-matching rules and "dramatically out-performs Maple and Mathematica" see
+More info about it:
+
+The rule-based integrator Rubi by Albert D. Rich consists of about 10,000 pattern-matching rules and "dramatically out-performs Maple and Mathematica" see
 
 * http://www.apmaths.uwo.ca/~arich/
 

[slel]

comment:3

This depends on a SymPy upgrade ticket.

In #26550, SageMath upgraded to SymPy 1.3 where rubi support is improved.

For remaining issues in SymPy see

• SymPy rubi integrator issues

[embray]

comment:4

Ticket retargeted after milestone closed (if you don't believe this ticket is appropriate for the Sage 8.8 release please retarget manually)