Questions about implementation of Symja Integrate function based on Rubi rules

[robert-dodier]

I am looking at the implementation of the Symja Integrate function which, from what I see, is based on a Java translation of Rubi rules. I have a couple of basic questions about that.

• Does Symja have any other integration algorithms aside from Rubi? I don't see anything, but I might have missed something.
• Is there a way to get some report from Integrate about how many rules were tried and which one eventually matched, if any?
• Does the Integrate function try one rule after another, so the execution time is approximately proportional to the number of rules tried?

Thanks for any light you can shed on these questions.

[axkr]

I am looking at the implementation of the Symja Integrate function which, from what I see, is based on a Java translation of Rubi rules. I have a couple of basic questions about that.

* Does Symja have any other integration algorithms aside from Rubi? I don't see anything, but I might have missed something.

The "basic integration rules" are hardcoded here:

• https://github.com/axkr/symja_android_library/blob/master/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/reflection/system/Integrate.java

* Is there a way to get some report from `Integrate` about how many rules were tried and which one eventually matched, if any?

No there is no way out of the box. For debugging I'm enabling the output in Java. The priority should be the same as the line number of the Rubi rule:

• symja_android_library/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/patternmatching/RulesData.java

  Line 433 in c0042e9

  // if (patternEvaluator.fLhsPatternExpr.isAST(S.Integrate)) {

In theory we can implement a IEvalStepListener (which is used for the Trace function) with the required information:

• https://github.com/axkr/symja_android_library/blob/master/symja_android_library/doc/functions/Trace.md

* Does the `Integrate` function try one rule after another, so the execution time is approximately proportional to the number of rules tried?

Yes one rule is tried after the other. Sometimes rules can be skipped because of unequal patternHash values.

In #1009 I want to create the java source for a decision tree from pattern-matching rules.
I have uncommited changes for a very "basic idea" (means not usable for the Rubi rules yet) how to create the decision tree.