Albert Rich schrieb:   
   >   
   > On Saturday, April 30, 2016 at 9:49:41 PM UTC-10, clicl...@freenet.de wrote:   
   > >   
   > > 16*3 = 48 rules; but distinguishing polynomials by degree only, this   
   > > would better be counted as 3*3 = 9 rules.   
   >   
   > If you are so curious about the need for the new rules in Rubi 4.92,   
   > you can compare the current source now posted on Rubi's website with   
   > the previous source.   
      
   My curiosity was more about your way of counting Rubi rules. When once   
   no serious computer algebra system can afford not to implement Rubi,   
   there will be a lot of curiosity about its set of integration rules :).   
      
   >   
   > > It seems to be settled in your mind by now that Rubi's   
   > > pattern-matching activities should be quickly forgotten once version   
   > > 5 is out and stable.   
   >   
   > I would dearly love to forget Rubi 4, but there is a lot of work to do   
   > before Rubi 5 is ready for prime-time:   
   >   
   > 1.  In order for Rubi 5 to display integration steps, like Rubi 4   
   > does, will require implementing an if-then-else tree interpreter that   
   > can reconstruct the rule's application conditions as it descends   
   > through the tree so they can be displayed to the user.   
      
   This suggests that the primary code for Rubi 5 is to be some kind of   
   abstract decision tree rather than code capable of being executed on a   
   familiar system like Mathematica; else the interpreter workings too   
   would have to be specific to the target system to some extent.   
   Especially in the latter case, the desired display of integration steps   
   would amount to executing the code in a kind of "trace" mode, where code   
   mark-up like "breakpoints" placed where rules are actually applied may   
   facilitate the extraction of their symbolic description, of the   
   conditions for their mathematical validity, and of the actual arguments   
   at each integration step. Alternatively, an automatic compilation from   
   abstract tree to specific code could generate and either store or insert   
   the required "debugging" information.   
      
   The ability of Rubi to display the mathematical rules that comprise the   
   evaluation of an integral looks indispensable to me. But to know how the   
   rules are chosen in the course of a particular evaluation should be of   
   little value to users; if they really want to know, they can inspect the   
   code. An actual sequence of rules will often look sensible or even   
   suggest itself in view of how the final closed-form antiderivative is   
   approached, but the choice among alternative routes can also be more or   
   less arbitrary, and some key rule may even be chosen because another   
   branch was silently tested and did not lead to a closed-form result.   
      
   >   
   > 2.  In order to display Rubi 5's rule-based decision-tree in   
   > human-readable form, like the list of pattern-matching rules currently   
   > displayed on the website, will require reconstructing the rules   
   > implicitly stored in the tree and storing them as a list of   
   > pattern-matching rules.   
      
   This does not look important to me. I found what I saw of your system   
   specific if-then-else code quite readable, much as I did the Mathematica   
   rules defining Rubi 2.   
      
   >   
   > > On that occasion, you may thus even think of renaming Rubi and   
   > > restarting at version 1 :).   
   >   
   > No, I think "Rubi" is a great name for a rule-based integrator, no   
   > matter whether the rules are selected using pattern-matching or a   
   > decision-tree.   
   >   
      
   Yes, this was at the bottom of my remark: Rubi won't remain Rubi unless   
   every integrator call breaks down into a sequence of rule applications   
   that can be automatically displayed as fairly elementary mathematical   
   transformation steps readily verifiable by users. Some of the decisions   
   underlying its mathematical design, such as shunning solvers for systems   
   of equations, may indeed be questioned otherwise.   
      
   Martin.   
      
   --- SoupGate-Win32 v1.05   
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