Clark Smith  wrote:   
   > On Thu, 13 Apr 2017 02:18:37 +0000, antispam wrote:   
   >   
   > > Clark Smith  wrote:   
   > >> On Wed, 12 Apr 2017 16:43:24 -0700, Richard Fateman wrote:   
   > >>   
   > >> > On 4/12/2017 12:19 PM, Clark Smith wrote:   
   > >> >>      Are there any symbolic systems these days that ship with a full   
   > >> >> implementation of the Risch algorithm?   
   > >> >>   
   > >> > 1. Probably not.   
   > >> > 2. It is not an algorithm.   
   > >> >   
   > >> > Why do you ask?   
   > >>   
   > >>         Out of curiosity - I seem to recall that Axiom, when it was   
   > >> called Scratchpad, claimed to have a near complete implementation.   
   > >   
   > > "near complete" is very imprecise statement.  In particular how you   
   > > measure "nearness".  Even quite incomplete system may show good results   
   > > on simple minded test, so looking at performance may give too rosy   
   > > picture.  Another point of view is to look how much code in missing   
   > > compared to complete implementation. Currently there is no complete   
   > > implementation of full algorthm, so such criteria is hard to apply.  For   
   > > transcendental part FriCAS has complete implementation (based on Axiom).   
   > >  Axiom used about 8000 lines of code for integration of which probably   
   > > about 4000 lines were specific to algebraic part.  So we can estimate   
   > > transcendental part at less than 4000 lines.   
   > > To get complete implementation in transcendental case FriCAS added about   
   > > 2500 lines of code.  In the process Axiom implementation was simplified   
   > > and about 1000 lines of code were removed.  Some of removed parts were   
   > > replaced by new code, but some simplifications would be possible even   
   > > without adding new code.  So we get somewhat fuzzy estimante that Axiom   
   > > had 60-70% of needed code -- I my book missing 30% is fairly incomplete.   
   > >   
   > > Compared to Axiom FriCAS can handle more algebraic cases,   
   > > but still there are quite large gaps.   
   >   
   >         That's very useful information, thank you. I am a bit confused   
   > though for, in your previous response, you claim that it is not an   
   > algorithm, whereas in this one you seem to imply that it is. I would be   
   > interested to learn what you mean precisely when you claim it is not an   
   > algorithm.   
      
   Claim that it is not an algorithm was done by Richard Fateman.   
   In theoretical formulation Risch algorithm takes as argument function   
   form a differential field.  In particular as data needs description   
   of the differential field.  Normally symbolic integration is   
   considered as taking an expression as input and producing   
   expression as output.  Passing from expressions to differential   
   fields is the controversial step.  Richard gave link to an old   
   post where he stated his objections.   
      
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