From: nma@12000.org   
      
   On 3/21/2017 12:27 PM, clicliclic@freenet.de wrote:   
      
   >   
   > It should suffice to let them loose on the Timofeev textbook suite: the   
   > percentages of integrals solved were pretty close to those for the full   
   > gamut of tests from Albert's website.   
   >   
   > As regards Sympy, the replacement of "^" by "**" is easily accomplished   
   > with the help of an editor. The only symbols used in the Timofeev suite   
   > are [A, B, a, b, b1, c, c1, k, l, m, n, r, s, x], which may simply be   
   > defined for every integral regardless of actual use. Nonelementary   
   > functions appearing in Albert's "optimal" evaluations are [Ei(x),   
   > gamma(n, x), hypergeometric(a, b, x), polylog(n,x)]. My analysis here is   
   > based on the Maxima file of the Timofeev problems.   
   >   
      
   I have translated Timofeev to sympy, and I can run the integrals now   
   via sympy.   
      
   But there were many many changes needed. Not only that, I just found that   
   sympy changes all exact numbers to floating point. For example:   
      
   >python   
   >>> from sympy import *   
   >>> x=symbols('x')   
   >>> integrate(1/4/sin(1/3*x),x)   
      
   0.375*log(cos(0.333333333333333*x) - 1) - 0.375*log(cos(0.333333333333333*x) +   
   1)   
      
   The above is #4 in Timofeev. Notice how the output is all   
   decimal. It turns out, one has to tell sympy not to do this   
   by changing the input to   
      
   >>> integrate(S('1/4')/sin(S('1/3')*x),x)   
      
        3*log(cos(x/3) - 1)/8 - 3*log(cos(x/3) + 1)/8   
      
   So, unless there is a way to tell sympy not to change exact   
   numbers to floating point number, I would have to do change   
   each number n in the test file to become S('n')?  63,000   
   integrals?  Not practical.   
      
   Will try to ask if there is an option to sympy, so that it   
   will do this automatically. This is very strange for a computer   
   algebra system to do this.   
      
   ps. but so far, other than few exceptions I got from some problems,   
   sympy seems to be holding itself fairly well in Timofeev test.   
      
   > I expect both Sympy and Giac/Xcas to succeed on somewhere between 50%   
   > and 70% of these textbook problems. It would be nice if the results   
   > could be graded as discussed earlier.   
   >   
   > FriCAS should be taught to distinguish single-valued from multivalued   
   > functions and correct its Risch-conditioning of integrands for a test on   
   > the full suite to be meaningful.   
   >   
   > Martin.   
   >   
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
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