>> In fact they developed around the discussion of
>> Albert Rich's Rubi (RUle-Based Integration). It is worth to look this up:
>> http://www.apmaths.uwo.ca/~arich/
> if their claim to outperform Wolfram
> Mathematica is correct, that could become the strongest integrator ever.
It was one of the motivations of the 'independent test suite' (aka the
Timofeev test suite cited above, still under construction) to verify this claim.
As of today the result is: "Rubi 4.2 gets all the Timofeev examples
from Chapters 1, 3 and 7 with the exception of #10 and #11 from Chapter 7."
These are number 710 and 711 in my enumeration.
[710] Timofeev
integrand : (2*x + sin(2*x))/(x*sin(x) + cos(x))**2
antideriv : -2*cos(x)/(x*sin(x) + cos(x))
sympy : Integral((2*x + sin(2*x))/(x*sin(x) + cos(x))**2, x)
comment : Unevaluated or not an elementary solution!
time : 921.0
[711] Timofeev
integrand : x**2/(x*cos(x) - sin(x))**2
antideriv : (x*sin(x) + cos(x))/(x*cos(x) - sin(x))
sympy : Integral(x**2/(x*cos(x) - sin(x))**2, x)
comment : Unevaluated or not an elementary solution!
time : 81.0
> Considering that, I believe that at the time integration algorithms like
> Risch were invented ('60s and '70s), computers had very small hard memory,
> and rule-based pattern matching was infeasible at that time. It should be
> reconsidered nowadays.
Absolutely! And I think SymPy would be an excellent place to do this.
Peter
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