Alasdair McAndrew wrote: > > Is there a list somewhere of integrals which can be solved in closed form > by Axiom/FriCAS, but cannot be solved by the most recent versions of > Maple/Mathematica? I would be very interested in seeing such a list - but > I don't myself have access at the moment to either Maple or Mathematica.
Personaly I have access to Maple 15 and Mathematica 8, which are not the newest versions. At http://12000.org/my_notes/CAS_integration_tests/index.htm Nasser M. Abbasi posted results of running Maple 2015.1 and Mathematica 10.1 trough Rubi testsuite. Below are some examples from this testsuite, which Nasser reports as unevaluated by Mathematica and Maple. Note: Rubi testsuite strongly favours pattern matchers and does not contain many difficulties which complete algorithm is supposed to handle. Still, for some classes of integrals which FriCAS can do in systematic way you can find there examples which are beyond Mathematica and Maple. BTW: I can provide several examples which are beyond Rubi, Maple 15 and Mathematica 8, but can not check them with newer versions. integrate(f^(c*(b*x+a)^3)*x^2,x) (1) 3 3 2 2 2 3 +------------+2 (b c x + 3a b c x + 3a b c x + a c)log(f) 3| 3 %e \|- b c log(f) + - 2 1 3 3 2 2 2 3 a b c log(f)Gamma(-,(- b c x - 3a b c x - 3a b c x - a c)log(f)) 3 * +------------+ 3| 3 \|- b c log(f) + 2 2 3 3 2 2 2 3 2a b c log(f)Gamma(-,(- b c x - 3a b c x - 3a b c x - a c)log(f)) 3 / +------------+2 3 3| 3 3b c log(f)\|- b c log(f) Type: Union(Expression(Integer),...) integrate(exp(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3)*x^4,x) (2) 3 3 2 2 2 3 +----+2 2 2 2 b x + 3a b x + 3a b x + a 3| 3 (3b x - 6a b x + 9a )%e \|- b + +----+ 4 1 3 3 2 2 2 3 3| 3 (- 3a - 4a)b Gamma(-,- b x - 3a b x - 3a b x - a )\|- b 3 + 3 2 2 3 3 2 2 2 3 (12a + 2)b Gamma(-,- b x - 3a b x - 3a b x - a ) 3 / +----+2 5 3| 3 9b \|- b Type: Union(Expression(Integer),...) integrate(exp(e*(d*x+c)^3)*(b*x+a)^3,x) (3) 3 3 2 2 2 3 +-----+2 3 2 3 d e x + 3c d e x + 3c d e x + c e 3| 3 (3b d x + 9a b d - 6b c)%e \|- d e + 3 4 2 3 2 2 2 3 3 3 ((- 3a d + 9a b c d - 9a b c d + 3b c d)e + b d) * +-----+ 1 3 3 2 2 2 3 3| 3 Gamma(-,- d e x - 3c d e x - 3c d e x - c e)\|- d e 3 + 2 4 2 3 3 2 2 (- 9a b d + 18a b c d - 9b c d )e * 2 3 3 2 2 2 3 Gamma(-,- d e x - 3c d e x - 3c d e x - c e) 3 / +-----+2 4 3| 3 9d e \|- d e Type: Union(Expression(Integer),...) -- Waldek Hebisch _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org https://lists.nongnu.org/mailman/listinfo/axiom-developer
