Is Mathematica more incomplete than the other math solver software packages?

[kent davidge]

I only have access to mathematica currently. Regarding specifically its power to solve integrals, is it more unable to solve integrals than others like Maple? If the answer is yes, then I will move to purchase Maple.

 

[Dale]

My experience is the opposite. Usually if Mathematica cannot solve it then no closed form solution exists

 

[kent davidge]

I'm asking this because it doesn't solve a lot of integrals. Of course if the integrals themselves cannot be solved analytically, then its not mathematicas fault. However, it seems that at least some of them can be solved.

The good thing is that I didn't have to buy it. I use it at the university.

 

[Orodruin]

My experience is the opposite. Usually if Mathematica cannot solve it then no closed form solution exists

Not only that, my experience is also that Mathematica is much better at computing "difficult" integrals numerically, such as integrals with infinity as the boundary or with a diverging integrand.

 

[Dale]

I have tried dedicated CAS systems Mathematica and Maple and add-on symbolic libraries for Matlab and Python and also SageMath which is somehow halfway between the two extremes. Both Maple and Mathematica are far better for CAS tasks than the other options, but my experience was that Mathematica had a substantial edge over Maple. However, that was also years ago, so I am not sure if the gap has closed or widened.

 

[JonMcLoone]

There is an independent benchmark of 72,000 integrals at
https://www.12000.org/my_notes/CAS_integration_tests/index.htm

Mathematica fails on 1.8% of the tests, Maple on 17.2%, Maxima on 57.2% and Sympy fails on 67.7%

 

[klotza]

I am more familiar with Maple, but have used Mathematica a bit. I am more used to Maple because I learned it first, and did my undergrad honors thesis in general relativity with it. The main things I use Maple for are simplifying gross expressions, finding the minima of gross functions, and solving integrals and ODEs. I used Mathematica last year for a knot theory project, because there's a very nice extension that let's you symbolically work with various knot properties. Overall, I would say that Mathematica is better in its ability to solve integrals and ODEs, while I do prefer the notation of Maple and I know the tricks of simplification a bit better. The general consensus, beyond my own personal experience, is that Mathematica is more complete.