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I only have experience with OpenAxiom & Axiom; however, the core definition language (Spad) is a dependently typed module-centric modern language... from 1981.
by thechao 8y ago
I only have experience with OpenAxiom & Axiom; however, the core definition language (Spad) is a dependently typed module-centric modern language... from 1981. It’s like an alternative “what if” language designed by mathematicians to write CASes. It has the oldest implementation of list- and set- comprehensions I know of. (Disclosure: I wrote a paper about adding JET-based forward AD using single-definition generics to the language.) The packages contain a complete implementation of the Risch algorithm; I’m not sure Mathematica has managed that.
- qubex 8y agoAccording to [0], ”For indefinite integrals, an extended version of the Risch algorithm is used whenever both the integrand and integral can be expressed in terms of elementary functions, exponential integral functions, polylogarithms, and other related functions.” [0] http://reference.wolfram.com/language/tutorial/SomeNotesOnInternalImplementation.html#23196 http://reference.wolfram.com/language/tutorial/SomeNotesOnIn...
- reikonomusha 8y agoMost CASes use some form of Risch, but there are various levels of implementation. Axiom is the only known CAS that implements all of the mathematics for every case of Risch, the so-called “algebraic” and “transcendental” cases. Wolfram’s page uses vague language (“an extended form of”) and doesn’t actually confirm with precision what it is able to do.