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Is there a generally available (commercial or not) complete implementation of the Risch algorithm for determining whether an elementary function has an elementary antiderivative?

The Wikipedia article on symbolic integration claims that the general case of the Risch algorithm was solved and implemented in Axiom by Manuel Bronstein, and an answer to another MO question says the same thing. However, I have some doubts, based on the following comment by Manuel Bronstein himself on the USENET newsgroup sci.math.symbolic on September 5, 2003:

If Axiom returns an unevaluated integral, then it has proven that no elementary antiderivative exists. There are however some cases where Axiom can return an error message saying that you've hit an unimplemented branch of the algorithm, in which case it cannot conclude. So Richard was right in pointing out that the Risch algorithm is not fully implemented there either. Axiom is unique in making the difference between unimplemented branches and proofs of non-integrability, and also in actually proving the algebraic independence of the building blocks of the integrand before concluding nonintegrability (others typically assume this independence after performing some heuristic dependence checking).

Bronstein unfortunately passed away on June 6, 2005. It is possible that he completed the implementation before he died, but I haven't been able to confirm that. I do know that Bronstein never managed to finish his intended book on the integration of algebraic functions. [EDIT: As a further check, I emailed Barry Trager. He confirmed that the implementation that he and Bronstein worked on was not complete. He did not know much about other implementations but was not aware of any complete implementations.]

I have access to Maple 2018, and it doesn't seem to have a complete implementation either. A useful test case is the following integral, taken from the (apparently unpublished) paper Trager's algorithm for the integration of algebraic functions revisited by Daniel Schultz: $$\int \frac{29x^2+18x-3}{\sqrt{x^6+4x^5+6x^4-12x^3+33x^2-16x}}\,dx$$ Schultz explicitly provides an elementary antiderivative in his paper, but Maple 2018 returns the integral unevaluated.

Is there a generally available (commercial or not) complete implementation of the Risch algorithm for determining whether an elementary function has an elementary antiderivative?

The Wikipedia article on symbolic integration claims that the general case of the Risch algorithm was solved and implemented in Axiom by Manuel Bronstein, and an answer to another MO question says the same thing. However, I have some doubts, based on the following comment by Manuel Bronstein himself on the USENET newsgroup sci.math.symbolic on September 5, 2003:

If Axiom returns an unevaluated integral, then it has proven that no elementary antiderivative exists. There are however some cases where Axiom can return an error message saying that you've hit an unimplemented branch of the algorithm, in which case it cannot conclude. So Richard was right in pointing out that the Risch algorithm is not fully implemented there either. Axiom is unique in making the difference between unimplemented branches and proofs of non-integrability, and also in actually proving the algebraic independence of the building blocks of the integrand before concluding nonintegrability (others typically assume this independence after performing some heuristic dependence checking).

Bronstein unfortunately passed away on June 6, 2005. It is possible that he completed the implementation before he died, but I haven't been able to confirm that. I do know that Bronstein never managed to finish his intended book on the integration of algebraic functions. [EDIT: As a further check, I emailed Barry Trager. He confirmed that the implementation that he and Bronstein worked on was not complete. He did not know much about other implementations but was not aware of any complete implementations.]

I have access to Maple 2018, and it doesn't seem to have a complete implementation either. A useful test case is the following integral, taken from the (apparently unpublished) paper Trager's algorithm for the integration of algebraic functions revisited by Daniel Schultz: $$\int \frac{29x^2+18x-3}{\sqrt{x^6+4x^5+6x^4-12x^3+33x^2-16x}}\,dx$$ Schultz explicitly provides an elementary antiderivative in his paper, but Maple 2018 returns the integral unevaluated.

Is there a generally available (commercial or not) complete implementation of the Risch algorithm for determining whether an elementary function has an elementary antiderivative?

The Wikipedia article on symbolic integration claims that the general case of the Risch algorithm was solved and implemented in Axiom by Manuel Bronstein, and an answer to another MO question says the same thing. However, I have some doubts, based on the following comment by Manuel Bronstein himself on the USENET newsgroup sci.math.symbolic on September 5, 2003:

If Axiom returns an unevaluated integral, then it has proven that no elementary antiderivative exists. There are however some cases where Axiom can return an error message saying that you've hit an unimplemented branch of the algorithm, in which case it cannot conclude. So Richard was right in pointing out that the Risch algorithm is not fully implemented there either. Axiom is unique in making the difference between unimplemented branches and proofs of non-integrability, and also in actually proving the algebraic independence of the building blocks of the integrand before concluding nonintegrability (others typically assume this independence after performing some heuristic dependence checking).

Bronstein unfortunately passed away on June 6, 2005. It is possible that he completed the implementation before he died, but I haven't been able to confirm that. I do know that Bronstein never managed to finish his intended book on the integration of algebraic functions. [EDIT: As a further check, I emailed Barry Trager. He confirmed that the implementation that he and Bronstein worked on was not complete. He did not know much about other implementations but was not aware of any complete implementations.]

I have access to Maple 2018, and it doesn't seem to have a complete implementation either. A useful test case is the following integral, taken from the (apparently unpublished) paper Trager's algorithm for the integration of algebraic functions revisited by Daniel Schultz: $$\int \frac{29x^2+18x-3}{\sqrt{x^6+4x^5+6x^4-12x^3+33x^2-16x}}\,dx$$ Schultz explicitly provides an elementary antiderivative in his paper, but Maple 2018 returns the integral unevaluated.

Is there a generally available (commercial or not) complete implementation of the Risch algorithm for determining whether an elementary function has an elementary antiderivative?

The Wikipedia article on symbolic integration claims that the general case of the Risch algorithm was solved and implemented in Axiom by Manuel Bronstein, and an answer to another MO question says the same thing. However, I have some doubts, based on the following comment by Manuel Bronstein himself on the USENET newsgroup sci.math.symbolic on September 5, 2003:

If Axiom returns an unevaluated integral, then it has proven that no elementary antiderivative exists. There are however some cases where Axiom can return an error message saying that you've hit an unimplemented branch of the algorithm, in which case it cannot conclude. So Richard was right in pointing out that the Risch algorithm is not fully implemented there either. Axiom is unique in making the difference between unimplemented branches and proofs of non-integrability, and also in actually proving the algebraic independence of the building blocks of the integrand before concluding nonintegrability (others typically assume this independence after performing some heuristic dependence checking).

Bronstein unfortunately passed away on June 6, 2005. It is possible that he completed the implementation before he died, but I haven't been able to confirm that. I do know that Bronstein never managed to finish his intended book on the integration of algebraic functions. [EDIT: As a further check, I emailed Barry Trager. He confirmed that the implementation that he and Bronstein worked on was not complete. He did not know much about other implementations but was not aware of any complete implementations.]

I have access to Maple 2018, and it doesn't seem to have a complete implementation either. A useful test case is the following integral, taken from the (apparently unpublished) paper Trager's algorithm for the integration of algebraic functions revisited by Daniel Schultz: $$\int \frac{29x^2+18x-3}{\sqrt{x^6+4x^5+6x^4-12x^3+33x^2-16x}}\,dx$$ Schultz explicitly provides an elementary antiderivative in his paper, but Maple 2018 returns the integral unevaluated.

Is there a generally available (commercial or not) complete implementation of the Risch algorithm for determining whether an elementary function has an elementary antiderivative?

The Wikipedia article on symbolic integration claims that the general case of the Risch algorithm was solved and implemented in Axiom by Manuel Bronstein, and an answer to another MO question says the same thing. However, I have some doubts, based on the following comment by Manuel Bronstein himself on the USENET newsgroup sci.math.symbolic on September 5, 2003:

If Axiom returns an unevaluated integral, then it has proven that no elementary antiderivative exists. There are however some cases where Axiom can return an error message saying that you've hit an unimplemented branch of the algorithm, in which case it cannot conclude. So Richard was right in pointing out that the Risch algorithm is not fully implemented there either. Axiom is unique in making the difference between unimplemented branches and proofs of non-integrability, and also in actually proving the algebraic independence of the building blocks of the integrand before concluding nonintegrability (others typically assume this independence after performing some heuristic dependence checking).

Bronstein unfortunately passed away on June 6, 2005. It is possible that he completed the implementation before he died, but I haven't been able to confirm that. I do know that Bronstein never managed to finish his intended book on the integration of algebraic functions.

I have access to Maple 2018, and it doesn't seem to have a complete implementation either. A useful test case is the following integral, taken from the (apparently unpublished) paper Trager's algorithm for the integration of algebraic functions revisited by Daniel Schultz: $$\int \frac{29x^2+18x-3}{\sqrt{x^6+4x^5+6x^4-12x^3+33x^2-16x}}\,dx$$ Schultz explicitly provides an elementary antiderivative in his paper, but Maple 2018 returns the integral unevaluated.

Is there a generally available (commercial or not) complete implementation of the Risch algorithm for determining whether an elementary function has an elementary antiderivative?

The Wikipedia article on symbolic integration claims that the general case of the Risch algorithm was solved and implemented in Axiom by Manuel Bronstein, and an answer to another MO question says the same thing. However, I have some doubts, based on the following comment by Manuel Bronstein himself on the USENET newsgroup sci.math.symbolic on September 5, 2003:

If Axiom returns an unevaluated integral, then it has proven that no elementary antiderivative exists. There are however some cases where Axiom can return an error message saying that you've hit an unimplemented branch of the algorithm, in which case it cannot conclude. So Richard was right in pointing out that the Risch algorithm is not fully implemented there either. Axiom is unique in making the difference between unimplemented branches and proofs of non-integrability, and also in actually proving the algebraic independence of the building blocks of the integrand before concluding nonintegrability (others typically assume this independence after performing some heuristic dependence checking).

Bronstein unfortunately passed away on June 6, 2005. It is possible that he completed the implementation before he died, but I haven't been able to confirm that. I do know that Bronstein never managed to finish his intended book on the integration of algebraic functions. [EDIT: As a further check, I emailed Barry Trager. He confirmed that the implementation that he and Bronstein worked on was not complete. He did not know much about other implementations but was not aware of any complete implementations.]

I have access to Maple 2018, and it doesn't seem to have a complete implementation either. A useful test case is the following integral, taken from the (apparently unpublished) paper Trager's algorithm for the integration of algebraic functions revisited by Daniel Schultz: $$\int \frac{29x^2+18x-3}{\sqrt{x^6+4x^5+6x^4-12x^3+33x^2-16x}}\,dx$$ Schultz explicitly provides an elementary antiderivative in his paper, but Maple 2018 returns the integral unevaluated.