Opened 5 years ago

Last modified 5 years ago

## #16816 new enhancement

# symbolic sums of roots

Reported by: | kcrisman | Owned by: | |
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Priority: | major | Milestone: | |

Component: | calculus | Keywords: | |

Cc: | Merged in: | ||

Authors: | Reviewers: | ||

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description

See this sage-devel discussion, where it is pointed out that both Maxima and Sympy can return solutions to integrals using a symbolic sum of roots, e.g.

sage: f=1/(x^4+x^3+1) sage: fm=f._maxima_() sage: fm.integrate() 'integrate(1/(x^4+x^3+1),x) sage: fs=f._sympy_() sage: fs.integrate() RootSum(229*_t**4 + 6*_t**2 + _t + 1, Lambda(_t, _t*log(-37785*_t**3/3547 - 5496*_t**2/3547 + 12979*_t/3547 + x + 691/3547)))

(Thanks to mmarco for this.)

Perhaps this shouldn't be the default return for integrals but it certainly could be useful.

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The object itself can be created in pynac using algebraic numbers. The problem is to handle it then. I posted an example in the sage-devel discussion.