Opened 7 years ago

## #18900 new enhancement

# let solve delegate to roots

Reported by: | Ralf Stephan | Owned by: | |
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Priority: | major | Milestone: | sage-6.8 |

Component: | symbolics | Keywords: | |

Cc: | Merged in: | ||

Authors: | Reviewers: | ||

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

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description

A natural convenience improvement is possible. At the moment:

sage: z = var('z') sage: f = 1 - z - z^2 - z^3 - z^4 - z^5 sage: solve(f == 0,z) [0 == z^5 + z^4 + z^3 + z^2 + z - 1] sage: f.roots(ring=QQbar) [(0.5086603916420041?, 1), (-1.011836827437571? - 0.6839585956421031?*I, 1), (-1.011836827437571? + 0.6839585956421031?*I, 1), (0.2575066316165687? - 1.118790314198966?*I, 1), (0.2575066316165687? + 1.118790314198966?*I, 1)]

Algebraists know how to use Sage's ring elements, so they are not relevant here. Calculus users are satisfied to get all roots in the most general ring, i.e., `QQbar`

for degree >3. So, in the uni polynomial case this should be the default behaviour instead of Maxima which does nothing.

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