Opened 10 years ago

Last modified 8 years ago

## #14215 new enhancement

# solve with sqrt seems less than powerful

Reported by: | Karl-Dieter Crisman | Owned by: | Burcin Erocal |
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Priority: | major | Milestone: | sage-6.4 |

Component: | symbolics | Keywords: | |

Cc: | Merged in: | ||

Authors: | Reviewers: | ||

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

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description

sage: eq = x == sqrt(x) sage: solve(eq,x) [x == sqrt(x)] sage: solve(eq,x,to_poly_solve=True) [x == 0, x == 1] sage: eq = x^2 == sqrt(x) sage: solve(eq,x,to_poly_solve=True) [x == x^(1/4), x == 0] sage: eq = x^2 == -sqrt(x) sage: solve(eq,x,to_poly_solve=True) [x == sqrt(-sqrt(x)), x == 1/2*I*sqrt(3) - 1/2, x == 0, x == -1/2*I*sqrt(3) - 1/2] sage: eq = a*x**2 == -sqrt(x) sage: solve(eq,x,to_poly_solve=True) [x == -sqrt(-sqrt(x)/a), x == sqrt(-sqrt(x)/a)]

This is a simplification of an example a user posted on the Sage Facebook page.

### Change History (6)

### comment:1 Changed 10 years ago by

### comment:2 Changed 10 years ago by

The suggestion was made there that Sympy might be better at this. Is it? At least here it is giving answers - I don't think any are erroneous or missing, but I didn't check very hard, either.

sage: from sympy import solve as ssolve sage: ssolve(x-sqrt(x),x) [1, 0] sage: ssolve(x^2-sqrt(x),x) [1, 0] sage: ssolve(x^2+sqrt(x),x) [-1/2 + 3**(1/2)*I/2, -1/2 - 3**(1/2)*I/2, 0] sage: ssolve(a*x^2+sqrt(x),x) [(-1/a)**(2/3), 0, (-1/a)**(2/3)*(-1 - 3**(1/2)*I)/2, (-1/a)**(2/3)*(-1 + 3**(1/2)*I)/2]

Does anyone know whether sympy's solve capabilities is a strict superset of Maxima's? I assume not.

### comment:3 Changed 9 years ago by

Milestone: | sage-5.11 → sage-5.12 |
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### comment:4 Changed 9 years ago by

Milestone: | sage-6.1 → sage-6.2 |
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### comment:5 Changed 9 years ago by

Milestone: | sage-6.2 → sage-6.3 |
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### comment:6 Changed 8 years ago by

Milestone: | sage-6.3 → sage-6.4 |
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This seems to be a general weakness in Maxima's solve; if someone wants to change this to a bug and not an enhancement, be my guest.