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## [Axiom-developer] ? AXIOM BUG: solve(log(z)^5=1, z)

**From**: |
Vladimir Bondarenko |

**Subject**: |
[Axiom-developer] ? AXIOM BUG: solve(log(z)^5=1, z) |

**Date**: |
Sun, 30 Jan 2005 17:20:16 +0200 |

Hello *,
Any comments on the following?
This *reminds* a bug, but I'd prefer to ask an AXIOM expert
proficient in manipulations to confirm or to reject this.
The set of solutions depends on 2 parameters... suspicious
in the case. But, in principle, AXIOM maybe has rewritten
identically the original equation as a system of 4 equations
in 2 variables, and after certain jiggery-pokery it would be
possible to construct something like product(z-z_j, j = 1..5)
= 1 ... but I have other flaming ideas to try :)
-> solve(log(z)^5=1, z)
%z178 %z179
[z= %e, z= %e , z= %e ,
z =
%e
**
+------------------------------------------------------+
| 2 2
\|- 3%z179 + (- 2%z178 - 2)%z179 - 3%z178 - 2%z178 - 3 - %z179
+
- %z178 - 1
/
2
,
z =
1
/
%e
**
+------------------------------------------------------+
| 2 2
\|- 3%z179 + (- 2%z178 - 2)%z179 - 3%z178 - 2%z178 - 3 + %z179
+
%z178 + 1
/
2
]
Compare:
Maple 9.5.2> solve(log(z)^5=1, z);
exp(1),
exp(RootOf(_Z^4+_Z^3+_Z^2+_Z+1,-.8090169944-.5877852523*I)),
exp(RootOf(_Z^4+_Z^3+_Z^2+_Z+1,-.8090169944+.5877852523*I)),
exp(RootOf(_Z^4+_Z^3+_Z^2+_Z+1,.3090169944-.9510565163*I)),
exp(RootOf(_Z^4+_Z^3+_Z^2+_Z+1,.3090169944+.9510565163*I))
Maple 9.5.2> evalf(%);
2.718281828,
.3705619960-.2469250089*I,
.3705619960+.2469250089*I,
.7911311121-1.108777941*I,
.7911311121+1.108777941*I
Best wishes,
Vladimir Bondarenko
http://www.cybertester.com/
http://maple.bug-list.org/
http://www.CAS-testing.org/

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**[Axiom-developer] ? AXIOM BUG: solve(log(z)^5=1, z)**,
*Vladimir Bondarenko* **<=**