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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 *,

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,

http://www.cybertester.com/
http://maple.bug-list.org/
http://www.CAS-testing.org/

```