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

[Vladimir Bondarenko]

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

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