Re: Fifth Degree Equation

In article <27138620.1149088702240.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
bassam king karzeddin <bassam@xxxxxxxxxx> wrote:

|>Is there a method to decide fast whether the reduced form of quintique
|>equation with integer coefficients is solvable or not

Use Maple's "galois" command.

|>Examples, consider the following equations

|>x^5 +5*x +4 = 0

galois(x^5+5*x+4);

"5T5", {"S(5)"}, "-", 120, {"(1 5)", "(4 5)", "(2 5)", "(3 5)"}

Note that S(5) is not solvable. If you want to check:

group[DerivedS](permgroup(5,%[-1]));

[permgroup(5, {[[1, 5]], [[2, 5]], [[3, 5]], [[4, 5]]}),

permgroup(5, {[], [[1, 5, 2]], [[1, 5, 3]], [[1, 5, 4]]})]

and note that this derived series doesn't end in the trivial group.

|>x^5 -(214524)*x +969408 = 0

galois(x^5 -(214524)*x +969408);

Error, (in galois) first argument must be irreducible

factor(x^5 -(214524)*x +969408);

3 2 2
(x - 18 x + 426 x - 9504) (x + 18 x - 102)

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.