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Topic: radicals: zero-equivalence [was: Error in Maple V Release 4]
Replies: 2   Last Post: Dec 12, 1996 6:24 AM

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 Chris Hecker Posts: 53 Registered: 12/8/04
Re: radicals: zero-equivalence [was: Error in Maple V Release 4]
Posted: Dec 6, 1996 6:17 AM
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Bill Dubuque <wgd@martigny.ai.mit.edu> writes:
>> : Consider f := x^3 - 12*x^2 + 20*x + 59
>> : Using solve(f,x), Maple returns 3 imagionary solutions. This is incorrect
>> : since all odd degree polynomials must have at least one real solution.
>> Mathematica also returns the imaginaries without simplification, likewise

As another datapoint, MuPAD returns the 3 real roots directly from
solve(f,x);

I cannot, however, seem to get MuPAD to plug the values back in and
simplify them down to 0, even though they're verifiably numerically 0.

Chris

----------
Here it is if you care:

>> f := x^3 - 12*x^2 + 20*x + 59;

2 3
20 x - 12 x + x + 59

>> PRETTY_PRINT:=FALSE:
>> solve(f,x);

{(3^(1/2)*7^(1/2)*56/9)^(1/3)*cos(PI*1/3 +
atan(108^(1/2)*84541^(1/2)*1/59\
4)*(-1/3)) + (3^(1/2)*7^(1/2)*56/9)^(1/3)*cos(PI*(-1/3) +
atan(108^(1/2)*8\
4541^(1/2)*1/594)*1/3) + 4,
3^(1/2)*(3^(1/2)*7^(1/2)*56/9)^(1/3)*sin(PI*1/\
3 + atan(108^(1/2)*84541^(1/2)*1/594)*(-1/3)) +
(3^(1/2)*7^(1/2)*56/9)^(1/\
3)*cos(PI*1/3 + atan(108^(1/2)*84541^(1/2)*1/594)*(-1/3))*(-1/2) +
(3^(1/2\
)*7^(1/2)*56/9)^(1/3)*cos(PI*(-1/3) +
atan(108^(1/2)*84541^(1/2)*1/594)*1/\
3)*(-1/2) + 4, -3^(1/2)*(3^(1/2)*7^(1/2)*56/9)^(1/3)*sin(PI*1/3 +
atan(108\
^(1/2)*84541^(1/2)*1/594)*(-1/3)) +
(3^(1/2)*7^(1/2)*56/9)^(1/3)*cos(PI*1/\
3 + atan(108^(1/2)*84541^(1/2)*1/594)*(-1/3))*(-1/2) +
(3^(1/2)*7^(1/2)*56\
/9)^(1/3)*cos(PI*(-1/3) + atan(108^(1/2)*84541^(1/2)*1/594)*1/3)*(-1/2)
+ \
4}

Date Subject Author
12/6/96 Chris Hecker
12/12/96 H.-G. Graebe

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