MaplePrimes - answers and comments on Question, evalf fails to deliver RootOf numerical value

This works

Markiyan Hirnyk — Wed, 06 Mar 2013 23:39:42 Z

> evalf(evala(RootOf(Z^6-3*Z^4+3*Z^2+Z-1, index = 2)));

1.26780484185225 + 0.395315011623840 I

Notice RootOf instead of RoofOf and index=2. See ?RootOf for more info and screen_06.03.13.docx .

PS. Also see screen2_0.docx . Unfortunately, Carl Love deleted his very interesting answer.

If I rightly understood…

one_man — Thu, 07 Mar 2013 10:57:58 Z

restart; with(RootFinding):

Z := x+I*y;

f := Z^6-3*Z^4+3*Z^2+Z-1;

Isolate([evalc(Re(f)), evalc(Im(f))], [x, y]);

...

one_man — Thu, 07 Mar 2013 12:26:08 Z

restart; with(RootFinding):

f := Z^6-3*Z^4+3*Z^2+Z-1;

rhs(op(1, Isolate(f, Z)));

rhs(op(2, Isolate(f, Z)));

Truth

Markiyan Hirnyk — Thu, 07 Mar 2013 01:18:05 Z

@Carl Love Have you tried to tell the truth?

PS. See the screen in http://www.mapleprimes.com/questions/142626-Special-Whittaker-Functions#comment142632 .

PPS. For the MaplePrimes users' convenience screen25.01.13.docx

Thanks but it does not work.

Sergio Parreiras — Thu, 07 Mar 2013 03:21:56 Z

"RoofOf" was a typo in my original question but index=real[2] was not a typo. It was generated by a Maple command: the culprit is the SemiAlgebraic command that produces an output RootOf with index=real[2] and evalf is not able to look only among the real roots. The proposed "solution" than the one in my question, it uses index=2 which evalf can manage. The RootOf problem where evalf fails was generated with the following code in Maple 16. The code and its output are in the file. RootOf_problem.mw

So my question is: can we either numerically evaluated RootOf when it has index=real[k] where k is some integer or can we convert this representation to the more usual one where index=k ?

By fsolve and NextZero

Markiyan Hirnyk — Thu, 07 Mar 2013 10:35:48 Z

@Sergio Parreiras It were better to see that explanation in your original question. Up tp Maple 16 Help,

"The command SolveTools[SemiAlgebraic] computes the solutions of a polynomial system consisting of a combination of equations, inequations, and inequalities". The RootOf construction is not an equation.

What you want can be obtained as follows.

> fsolve(Z^6-3*Z^4+3*Z^2+Z-1 = 0);
-1.461069519, 0.4710736687

(Compare with

> fsolve(Z^6-3*Z^4+3*Z^2+Z-1 = 0, complex);

HFloat(-1.4610695186751106),

-HFloat(0.7728069168535097) - HFloat(0.47602831765236625) I,

-HFloat(0.7728069168535097) + HFloat(0.47602831765236625) I,

HFloat(0.4710736686776272),

HFloat(1.2678048418522514) - HFloat(0.3953150116238396) I,

HFloat(1.2678048418522514) + HFloat(0.3953150116238396) I)

or by

> r1 := RootFinding:-NextZero(Z -> Z^6-3*Z^4+3*Z^2+Z-1 , -100);

                          -1.461069519
> r2 := RootFinding:-NextZero(Z -> Z^6-3*Z^4+3*Z^2+Z-1 , r1);

                          0.4710736686
> r3 := RootFinding:-NextZero(Z ->Z^6-3*Z^4+3*Z^2+Z-1 , r2);

                              FAIL

See ?fsolve , ?fsolve,details , and ?NextZero for info.

PS. I think is a bug or an unfinished job when creating the command ?SemiAlgebraic .