MaplePrimes - answers and comments on Question, complex trigonometric function roots

RootFinding:-Analytic

Carl Love — Tue, 26 Feb 2013 18:09:34 Z

Check out command ?RootFinding,Analytic.

It is not so simple

Markiyan Hirnyk — Tue, 26 Feb 2013 18:51:14 Z

For example,

> RootFinding:-Analytic(eval(x*tan(x)-I*i*Pi/(1+I*i*Pi), i = 10), x = -20-I .. 20+I);

          9.52923268657400 + 0.00326517479698914 I,

            6.43715491271645 + 0.00471278259201937 I,

            3.42540003091137 + 0.00793305492302150 I,

            -9.52923268657400 - 0.00326517479698914 I
> RootFinding:-Analytic(eval(x*tan(x)-I*i*Pi/(1+I*i*Pi), i = 10), x = -10-I .. 10+I);

          6.43715491271645 + 0.00471278259201936 I,

            -6.43715491271645 - 0.00471278259202726 I

continue

Preben Alsholm — Tue, 26 Feb 2013 20:18:33 Z

@Markiyan Hirnyk By doing successively

RootFinding:-Analytic(eval(x*tan(x)-I*i*Pi/(1+I*i*Pi), i = 10), x = -20-I .. 20+I);
RootFinding:-Analytic(eval(x*tan(x)-I*i*Pi/(1+I*i*Pi), i = 10), x = -20-I .. 20+I,continue);

you find 6 roots.

Rewriting the equation helps

Preben Alsholm — Tue, 26 Feb 2013 20:47:40 Z

restart;
eq1:=eval(x*tan(x)-I*i*Pi/(1+I*i*Pi), i = 10);
eq2:=eval((1+I*i*Pi)*x*sin(x)-I*i*Pi*cos(x), i = 10);
res:=RootFinding:-Analytic(eq2, x = -20-I .. 20+I);
nops([res]);
#Check:
evalf(eval~(eq1,x=~[res]));
simplify(fnormal(%,8));

2D results

mahdi1625 — Wed, 27 Feb 2013 19:27:12 Z

Dear @Markiyan Hirnyk

Thank you very much

...and i use the following code to obtain 2D results

for i from 1 by 1 to 10 do;
A[i]:=RootFinding:-Analytic(eval(x*tan(x)-I*i*Pi/(1+I*i*Pi)), x = 0+0I .. 10+I));
od;

to call the second root for i=1 I use A[1][2]

-Is there any way to program the problem so that one can call the above elemet as A[1,2]?

2d

Markiyan Hirnyk — Wed, 27 Feb 2013 20:07:44 Z

For example, it can be done as follows. >A := [$1 .. 10];# alist A is created, nops(A)=10 >for i to 10 do A[i] := [RootFinding:-Analytic(eval(x*sin(x)-I*i*Pi*cos(x)/(1+I*i*Pi)), x = 0+0*I .. 10+I)] end do: #up to the suggestion of Preben Alsholm > A[1, 3]; 0.843847344525500 + 0.0968840538073335 I > convert(A, Array): > A[1, 3]; 0.843847344525500 + 0.0968840538073335 I I don't see Menu when posting. This is the reason of such appearance of my code.