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how i can calculate roots of the characteristic polynomial equations {dsys and dsys2}
and dsolve them with arbitrary initial condition for differennt amont of m and n?

restart; a := 1; b := 2; Number := 10; q := 1; omega := 0.2e-1

Q1 := besselj(0, xi*b)*(eval(diff(bessely(0, xi*r), r), r = a))-(eval(diff(besselj(0, xi*r), r), r = a))*bessely(0, xi*b):

J := 0:

m := 0:

U1 := (int(r*K1[m]*(diff(K_01[m], r)+K_01[m]/r), r = a .. b))/(int(r*K1[m]^2, r = a .. b)); -1; U2 := -(int(r*K_01[m]*(diff(K1[m], r)), r = a .. b))/(int(r*K_01[m]^2, r = a .. b)); -1; U3 := (int(r^2*omega^2*K_01[m], r = a .. b))/(int(r*K_01[m]^2, r = a .. b))



Q2 := besselj(1, eta*b)*(eval(diff(bessely(1, eta*r), r), r = a))-(eval(diff(besselj(1, eta*r), r), r = a))*bessely(1, eta*b):

E2 := unapply(Q2, eta):

m := 0:

dsys := {diff(S_mn(t), t, t, t)+xi[m]^2*(diff(S_mn(t), t, t))+(-U1*U2+eta__n^2)*(diff(S_mn(t), t))+xi[m]^2*eta__n^2*S_mn(t) = -(2*U2*b_m/(Pi*xi[m])*(-besselj(0, xi[m]*b)/besselj(1, xi[m]*a)))*q+xi[m]^2*U3}; 1; dsolve(dsys)

{S_mn(t) = (3111111111/5000000000000)/(K_01[12]*eta__n^2)+_C1*cos(eta__n*t)+_C2*sin(eta__n*t)+_C3*exp(-xi[12]^2*t)}


dsys2 := {diff(Q_mn(t), t, t, t)+xi[m]^2*(diff(Q_mn(t), t, t))+(-U1*U2+eta__n^2)*(diff(Q_mn(t), t))+xi[m]^2*eta__n^2*Q_mn(t) = -2*besselj(0, xi[m]*b)*U1*U2*b_m*(1-exp(-xi[m]^2*t))/(besselj(1, xi[m]*a)*Pi*xi[m]^3)}; 1; dsolve(dsys2)

{Q_mn(t) = _C1*exp(-xi[12]^2*t)+_C2*sin(eta__n*t)+_C3*cos(eta__n*t)}







Dear all,

I have a question: how to compute the roots of exp(z) = -1 with z in C? 

I tried: 

fsolve( exp(z) = -1, z, complex );

But it only gives one root (0.1671148658e-3+4.934802220*10^9*I) which does not even seem to be correct. I would prefere smth like z_n = I*(2*n-1)*pi or at least multiple roots...

By using

solve(exp(x) = -1, x);

it returns I*Pi.


MATLAB MuPAD gives the desired result:

solve(exp(x) = -1, x)

(PI*I + 2*PI*k*I, k in Z)




when the kummerM function equal to 0?????


-(((beta*eta^2-(1/2)*beta+1)*p^2-(1/2)*beta^3)*KummerM((1/4)*((-beta+2)*p^2-beta^3)/p^2, 1, beta*eta^2)+(1/2)*KummerM((1/4)*((-beta+6)*p^2-beta^3)/p^2, 1, beta*eta^2)*((beta-2)*p^2+beta^3))*exp(-(1/2)*beta*eta^2)/(p^2*beta)=0

how solve this equation unitage beta?

What is the easiest way to ask roots of a polynomial on a finite field. For example asking roots of x^2+xy+y on GF(8)? I was thinking to run a two for on members of GF(8) and ask to check it but I couldn't do it using Galois package or maybe I couldn't use that package. Thanks for any help.


I would like to plot a vertical line each time my function is null and is increasing.

Here an extract of my code:


LignesVerticales=implicitplot(x=To complete, colour=yellow,linestyle=3, thickness=2):

With Roots function, I could obtain the zero-crossings.

With the derative of the functions, I could obtain a vector which gives me when the derivative is positive or not.

I would like now to obtain the list of the zero-crossing values which are increasing but I have difficulties to obtain it. 

By list manipulation, it should be easy to do. 

May you help to plot obtain this list so that I can plot the desired vertical lines?

Thank you for your help

I'm trying to create a routine to perform the test of rational roots , but I'm having some problems. Below is the routine I created :

But the program is only printing " aux = -24 " . I don't know what it can be .

I need to modify my code , but I don't know where. Can someone help me? Thank you!

There is something wroung with the t0.

How to correct it?

can anyone please help me to find roots of (2*cos(0.5*x)*sin(0.5*x)*cos(3.775*x)+2.2075*((cos(0.5*x))^2)*sin(3.775*x)-0.453*((sin(0.5*x))^2)*sin(3.775*x)=0 ?

i type on maple like this:


but it said the solutions may have been lost

thanks before



I am trying to find the roots of Hankel function H1(2, z)?


j := 1;
for i from 0 to 10 do z0 := i*step+z_min; x[j] := fsolve(f = 0, z = z0, complex) end do;

for p to 10 do for j from p+1 to 9 do if `and`(Re(x[j])-Re(x[p]) < 0.1e-4, Im(x[j])-Im(x[p]) < 0.1e-4) then for i from j to 10 do x[i] := x[i+1] end do; p := p-1; break end if end do end do;


the first of these two processes works fine however the second does not. The second on is to get rid of same value solutions! I am not sure if I have missed anything and also is there a way to determine a max value in the complex domain and use it in a for loop?



any help would be great 


I'm relatively new to using Maple.

I'm looking for information on how the "factor" function works. I printed its definition, and it refers to "factor/factor" and I can't find any more information on this. I'd like to know so that I could have more trust that it works correctly. Specifically, I'd like to be able to believe that if it does not factor a cubic, then the cubic is irreducible.

I'm specifically looking for rational roots of cubic polynomials. The "solve" function seems to work, and gives me the roots in terms of square roots, cubic roots and rationals. I have no idea why I should believe that "type(x,rational)" would work when the description of "x" is quite complicated.

Does anyone know anything about how "factor" works, or how "type" works when testing whether an expression evaluates to a rational number? Any information would be much appreciated.



I'm have used a program to find the roots of a function 


/ 1 \
x cos(x) - sin(x) sin|---- x|
\1000 /

x_max:=50; x_min:=-50; step:=2; i_max:=(x_max-x_min)/step;

for i from 0 to i_max by 1 do


and my output was of the form of multiple "potential" roots and a bunch of which are the same. So I tried to get rid of the ones which were the same before actually finding the ones which ARE roots. To do that I done....



j := 1; for j to 50 do if x[j]-x[j+1] = 0 then ignore(x[j]) else print(x[j]) end if end do:


and it got rid of the ones which are of the above form but some roots are the same and seperated by more than 1 ... i.e x[ j ]= x[j + 2] or some other number. 


Basically I am trying to generalise the above for loop for all "numbers" instead of 1 but when I try some things the for loop doesnt like it. 

Any help would be good!



Here is a serious achievement of the Roots command:



plot(2^x+3^x+6^x-x^2, x = -6 .. 2, gridlines = false);


The solve command also does the job here:

sol := solve(2^x+3^x+6^x-x^2);



The RealDomain:-solve command fails here.

I wonder how Maple solves it. It would be kind of Maple developers and experts to explain that.

PS. I tried printlevel:=10, but understood the output a little.



Please help, here is my code:


local i,g,B,n,L,tk;

if B<1 then g:=numer(g);fi;
while has(L,0) do
if L=[] then RETURN([]);fi;
L:=map(proc(x,y) [op(1,x)*y,op(2,x)*y];end,L,B);


I dont know why i cant run this code, it always report: 

Error, (in findproot) improper op or subscript selector

option hfloat;
local a;
if nops(a)>=1 then seq([v,a[i]],i=1..nops(a));
end if;
end proc:

The final figure is different between maple12 and maple17.

On 17, unwanted points apprear.

is it a bug?

Hi all, I want to determine the roots of this figure that attached here. But the function has 5 parameters so the code doesn't work for it! Help me.

I have another question: The code that attached, determine the roots on horizontal axis, how could I find the values of root on vertical axis?In this figure I want to know the value of F(0) that cut the vertical axis?


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