Items tagged with roots


hey guys ,


i have problem to obtain roots for a higher order equation


thanks for your

When I execute the following code in Maplesoft on my computer, there are no problems.  However when I execute the same code in mapleTA occasionally Maple only finds a single input value corresponding with h_given.  Anybody have any idea what is going on?

Basically I have a function, f,  that I am only interested in plotting and analyzing real-valued inputs, t, from =0 to 100 (or so).  At some point I assign an output value, h_given, and I wish to find the correlated real-valued inputs.  From the graph you can clearly see that there are 2 inputs, however the script occassionally only produces 1 output. (when running on mapleTA).

Thanks in advance,

a := MapleTA:-Builtin:-range(1800, 2300, 100):
b := (1/10)*MapleTA:-Builtin:-range(4, 8, 1):
timeT := MapleTA:-Builtin:-range(70, 100, 10):
f := -t*(b*t-b*timeT)^2*(cos(.15*t+4)^2-3)/a:
maxs := NLPSolve(f, t = 0 .. timeT, maximize):
maxim := maxs[1]:
graph := plot(f, t = 0 .. timeT, gridlines = true, 0 .. maxim+10, labels = [t, h(t)], labeldirections = [horizontal, vertical]);
h_given := 10;
expr := h_given-f:
answer_t := Student:-Calculus1:-Roots(expr, t = 0 .. timeT+5);
evalf(answer_t, 2);

I want to solve for the roots of a polynomial, such as a x^2+b x + c = 0, for which the output is only the positive root. All coefficients/variables in the polynomial are positive. 

Recently, someone posted an answer to a question where at some point they performed this task and their solution was really slick. But I can't find it. The answer used either solve, or eval or something like that. (Yes, I did perform a search via the MaplePrimes search before asking this question.) 


Hi guys,

I would like to compute the complex roots of the following equations

u*(BesselJ(0,u)^2 + BesselJ(1,u)^2) = 2 BesselJ(0,u)*BesselJ(1,u)

The function fsolve in Maple gives only 0. I was wondering whether other complex solutions could be obtained as well.

Your help is highly appreciated.




I have to find the root of an equation corresponding to the maximum absolute value. I am using root finding package to get all the roots. But after getting all the roots i am not able to apply abs function. Maple sheet is attached.






Digits := 30



x := proc (t) options operator, arrow; x0*exp(lambda*t) end proc:

phi := proc (t) options operator, arrow; phi0*exp(lambda*t) end proc:

eqm1 := collect(simplify(coeff(expand(diff(x(t), `$`(t, 2))+(2*0)*beta*(diff(x(t), t))+0*x(t)+n*psi*(-v*(phi(t)-phi(t-2*Pi/(n*omega0)))+x(t)-x(t-2*Pi/(n*omega0)))), exp(lambda*t))), {phi0, x0})



eqm2 := collect(simplify(coeff(expand(diff(phi(t), `$`(t, 2))+(2*0)*(diff(phi(t), t))+phi(t)+n*(-v*(phi(t)-phi(t-2*Pi/(n*omega0)))+x(t)-x(t-2*Pi/(n*omega0)))), exp(lambda*t))), {phi0, x0})



mode := simplify(evalc(Re(evalc(subs(lambda = I*Omega, solve(subs(x0 = m*phi0, eqm1), m)))))^2+evalc(Im(evalc(subs(lambda = I*Omega, solve(subs(x0 = m*phi0, eqm1), m)))))^2)



A, b := GenerateMatrix([eqm1, eqm2], [x0, phi0])

A, b := Matrix(2, 2, {(1, 1) = lambda^2+n*psi-n*psi*exp(-2*lambda*Pi/(n*omega0)), (1, 2) = -n*psi*v+n*psi*v*exp(-2*lambda*Pi/(n*omega0)), (2, 1) = n-n*exp(-2*lambda*Pi/(n*omega0)), (2, 2) = -n*v+n*v*exp(-2*lambda*Pi/(n*omega0))+lambda^2+1}), Vector(2, {(1) = 0, (2) = 0})



eq := subs(n = 6, psi = 1000, omega0 = 1.15, v = 0.1e-1, Determinant(A))



zeros := RootFinding:-Analytic(eq, lambda, re = 0 .. 400, im = -200 .. 200)

0.899769545162895563524511282265e-56, 0.813609592584011756247655681635e-1-20.6993361029378520006643410260*I, .242743338419727199544214811606-34.4961764258358768825593120288*I, .440964962950043888796944083291-100.074138054178692973033664525*I, .107710271188082726666762251538-106.954651646879437684160623413*I, 1.12290283496379505456476079030-62.0290638297730162295171014475*I, .879463466045683309032252293625-93.2168861049771086211729407830*I, 2.54860869821265794971735119535-80.1919866273564551209847942490*I, 1.52678990439144770439544731898-86.4450560720567958301493690195*I, 2.62945288424037545703549470125-75.0161229879790946191171617450*I, 1.68779005203728587549371003511-68.8012471850312399391042105550*I, .776570081405504740452992339900-55.1681878011205261920670466495*I, 0.851171007270465178285429398270e-9+1.00000500045406723708450960132*I, 0.851171007270465178285445699470e-9-1.00000500045406723708450960133*I, 0.874874719902730972066854301075e-2-6.89997772561385443312823760560*I, 0.354201863215292148351069041542e-1-13.7998152076043523748759861636*I, .369195444156713173497807954493-41.3921704506707022569621870947*I, .540047057129385026999638567235-48.2843908783769449582520027744*I, .149078330738225743331408017894-27.5982749361891156626731068484*I, .369195444156713173497807954500+41.3921704506707022569621870948*I, .440964962950043888796944083291+100.074138054178692973033664525*I, .107710271188082726666762251538+106.954651646879437684160623413*I, 1.12290283496379505456476079030+62.0290638297730162295171014475*I, .879463466045683309032252293625+93.2168861049771086211729407830*I, 2.54860869821265794971735119535+80.1919866273564551209847942490*I, 1.52678990439144770439544731898+86.4450560720567958301493690195*I, 2.62945288424037545703549470125+75.0161229879790946191171617450*I, 1.68779005203728587549371003511+68.8012471850312399391042105550*I, .776570081405504740452992339900+55.1681878011205261920670466495*I, 0.813609592584011756247655681660e-1+20.6993361029378520006643410260*I, 0.354201863215292148351069041261e-1+13.7998152076043523748759861634*I, 0.874874719902730972066854301075e-2+6.89997772561385443312823760560*I, .540047057129385026999638567235+48.2843908783769449582520027744*I, .242743338419727199544214811602+34.4961764258358768825593120288*I, .149078330738225743331408017894+27.5982749361891156626731068484*I


" 1)"

Error, missing operation

" 1)"




I will be really thankful for the help.



I am having 26th degree polynomial univariate equation , I used Isolate to get the roots. but I am getting some extra roots which are not true they I even tried to substitute those roots in original equation then I got non zero answer instead of getting nearly zero answer.How is it possible??


equation looks like:


Solutions i got:

[t = -4.162501845, t = -2.295186769, t = -1.300314688, t = -.8048430445, t = -0.6596008501e-1, t = -0.4212510777e-1, t = 0.4212510777e-1, t = 0.6596008501e-1, t = .8048430445, t = 1.300314688, t = 2.295186769, t = 4.162501845]

t=4.162501845 give me non zero answer when I substitute it in the equation given above:

I got this answer: 4.750212083*10^39




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)




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'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'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.



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