Items tagged with rootfinding

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iam trying to apply newton method on non liner system but i have a problem for apply while loop inside other while loop 
any help please

with(VectorCalculus):

NULL

f[1] := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(x^2, VectorCalculus:-`-`(VectorCalculus:-`*`(z, exp(y)))), VectorCalculus:-`-`(VectorCalculus:-`*`(y, exp(z)))), 61):

f[2] := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(x, y), z), VectorCalculus:-`-`(exp(x))), -3):

f[3] := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(x^2, y^2), z^2), -14):

F := Matrix([[f[1]], [f[2]], [f[3]]]):

FF := eval(F, [x = x[k], y = y[k], z = z[k]]):

X := Matrix([[x], [y], [z]]):

XX := eval(X, [x = x[k], y = y[k], z = z[k]]):

J := Jacobian([f[1], f[2], f[3]], [x, y, z]):

JJ := eval(J, [x = x[k], y = y[k], z = z[k]])

JJ := Matrix(3, 3, {(1, 1) = 2*x[k], (1, 2) = -z[k]*exp(y[k])-exp(z[k]), (1, 3) = -exp(y[k])-y[k]*exp(z[k]), (2, 1) = y[k]*z[k]-exp(x[k]), (2, 2) = x[k]*z[k], (2, 3) = x[k]*y[k], (3, 1) = 2*x[k], (3, 2) = 2*y[k], (3, 3) = 2*z[k]})

(1)

``

k := 0:

xi := convert(exp(-10), float):

maxval := 10^4:

NULL

while convert(Norm(FF, 2), float) > xi do alpha[k] := min(1, alpha[k]/lambda); L := 1/JJ.FF; K := -L*alpha[k]+XX; x[k+1] := evalf(Determinant(K[1])); y[k+1] := evalf(Determinant(K[2])); z[k+1] := evalf(Determinant(K[3])); A := convert(Norm(FFF, 2), float)^2; B := convert(Norm(FF, 2), float)^2; while A > B do L := 1/JJ.FF; alpha[k+1] := lambda*alpha[k]; K := -L*alpha[k+1]+XX; x[k+1] := evalf(Determinant(K[1])); y[k+1] := evalf(Determinant(K[2])); z[k+1] := evalf(Determinant(K[3])) end do; k := k+1 end do

alpha[0] := 1

 

L := Matrix(3, 1, {(1, 1) = -(12900-300*exp(8)-1200*exp(2))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)-(2*exp(8)+31*exp(2))*(77-exp(5))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)-(395/2)*(7*exp(8)-4*exp(2))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500), (2, 1) = (84+exp(5))*(86-2*exp(8)-8*exp(2))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)+(5/2)*(4+exp(8)+8*exp(2))*(77-exp(5))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)+(79/4)*(exp(8)*exp(5)+8*exp(2)*exp(5)-16*exp(8)-128*exp(2)-400)/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500), (3, 1) = -(-39+4*exp(5))*(86-2*exp(8)-8*exp(2))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)-(5/2)*(16+2*exp(8)+exp(2))*(77-exp(5))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)-(79/4)*(2*exp(8)*exp(5)+exp(2)*exp(5)-32*exp(8)-16*exp(2)-100)/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)})

 

K := Matrix(3, 1, {(1, 1) = 5+(12900-300*exp(8)-1200*exp(2))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)+(2*exp(8)+31*exp(2))*(77-exp(5))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)+(395/2)*(7*exp(8)-4*exp(2))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500), (2, 1) = 8-(84+exp(5))*(86-2*exp(8)-8*exp(2))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)-(5/2)*(4+exp(8)+8*exp(2))*(77-exp(5))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)-(79/4)*(exp(8)*exp(5)+8*exp(2)*exp(5)-16*exp(8)-128*exp(2)-400)/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500), (3, 1) = 2+(-39+4*exp(5))*(86-2*exp(8)-8*exp(2))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)+(5/2)*(16+2*exp(8)+exp(2))*(77-exp(5))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)+(79/4)*(2*exp(8)*exp(5)+exp(2)*exp(5)-32*exp(8)-16*exp(2)-100)/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)})

 

14.35960152

 

-12.24471811

 

39.82986865

 

HFloat(5.911285325999999e36)

 

35235903.22

 

Warning,  computation interrupted

 

 

 

Dears,

I have seen a Mathematica code which I would like to have it in Maple, since I do not know that program. Let f(z) an analytic function, say f(z):=1+2^{z+1}+3^{z}. To find the roots of f(z) in a regingion, we can use in Maple the command "Analytic" (of the package "RootFinding"). However, in Mathematica is used the following:

L = 20; Monitor[zeros = Flatten@Table[N[z /. Solve[f[z] ⩵ 0 && k L ≤ Re[z] ≤ k L + L && -10 < Im[z] < 10, z], 25],{k, 300}],k];

What means the "N[z/. Solve..." instruction? Also, the following command:

SortBy[zeros, Re]; 

Can be "translated" to Maple?

 

Many thaks in advance for your comments!

With Regards,

G.

In using Isolate in RootFinding to compute roots of a real polynomial, the output contains, say, z= some number.  How to get rid of the "z =" so that I can declare that "some number" to be some variable?

Greetings Sirs,

I have recently aquired Maple for some mathematics, and being a new user, I basically google for everything at the moment.

While it has gone well so far, I seem to have hit a bump that I cannot figure out.

I have a function: f(x)=3.2+0.4sin(1.25x), 0<x<5

Trying to find the places where "f(x)=3.5" would normally be done with the equation "3.5=3.2+0.4sin(1.25x)", and when I solve for the equation in Maple I get a solution too.

Problem is though, I know there is supposed to be multiple solutions. Having used wolframalpha, and being capable of seeing the plot in Maple, I know there is two points within the period "x=0..5" that is the solution.

But when I try to solve the equation, I get only one solution per solve, and the second solve doesn't make much sense for me. These are what I use:

As you can see, in the first solve the entire function is being taking into consideration, yet I only get one solution... In the second solve I have tried specifying a period, but I still only get one solution.

Basically any help here is appreciated, because from what I understand, having read google, the solve command or fsolve command is supposed to give multiple results if they are there.

With appreciation,
Ciesi

(Edit: Image size changed)

when i want to get awenser i have to solve it for 36 equation and 36 variabales
but maple will not give me a solution (just toss me back my variabales ) i dont know whats wrong
it will give me an awenser for lower like 20equ and 20var ?
parameters :

there is m for power an equation (equation^m) its between 2 , 2.5 , 3 , 4
and N give 2N+2var and 2N+2equ
its a hard calculation i copy it here hope u get it

h= "a number "

p := proc (x) c[-N-1]*x^2+1 end proc

dp := diff(p(x), x)

ddp := diff(p(x), x, x)

DELTA2 := piecewise(k <> j, -2*(-1)^(j-k)/(j-k)^2, k = j, -(1/3)*Pi^2)/h^2

DELTA1 := piecewise(k <> j, (-1)^(j-k)/(j-k), k = j, 0)/h

DELTA0 := piecewise(k <> j, 0, k = j, 1)

PHI := proc (x) ln(sinh(x)) end proc

dPHI := diff(PHI(x), x)

ddPHI := diff(PHI(x), x, x)
 

for i from -N-1 to N do x[i] := ln(exp(i*h)+(exp(2*i*h)+1)^(1/2)) end do

variabales : c[-N-1],c[-N],c[-N+1]...c[N-1],c[N] total 2N+2 var



My equations

POL := seq(simplify(eval(sum(c[k]*((eval(2*dPHI*DELTA1), x = x[j])+eval(x[j]*ddPHI*DELTA1, x = x[j])+x[j]*(eval(dPHI^2, x = x[j]))*DELTA2), k = -N .. N)+eval(ddp, x = x[j])+2*(sum(c[k]*(eval(x[j]*dPHI*DELTA1, x = x[j])+DELTA0), k = -N .. N)+eval(dp, x = x[j]))/x[j]+(c[j]*x[j]+p(x[j]))^m, x = x[j])), j = -N-1 .. N)

solving

K := fsolve({seq(POL[v] = 0, v = 1 .. 2*N+2)})

it can calculate for m=2.5 , N=15 , h=0.29669

if you can calculate it for m=3 , N=17 , h=0.41600

Regarding my recent question http://www.mapleprimes.com/questions/221909-How-To-Extract-Data-From-Implicit-Function I would like to share an interesting observation. Here the code of the program:

restart;
R0 := ln(y)+Re(Psi(1/2+(2*(p^2+(1/2)*sqrt(2*I+4*ksi_fs^2*p^2)*tanh(sqrt(2*I+4*ksi_fs^2*p^2)*x)/(tau+0.5e-2*a)))/y))+gamma+2*ln(2)
tau:= 10.000:ksi_fs:=10:p:=0.037:
R0p:= unapply(R0, [a,x]):
R0f:= proc(a,x)
local r:= fsolve(R0p(a,x), y= 0..1);
   `if`(r::float, r, Float(undefined))
end proc:
M:= Matrix(
   (100,100),
   (i,j)-> R0f(i, 1 + (j-1)*(0.5-0)/(100-1)),
   datatype= float[8]
);

After approximately 2 hours of calculations I get a message window

But I repeat this calculations on another computer with the same Windows 7 64 bit and Maple 17 I don't get such error and I obtain desired data.

So can Maple be sensitive to the hardware? 

hey guys ,

 

i have problem to obtain roots for a higher order equation

 

thanks for your helppp.mw


 

restart

G := 6.6743*10^(-8); 1; R := 1336599.126346; 1; rho := 2.2450*10^14; 1; c := 2.9799*10^10; 1; a := 1/(8/3*(6.67*10^(-8)*Pi*rho/c^2))^.5

0.6674300000e-7

 

1336599.126346

 

0.2245000000e15

 

0.2979900000e11

 

4715700.713/Pi^.5

(1)

y(x) = rho*c((1-(x/a)^2)^(1/2)-(1-(R/a)^2)^(1/2))^2/(3*(1-(R/a)^2)^(1/2)-(1-(x/a)^2)^(1/2))

y(x) = 0.1993516000e36/(3*(1-0.8033593953e-1*Pi^1.0)^(1/2)-(1-0.4496840993e-13*x^2*Pi^1.0)^(1/2))

(2)

``


 

Download y(x).mw

Hi!

I am an error with the use of the function "Analytic" of the packpage RootFinding. These are the procedures:

 

CreaCos := proc (C, n, m, t) local k, F; F := C[1][1]+(C[1][2]-C[1][1])*t; for k to n-1 do F := F, C[k+1][1]+((1/2)*C[k+1][2]-(1/2)*C[k+1][1])*(1-cos(Pi*m^k*t)) end do; return F end proc;

 

Then, for k=50, 100, 150... the instruction

works correctly. However, for higher values of k (for instance, k=250) returns the below error. Some idea or suggets about occurs this error?

Many thanks for your time! 

Error, (in RootFinding:-Analytic) unable to evaluate `@`(evalf, proc (x) option remember; table( [( 0.524900000000000000000000000000e-1+Float(undefined)*I ) = Float(undefined)+Float(undefined)*I ] ) 31250*Pi*sin(62500*Pi*x)/(7/18-(1/2)*cos(62500*Pi*x)) end proc) at the value 0.524900000000000000000000000000e-1+Float(undefined)*I. The expression to be solved was probably not analytic.

 

 

 

hy 
need help 
i made this code but i can not get the answer ,help me to find out where i did wrong.

thanx in advance




restart;
f:=x->(x^3+3*x^2-1);
n:=30;
tol:=1e-9;
a[0]:=0;
b[0]:=10;
Digits :=15;

 

printf("No root F(x) abs(x[i+1]-x[i])\n");

for i from 1 to n do
t[i-1] :=evalf( (b[i-1]-a[i-1])/(f(b[i-1])-f(a[i-1])));
c[i-1] := evalf((a[i-1]*f(b[i-1])-b[i-1]*f(a[i-1]))/(f(b[i-1])-f(a[i-1])));
x[i] :=evalf( x[i-1]-t[i-1]*f(x[i-1])^2/(f(x[i-1])-f(c[i-1])));

printf("%d %10.15f %10.15f %10.15e \n",i,x[i],f(x[i]),abs(x[i]-x[i-1]));
if f(a[i-1])*f(c[i-1])<0 then
a[i]:=a[i-1];
b[i]:=c[i-1];
else
a[i]:=c[i-1];
b[i]:=b[i-1];
if abs(f(x[i]))<tol then
print("approximate solution"= x[i]);
print("No of iterations"= i);
break;
end if;
end if;
end do:

Running the code costs a lot of time, I need some suggestions to make faster and more accurate. Thanks!

sonkok.mw

how i can find order of convergence of newton method by expanding taylor series?? plz send me code???

 

Hi,

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.

restart

with(plots):

with(LinearAlgebra):

with(DEtools):

with(ColorTools):

Digits := 30

30

(1)

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})

(-n*psi*v+n*psi*v*exp(-2*lambda*Pi/(n*omega0)))*phi0+(lambda^2+n*psi-n*psi*exp(-2*lambda*Pi/(n*omega0)))*x0

(2)

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})

(-n*v+n*v*exp(-2*lambda*Pi/(n*omega0))+lambda^2+1)*phi0+(n-n*exp(-2*lambda*Pi/(n*omega0)))*x0

(3)

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)

-2*n^2*psi^2*v^2*(-1+cos(2*Omega*Pi/(n*omega0)))/(Omega^4-2*Omega^2*n*psi+2*Omega^2*n*psi*cos(2*Omega*Pi/(n*omega0))+2*n^2*psi^2-2*n^2*psi^2*cos(2*Omega*Pi/(n*omega0)))

(4)

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})

(5)

with(RootFinding):

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

6000.94*lambda^2-5999.94*exp(-.289855072463768115942028985507*lambda*Pi)*lambda^2+lambda^4+6000-6000*exp(-.289855072463768115942028985507*lambda*Pi)

(6)

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

(7)

"zeros.select(int 1)"

Error, missing operation

"zeros.select(int 1)"

 

``


Download question.mw

I will be really thankful for the help.

Regards

Sunit


Here, I attached my maple code. I need to find root. I am using fsolve. But I am not geting the root. Please any one help me... to find the root.

reatart:NULL``

m1 := 0.3e-1;

0.3e-1

(1)

m2 := .4;

.4

(2)

m3 := 2.5;

2.5

(3)

m4 := .3;

.3

(4)

be := .1;

.1

(5)

rho := .1;

.1

(6)

ga := 25;

25

(7)

a := 3.142;

3.142

(8)

q := .5;

.5

(9)

z[0] := 3;

3

(10)

x[0] := 1.5152;

1.5152

(11)

w[0] := 1.1152;

1.1152

(12)

a1 := be*z[0];

.3

(13)

a2 := be*x[0];

.15152

(14)

a3 := rho*w[0];

.11152

(15)

a4 := rho*z[0];

.3

(16)

a5 := rho*w[0];

.11152

(17)

a6 := rho*z[0];

.3

(18)

b1 := a1*a4*ga+a4*ga*m1;

2.475

(19)

D1 := a1+m1+m2+m3+m4;

3.53

(20)

D2 := a1*m2+a1*m3+a1*m4-a2*ga+a3*ga+m1*m2+m1*m3+m1*m4+m2*m3+m2*m4+m3*m4;

1.92600

(21)

D3 := a1*a3*ga+a1*m2*m3+a1*m2*m4+a1*m3*m4-a2*ga*m1-a2*ga*m4+a3*ga*m1+a3*ga*m4+m1*m2*m3+m1*m3*m4+m2*m3*m4+m1*m2*m3;

1.4499000

(22)

D4 := a1*a3*a4*ga+a1*m2*m3*m4-a2*ga*m1*m4+a3*ga*m1*m4+m1*m2*m3*m4;

.3409200

(23)

G1 := -a1*a6-a6*m1-a6*m2-a6*m3;

-.969

(24)

G2 := -a1*a6*m2-a1*a6*m3+a2*a6*ga-a3*a6*ga+a4*a5*ga-a6*m1*m2-a6*m1*m3-a6*m2*m3;

.549300

(25)

G3 := -a1*a3*a6*ga-a1*a6*m2*m3+a2*a6*ga*m1-a3*a6*ga*m1-a6*m1*m2*m3;

-.3409200

(26)

A1 := w^(4*q)*cos(4*q*a*(1/2))+D1*w^(3*q)*cos(3*q*a*(1/2))+D2*w^(2*q)*cos(2*q*a*(1/2))+D3*w^q*cos((1/2)*q*a)+D4;

-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200

(27)

B1 := w^(4*q)*sin(4*q*a*(1/2))+D1*w^(3*q)*sin(3*q*a*(1/2))+D2*w^(2*q)*sin(2*q*a*(1/2))+D3*w^q*sin((1/2)*q*a);

-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5

(28)

A2 := -w^(3*q)*a6*cos(3*q*a*(1/2))+G1*w^(2*q)*cos(2*q*a*(1/2))+G2*w^q*cos((1/2)*q*a)+G3;

.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200

(29)

B2 := -w^(3*q)*a6*sin(3*q*a*(1/2))+G1*w^(2*q)*sin(2*q*a*(1/2))+G2*w^q*sin((1/2)*q*a);

-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5

(30)

C := .27601200;

.27601200

(31)

Q1 := 4*C^2*(A2^2+B2^2);

.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2

(32)

Q2 := -4*C*A2*(A1^2-A2^2+B1^2-B2^2-C^2);

-1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)

(33)

Q3 := (A1^2-A2^2+B1^2-B2^2-C^2)^2-4*C^2*B2^2;

((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)^2-.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2

(34)

V := simplify(-4*Q1*Q3+Q2^2);

-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2)

(35)

x := (-Q2+sqrt(V))/(2*Q1);

(1/2)*(1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)+(-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2))^(1/2))/(.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2)

(36)

E := -2*A1*C*x-A1^2+A2^2-B1^2+B2^2-C^2;

-.2760120000*(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)*(1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)+(-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2))^(1/2))/(.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2)-(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2+(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2-(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2+(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1

(37)

y := -E/(2*C*B1);

-1.811515442*(-.2760120000*(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)*(1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)+(-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2))^(1/2))/(.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2)-(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2+(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2-(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2+(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)/(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)

(38)

``

fsolve(x^2+y^2 = 1, w)

fsolve((1/4)*(1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)+(-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2))^(1/2))^2/(.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2)^2+3.281588197*(-.2760120000*(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)*(1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)+(-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2))^(1/2))/(.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2)-(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2+(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2-(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2+(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)^2/(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2 = 1, w)

(39)

``

 

Download root.mw

 For solving polynomial systems I used RootFinding[Isolate]. But after discussing the question http://www.mapleprimes.com/questions/211774-Roots-Of--Expz--1
I decided to compare Isolate and evalf(solve ([...], [...])). It seemed to me that solve some convenient. The only if in the equation there are integers as a real, they should be recorded with a decimal point. (For real solutions of this procedure should be used with (RealDomain).)  Examples:

SOLVE_ISOLATE.mw

I wonder why then the need Root Finding [Isolate]?

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