## Problem when solving equations...

Hello dears! Hope everything going fine with you. I have faced problem while solving the system of equations using fsolve command please find the attacment and fixed my problem.

I am very thankful to you for this favour.

VPM_Help.mw

Mob #: 0086-13001903838

## All roots of equation...

hi.i trust that attached equation has more answer but fsolve only gain some of them!!! how i can gain another that i know value of them?

another root  that i known, are : 0.165237712988657e-1    and     .103583272213766    and    .290071279318035

thanks

root.mw

## Problem with Determinant...

hi.after calculate Determinant of matrix  and gain value omega'' ω'' by fsolve rule ,when substuting result (ω) in matrix (q) and calculate Determinant again, this value is not zero!!!! may i use LUDecomposition?determinan.mw

## Finding a numerical solution to system of equation...

I have a system of equations in several variables and I just need one numerical solution of it, I tryed to use fsolve of Maple but it always show me some errors or gives back the command as the output.

aaghulu := {-6-4*y-x-(1+y)*x+sqrt((4*(1+y))*(2+x)*(4+2*y+x)+(-(1+y)*x+2+x)^2), (2*(4+2*y+x))*(1+y)-(1+y)*x+2+x+sqrt((4*(1+y))*(2+x)*(4+2*y+x)+(-(1+y)*x+2+x)^2)-(2+y)*(-(1+y)*x+2+x+sqrt((4*(1+y))*(2+x)*(4+2*y+x)+(-(1+y)*x+2+x)^2))};

fsolve(aaghulu, {x, y}, maxsols = 1);

I will be happy if someone guide me how to do these kinds of things using Maple.

## Problem with system in two unkowns...

Hello guys and gals!

I'm not strong enough with maple to get what the result I want.

It seems that it's because I'm asking for two lenths, and not a lenth and an angle, but I have no Idea how to tackle it diferently.

If you know a trick, please share it!

Here's an image:

http://imgur.com/xavAUoB

And here's the maple file attached (I think)

Thanks,

Happy new year!

## Understanding output of fsolve...

I am trying to solve 4 nonlinear equations for four variables using fsolve  and the output that i am getting is basically the same equations repeated after some time.  I even tried reducing one of the equations using assumptions from my side but it results in same behaviour..  Quite new to maple, would like some advice as to this behaviour. Thanks

Here's the file

fsolve_1.mw

PS- using do loop is part of the solving so i cannot remove that

## How to solve this equation?...

Hi all

How I use "solve" or "fsolve" for this equation ?

M2 := evalf[4](Matrix(4, 4, {(1, 1) = BesselJ(0, 0.5e-1*sqrt(0.1111111111e-16*omega^2-25.00027778)), (1, 2) = -BesselJ(0, 0.5e-1*sqrt(0.4444444445e-16*omega^2-25)), (1, 3) = -BesselY(0, 0.5e-1*sqrt(0.4444444445e-16*omega^2-25)), (1, 4) = 0, (2, 1) = (0.1111111111e-16*I)*omega*(1-25000000000000/omega^2)*BesselJ(1, 0.5e-1*sqrt(0.1111111111e-16*omega^2-25.00027778))/sqrt(0.1111111111e-16*omega^2-25.00027778), (2, 2) = -(0.4444444444e-16*I)*BesselJ(1, 0.5e-1*sqrt(0.4444444445e-16*omega^2-25))/sqrt(0.4444444445e-16*omega^2-25), (2, 3) = (0.4444444444e-16*I)*BesselY(1, 0.5e-1*sqrt(0.4444444445e-16*omega^2-25))/sqrt(0.4444444445e-16*omega^2-25), (2, 4) = 0, (3, 1) = 0, (3, 2) = BesselJ(0, 0.60e-1*sqrt(0.4444444445e-16*omega^2-25)), (3, 3) = BesselY(0, 0.60e-1*sqrt(0.4444444445e-16*omega^2-25)), (3, 4) = -BesselY(0, 0.60e-1*sqrt(0.1111111111e-16*omega^2-25)), (4, 1) = 0, (4, 2) = (0.4444444444e-16*I)*BesselJ(1, 0.60e-1*sqrt(0.4444444445e-16*omega^2-25))/sqrt(0.4444444445e-16*omega^2-25), (4, 3) = (0.4444444444e-16*I)*BesselY(1, 0.60e-1*sqrt(0.4444444445e-16*omega^2-25))/sqrt(0.4444444445e-16*omega^2-25), (4, 4) = -(0.1111111111e-16*I)*omega*BesselY(1, 0.60e-1*sqrt(0.1111111111e-16*omega^2-25))/sqrt(0.1111111111e-16*omega^2-25)})):

with(LinearAlgebra):
DETM2 := Determinant(M2):
solve(DETM2 = 0, omega);

Error, (in solve) cannot solve for an unknown function with other operations in its arguments

Is this Error because of combination of bessel functions? if I use asymptatic forms, does it work?

Thanks

## Creating matrix of fsolve output...

Hi Please I need help with making the output of my fslolve appear in a way that I can easily copy to an excel.

I am doing analysis for 3 countries and each time I produce a result I copy manually to excel and use 'text to column' and the 'transpose' excel options to arrange the results in order. I do this for almost 20 time because I want to see how hows in parameter affect the variables. is there a way I can convert this to a 32 by 3 matrix so that I can copy all at the same time instead of copying each variable at a time. here is my solve command

UK_SOL_FIRST:= fsolve(eval({eq||(1..32)}, Params_UK_FIRST), InitValue_UK_FIRST);
ES_SOL_FIRST:= fsolve(eval({eq||(1..32)}, Params_ES_FIRST), InitValue_ES_FIRST);
DK_SOL_FIRST:= fsolve(eval({eq||(1..32)}, Params_DK_FIRST), InitValue_DK_FIRST);

The Results

UK_SOL_FIRST:={A_ss = 14.36104896, C_ss = 1.445842138, I_ss = 0.3136706500,

K_ss = 12.54682600, K_v_ss = 125.4682600,

LT_ss = 0.01061009037, L_ss = 4.014721807, N_ss = 0.9307582996,

P_a_ss = 0.9336893751, P_ss = 0.8625403648,

Surp = 0.9890479879, U_b_ss = 0.1781599919,

U_ss = 0.1046105158, V_ss = 0.05052687912, W_max = 1.476989982,

W_min = 0.4879419937, W_ss = 1.826907218,

W_tilde = 3.478049987, Y_ss = 2.428417935, aa_ss = 21.67403493,

chhi = 0.4523413798, f_c_ss = 0.04880034560,

m_ss = 0.03536881539, p_d_ss = 0.9907986980,

x_T = 0.7023268636, y_d_ss = 10.57030302, y_f_ss = 1.174478111,

y_x_ss = 10.57030300, z_ss = 21.14060602,

Profit_ss = 4.094720376, phi_prod = 0.9753885739,

theta_ss = 0.4830000000}

ES_SOL_FIRST:={A_ss = 10.91702785, C_ss = 2.038687975, I_ss = 0.3058575000,

K_ss = 12.23430000, LT_ss = 0.1309315222, L_ss = 2.857497927,

N_ss = 0.8398656215, P_a_ss = 0.9680877046,

P_ss = 0.8638978804, Surp = 2.541617932, U_b_ss = 0.9095925505,

U_ss = 0.1819708847, V_ss = 0.03119500880, W_max = 3.252738093,

W_min = 0.7111201606, W_ss = 3.605202340,

W_tilde = 3.665280790, Y_ss = 2.367929032, aa_ss = 15.67939783,

betta = 0.9909865708, chhi = 0.2898275349,

f_c_ss = 0.6743530978, m_ss = 0.02183650616,

p_d_ss = 0.9939322922, x_T = 0.005556307841,

y_d_ss = 7.853422751, y_f_ss = 1.195945300,

y_x_ss = 7.978400682, z_ss = 15.83182343,

Profit_ss = 3.084421270, phi_prod = 1.009721394,

theta_ss = 0.1714285714}

DK_SOL_FIRST:={A_ss = 16.18893837, C_ss = 1.359886068, I_ss = 0.2487000000,

K_ss = 9.948000000, LT_ss = 0.02282780783, L_ss = 5.834365727,

N_ss = 0.9399351536, P_a_ss = 0.7054445707,

P_ss = 0.8796237740, Surp = 0.6511024854,

U_b_ss = 0.4572819488, U_ss = 0.08450316042,

V_ss = 0.03491187713, W_max = 1.293898615,

W_min = 0.6427961298, W_ss = 2.363825013,

W_tilde = 2.758200925, Y_ss = 1.755529412, aa_ss = 34.56310241,

betta = 0.9851712031, chhi = 0.4499333284,

f_c_ss = 0.1898151486, m_ss = 0.02443831399,

p_d_ss = 1.032636460, x_T = 0.1506134910, y_d_ss = 11.17773688,

y_f_ss = 0.9144278497, y_x_ss = 13.74561008,

z_ss = 24.92334696, Profit_ss = 4.926248216,

phi_prod = 0.7210969276, theta_ss = 0.4131428571}

## How to solve for variable xx?...

InputMatrix3aa := Matrix(3, 3, {(1, 1) = xx, (1, 2) = 283.6, (1, 3) = 285.4, (2, 1) = 283.6, (2, 2) = 285.4, (2, 3) = 0, (3, 1) = 285.4, (3, 2) = 0, (3, 3) = 0});
InputMatrix3 := Matrix(3, 3, {(1, 1) = 283.6, (1, 2) = 285.4, (1, 3) = 283.0, (2, 1) = 285.4, (2, 2) = 283.0, (2, 3) = 0, (3, 1) = 283.0, (3, 2) = 0, (3, 3) = 0});
InputMatrix3b := Matrix(3, 3, {(1, 1) = 285.4, (1, 2) = 283.0, (1, 3) = 287.6, (2, 1) = 283.0, (2, 2) = 287.6, (2, 3) = 0, (3, 1) = 287.6, (3, 2) = 0, (3, 3) = 0});
InputMatrix3c := Matrix(3, 3, {(1, 1) = 283.0, (1, 2) = 287.6, (1, 3) = 296.6, (2, 1) = 287.6, (2, 2) = 296.6, (2, 3) = 0, (3, 1) = 296.6, (3, 2) = 0, (3, 3) = 0});
InputMatrix3d := Matrix(3, 3, {(1, 1) = 287.6, (1, 2) = 296.6, (1, 3) = 286.2, (2, 1) = 296.6, (2, 2) = 286.2, (2, 3) = 0, (3, 1) = 286.2, (3, 2) = 0, (3, 3) = 0});

Old_Asso_eigenvector0 := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3aa), InputMatrix3aa)):
Old_Asso_eigenvector1 := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3), InputMatrix3)):
Old_Asso_eigenvector2 := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3b), InputMatrix3b)):
Old_Asso_eigenvector3 := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3c), InputMatrix3c)):
Old_Asso_eigenvector4 := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3d), InputMatrix3d)):

#AA2 := MatrixMatrixMultiply(Old_Asso_eigenvector3[2], MatrixInverse(Old_Asso_eigenvector2[2]));
#AA3 := MatrixMatrixMultiply(Old_Asso_eigenvector4[2], MatrixInverse(Old_Asso_eigenvector3[2]));

AA2 := MatrixMatrixMultiply(Old_Asso_eigenvector2[2], MatrixInverse(Old_Asso_eigenvector1[2]));
AA3 := MatrixMatrixMultiply(Old_Asso_eigenvector3[2], MatrixInverse(Old_Asso_eigenvector2[2]));

sol11 := solve([Re(AA2[1][1]) = sin(m*2+phi), Re(AA3[1][1]) = sin(m*3+phi)], [m,phi]);
if nops(sol11) > 1 then
sol11 := sol11[1];
end if:
sin(rhs(sol11[1])+rhs(sol11[2]));

sol12 := solve([Re(AA2[1][2]) = sin(m*2+phi), Re(AA3[1][2]) = sin(m*3+phi)], [m,phi]);
if nops(sol12) > 1 then
sol12 := sol12[1];
end if:
sin(rhs(sol12[1])+rhs(sol12[2]));

sol13 := solve([Re(AA2[1][3]) = sin(m*2+phi), Re(AA3[1][3]) = sin(m*3+phi)], [m,phi]);
if nops(sol13) > 1 then
sol13 := sol13[1];
end if:
sin(rhs(sol13[1])+rhs(sol13[2]));

#*************************************
sol21 := solve([Re(AA2[2][1]) = sin(m*2+phi), Re(AA3[2][1]) = sin(m*3+phi)], [m,phi]);
if nops(sol21) > 1 then
sol21 := sol21[1];
end if:
sin(rhs(sol21[1])+rhs(sol21[2]));

sol22 := solve([Re(AA2[2][2]) = sin(m*2+phi), Re(AA3[2][2]) = sin(m*3+phi)], [m,phi]);
if nops(sol22) > 1 then
sol22 := sol22[1];
end if:
sin(rhs(sol22[1])+rhs(sol22[2]));

sol23 := solve([Re(AA2[2][3]) = sin(m*2+phi), Re(AA3[2][3]) = sin(m*3+phi)], [m,phi]);
if nops(sol23) > 1 then
sol23 := sol23[1];
end if:
sin(rhs(sol23[1])+rhs(sol23[2]));

#**************************************
sol31 := solve([Re(AA2[3][1]) = sin(m*2+phi), Re(AA3[3][1]) = sin(m*3+phi)], [m,phi]);
if nops(sol31) > 1 then
sol31 := sol31[1];
end if:
sin(rhs(sol31[1])+rhs(sol31[2]));

sol32 := solve([Re(AA2[3][2]) = sin(m*2+phi), Re(AA3[3][2]) = sin(m*3+phi)], [m,phi]);
if nops(sol32) > 1 then
sol32 := sol32[1];
end if:
sin(rhs(sol32[1])+rhs(sol32[2]));

sol33 := solve([Re(AA2[3][3]) = sin(m*2+phi), Re(AA3[3][3]) = sin(m*3+phi)], [m,phi]);
if nops(sol33) > 1 then
sol33 := sol33[1];
end if:
sin(rhs(sol33[1])+rhs(sol33[2]));

#****************************************************

AAA1 := Matrix([[sin(rhs(sol11[1])+rhs(sol11[2])),sin(rhs(sol12[1])+rhs(sol12[2])),sin(rhs(sol13[1])+rhs(sol13[2]))],[sin(rhs(sol21[1])+rhs(sol21[2])),sin(rhs(sol22[1])+rhs(sol22[2])),sin(rhs(sol23[1])+rhs(sol23[2]))],[sin(rhs(sol31[1])+rhs(sol31[2])),sin(rhs(sol32[1])+rhs(sol32[2])),sin(rhs(sol33[1])+rhs(sol33[2]))]]);

MA := MatrixMatrixMultiply(Transpose(InputMatrix3aa), InputMatrix3aa) - lambda*IdentityMatrix(3):
eignvalues1 := evalf(solve(Determinant(MA), lambda)):
MA1 := MatrixMatrixMultiply(Transpose(InputMatrix3aa), InputMatrix3aa) - eignvalues1[1]*IdentityMatrix(3):
MA2 := MatrixMatrixMultiply(Transpose(InputMatrix3aa), InputMatrix3aa) - eignvalues1[2]*IdentityMatrix(3):
MA3 := MatrixMatrixMultiply(Transpose(InputMatrix3aa), InputMatrix3aa) - eignvalues1[3]*IdentityMatrix(3):
eigenvector1 := LinearSolve(MA1,<x,y,z>):
eigenvector2 := LinearSolve(MA2,<x,y,z>):
eigenvector3 := LinearSolve(MA3,<x,y,z>):

MR := MatrixMatrixMultiply(AAA1, Matrix([[Re(eigenvector1[1]),Re(eigenvector2[1]),Re(eigenvector3[1])],[Re(eigenvector1[2]),Re(eigenvector2[2]),Re(eigenvector3[2])],[Re(eigenvector1[3]),Re(eigenvector2[3]),Re(eigenvector3[3])]]));
ML := Re(Old_Asso_eigenvector1[2]);

solve(ML[1][1] = MR[1][1], xx);
with(Optimization):
Minimize(ML[1][1] - MR[1][1], {0 <= xx}, assume = nonnegative);

Error, (in Optimization:-NLPSolve) abs is not differentiable at non-real arguments;

## Error when fsolving ...

Error, (in fsolve/polynom) Digits cannot exceed 38654705646

I am using fsolve to find numerical approximations to the roots of many fairly large polynomials (degrees up to ~80).  I often get this error message and I'm not sure why.  Is there any workaround?  Any help is much appreciated.

## Complex solution...

This may be a trivial question, but does this factor fully with the newer versions of Maple, say at 900 digits?

Digits:=900;

rho_poly := -2201506283520*rho^32+(-17612050268160+104204630753280*I)*rho^31+(2237195146493952+737798139150336*I)*rho^30+(14065203494780928-29153528496783360*I)*rho^29+(-260893325886750720-161432056834818048*I)*rho^28+(-1240991775275876352+1727517243589263360*I)*rho^27+(8952004373272068096+6696323263091441664*I)*rho^26+(25553042370906292224-37948239682297921536*I)*rho^25+(-135024511500569280512-65293199430849134592*I)*rho^24+(-79740262928225402880+401487130320847241216*I)*rho^23+(956745211126674882560-164797793704574713856*I)*rho^22+(-1213375867282228772864-1655554058430246551552*I)*rho^21+(-1483956336776821211136+3604946201834409820160*I)*rho^20+(6525094787202650144768-1597915397190007586816*I)*rho^19+(-8575469412912592879616-6168391294117580865536*I)*rho^18+(2408139380338842796032+15004449784317106323456*I)*rho^17+(10583091471310114717696-17047513330720373194752*I)*rho^16+(-22619716982813548707840+8898637295768494915584*I)*rho^15+(26538067620972845277184+5129530051326543351808*I)*rho^14+(-21415800164460070789120-17268159356969925234688*I)*rho^13+(11916012071577094946816+22601135173030541677568*I)*rho^12+(-3551246770922037813248-21229478915196610975744*I)*rho^11+(-977434486760953073664+16249214903618313346048*I)*rho^10+(1977414870691507931136-10721551032564274826240*I)*rho^9+(-1197394212949208115968+6172794574205050632192*I)*rho^8+(280273257275327368320-2996290081120136529792*I)*rho^7+(108849195761508531648+1152454823926345101504*I)*rho^6+(-119736267114490955904-327757949185254534784*I)*rho^5+(49149411853848597568+63563541902968683712*I)*rho^4+(-11524495997215059744-7307364351434838944*I)*rho^3+(1585189353379709888+299568910286253408*I)*rho^2+(-116032795768295808+25487628220230528*I)*rho+3299863116538269-2454681763039104*I;;

## How to write loop?...

I want write loop for this code:

V := 24;

eq := {Eq2, Eq3};

ans := fsolve(eq, {a1 = 0, a3 = 0});

r := 0;

W1 := rhs(ans[1])*phi11(r)+rhs(ans[2])*phi21(r)

V and W1 is Variable, I change V and solve eq and determinen a1 and a3 after i calculated W1

I want write Loop for this,

can you help me????????/

## Solving numerically a system of non-linear equatio...

Hi, I'm trying to solve without success numerically the following system of 15 nonlinear equations. Could anyone help, please? Thanks

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 (1)
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## error with rule solve or fsolve...

hi.i am a problem with rule solve or fsolve in maple....please see attached file and say your comments

thanks

equ.mw

## Possible bug in "fsolve"...

As part of a project, I am numerically estimating the roots of many large polynomials. Occasionally, "fsolve" fails with strange errors related to "fsolve/refine2". Searches for these error messages have turned up nothing.

I've inluded the code below that causes the error on Maple 18.02. I apologize for the polynomial in question being so long, it's the shortest example I have. The error it generates is:

Error, (in fsolve/refine2) invalid input: evalf expects its 2nd argument, n, to be of type posint, but received undefined

Is this a bug? Or am I missing some fsolve option to prevent this? Note that it only happens when the "complex" flag is used.

=========

P := 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fsolve(P,complex);

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