Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

i have this problem -> f'^2 -ff''=f'''-k1(2f'f'''-ff''''-f''^2)+Ha^2(E1-f') with boundary conditions f(0)=0, f'(0)=1, f'(∞)=0.

since it is a fourth order equation, but only three bcs, it does not produce unique solution. so the solution of the equation may be seek in form of f=f0(eta)+k1f1(eta).

thus the equation will become 

f0'^2-f0f0''=f0'''+Ha^2(E1-f0')

and

f1'''-Ha^2f1'-2f0'f1'+f0f1''+f1f0''=2f0'f0'''-f0f0''''-f0''^2.

boundary conditions are 

f0(0)=0,f0'(0)=1,f0'(∞)=0

f1(0)=0,f1'(0)=0,f1'(∞)=0.

i had been clueless in solving this problem. please somebody help me with this problem.

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}

 

I''m looking to complete the following, and then use the 2nd to find what n for which Fn is divisible by f(3),  not sure where to start..any help much appreciated..

 

proc(f::procedure,s::posint,r::posint,c::posint)
description
"Indicate divisibility of f(n) by s for n <= cr.",
"Write 'D' for divisible, else 'n'; r rows and c cols.";
local i, j, str, char;

for i from 0 to r-1 do
str := "";
for j from 1 to c do
if (f(c*i+j) mod s) = 0 then
str := cat(str,"D")
else
str := cat(str,"n")
end if
end do;
print(str)
end do
end proc; # s_div_f

and

proc(s::posint,r::posint,c::posint)
description
"Indicate divisibility of Fib(n) by m for n <= cr.",
"Write 'D' for divisible, else 'n'; r rows and c cols.";
---MORE STUFF HERE---
end proc; # s_div_fib

 

Hello everybody,

 

I would like to know if there's a possibility to change the style of the errorbars in errorplot. I would espacially like to add short lines at both ends of each errorbar, orthogonal to those, similiar to the looks of errorbars in GNUplot.

 

I appreciate your help. Many thanks in advance!

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;

when one of element in matrix s variable below code is very slow

 

MA := MatrixMatrixMultiply(InputMatrix3aa - lambda*IdentityMatrix(3);
eignvalues1 := evalf(solve(Determinant(MA), lambda));
MA1 := MatrixMatrixMultiply(InputMatrix3aa - eignvalues1[1]*IdentityMatrix(3);
MA2 := MatrixMatrixMultiply(InputMatrix3aa - eignvalues1[2]*IdentityMatrix(3);
MA3 := MatrixMatrixMultiply(InputMatrix3aa - eignvalues1[3]*IdentityMatrix(3);
eignvector1 := LinearSolve(MA1,<x,y,z>);

eignvector2 := LinearSolve(MA2,<x,y,z>);

eignvector3 := LinearSolve(MA3,<x,y,z>);

hw2_unfinished.mw

There is something wroung with the t0.

How to correct it?

Why the interface typesettings option doesn't affect the content of a MathContainer?

I opened a new document. Then I inserted the command interface(typesetting=extended); to improve the visualization of a disequation's solution. It works in the worksheet, but it doesn't work in the content of a MathContainer.

Hello! I have written a algorithm. Can you help me find errors? thank you very much. sorry, my English is not very good!

LL:=proc(A::Matrix)
uses LA= LinearAlgebra;
local i, j, k, n:= LA:-RowDimension(A),
L:= Matrix(LA:-Dimensions(A));
L[1,1]:=sqrt(A[1,1]);
for j from 2 to n do
L[j,1]:=(A[j,1])/(L[1,1]);
end do;
for i from 2 to n-1 do
L[i,i]:=(A[i,i]-add(L[i,k]^(2),k=1..i-1))^(1/(2));
for j from i+1 to n do
L[j,i]:=(1/L[i,i])*(A[j,i]-add(L[j,k]*L[i,k],k=1..i-1));
end do;
end do;
L[n,n]:=(A[n,n]-add((L[n,k])^(2),k=1..n-1)^(1/(2));
L;

I want to know the mistakes i have made in the documents attached to get the expected results every time.

NULL

Case 1: control = works fine now.

M1 := K__1*A*(Matrix(2, 2, {(1, 1) = 1, (1, 2) = -1, (2, 1) = -1, (2, 2) = 1}))/l__1 = Matrix(2, 2, {(1, 1) = 0.30e-2, (1, 2) = -0.30e-2, (2, 1) = -0.30e-2, (2, 2) = 0.30e-2})

NULL

NULL

Case 2: control = prints answer in next line.M1 := K__1*A*(Matrix(2, 2, {(1, 1) = 1, (1, 2) = -1, (2, 1) = -1, (2, 2) = 1}))/l__1 = Matrix([[K__1*A/l__1, -K__1*A/l__1], [-K__1*A/l__1, K__1*A/l__1]]) = Matrix(2, 2, {(1, 1) = 0.300000000000000e-2, (1, 2) = -0.300000000000000e-2, (2, 1) = -0.300000000000000e-2, (2, 2) = 0.300000000000000e-2})

NULL

control = prints expression and answer in the next line.

case 3

M1 := K__1*A*(Matrix(2, 2, {(1, 1) = 1, (1, 2) = -1, (2, 1) = -1, (2, 2) = 1}))/l__1 = Matrix([[K__1*A/l__1, -K__1*A/l__1], [-K__1*A/l__1, K__1*A/l__1]]) = Matrix(2, 2, {(1, 1) = 0.300000000000000e-2, (1, 2) = -0.300000000000000e-2, (2, 1) = -0.300000000000000e-2, (2, 2) = 0.300000000000000e-2})

NULL

Numeric formating does not function in case2 and cae 3. I dont know shat hv i done for these things to occur. But what should i do?

NULL

 

Download onlineResultandNumeric_format_doesnot_work_in_some_casesWhy.mwonlineResultandNumeric_format_doesnot_work_in_some_casesWhy.mw

Ramakrishnan V

rukmini_ramki@hotmail.com

Hello,

 I am trying to solve an differential equation in Maple, but I have no response from Maple.Can someone give a look for me? The coefficients a and b cannot be zero.

 Thanks a lot.

 

Download edo_solução_A_U.mw

 

NULLIn TEXT MODE the greek letters phi and varphi behave peculiarly in text entries inside text box in drawing. If it is the first letter it prints alright. Otherwise they rverse themselves (phi to varphi and viceversa). Is this solvable?

 

NULL

 

Download A_DOUBT_on_phi_varphi.mw


 


 

 

Ramakrishnan V

rukmini_ramki@hotmail.com

 

``

 

I would appreciate if anyone lets me know how to write circular references  (say 1 inside a circle to refer element 1. At present i do a drawing insert text and using.

 

Also i do not know how to remove the boundary of the overall drawing.

NULL

 

Download A_DOUBT_to_be_sent_to_prime_community.mw

Ramakrishnan V

rukmini_ramki@hotmail.com

hello

I have recently install Maple17 on my computer (Windows10) and I need to use some Greece alphabet such as ß but I look everywhere in maple's icon and I just could find capital Greece alphabet.

does anybody know how can I find those?

Hello,

I'm having an issue with this and I can't seem to fix it. Any help is greatly appreciated! Thank you in advance!!! For some reason mapleprimes won't let me upload the worksheet so I have pasted it below this message.

 

Kind regards.

Gambia Man

with(LinearAlgebra); UseHardwareFloats; with(plots); interface(rtablesize = infinity); with(Statistics);
L := 4; U := 1;
V := proc (x, y) options operator, arrow; piecewise((1/4)*L <= x and x <= (1/2)*L and (1/4)*L <= y and y <= (1/2)*L, U) end proc;
plot3d(V(x, y), x = 0 .. L, y = 0 .. L);

Vij := proc (ni, mi, nj, mj) local Xi, Xj; option remember; global U, L; Xi := 2*sin(ni*evalf(Pi)*x/L)*sin(mi*evalf(Pi)*y/L)/L; Xj := 2*sin(nj*evalf(Pi)*x/L)*sin(mj*evalf(Pi)*y/L)/L; return U*(int(int(Xi*Xj, x = (1/4)*L .. (1/2)*L), y = (1/4)*L .. (1/2)*L)) end proc;
HamilMat := proc (K::integer) local ni, mi, nj, mj, N, Hamil, Eigenvec, i, j, res; option remember; global Vij, U, L; N := K^2; ni := Vector(N); mi := Vector(N); nj := Vector[row](N); mj := Vector[row](N); for i to N do for j to K do res := (i+K-j)/K; if type(res, integer) = true then ni[i] := j; nj[i] := j; mi[i] := res; mj[i] := res end if end do end do; Hamil := Matrix(N, shape = symmetric); for i to N do for j from i to N do if i <> j then Hamil(i, j) := Vij(ni[i], mi[i], nj[j], mj[j]) elif i = j then Hamil(i, j) := Vij(ni[i], mi[i], nj[j], mj[j])+(1/2)*(ni[i]^2+mi[i]^2)*Pi^2/L^2 end if end do end do; Eigenvec := Eigenvectors(Hamil, output = ['values', 'vectors']), Hamil end proc;
SigFigEi := proc (Location::integer, SigFig::integer, VecSize::integer) local values, Eig, i; global HamilMat, OptK; Eig := Vector(VecSize); for i from 2 to VecSize do Eig[i] := HamilMat(i)[1][Location]; if evalf(Eig(i), SigFig+1) = evalf(Eig(i-1), SigFig+1) then OptK := i; break end if end do; values := evalf(Eig[i], SigFig); return values, OptK end proc;
BasisFunc := proc (location) local ni, mi, func, i, j, p, N, res, BasisSol; global HamilMat, L, OptK; p := evalf(Pi); N := OptK^2; ni := Vector(N); mi := Vector(N); for i to N do for j to OptK do res := (i+OptK-j)/OptK; if type(res, integer) = true then ni[i] := j; mi[i] := res end if end do end do; func := Vector(N); for i to N do func[i] := HamilMat(OptK)[2][i][location]*sin(ni[i]*p*x/L)*sin(mi[i]*p*y/L) end do; BasisSol := unapply(add(func[i], i = 1 .. N), x, y); return plot3d(BasisSol(x, y), x = 0 .. L, y = 0 .. L), func end proc;
BasisFunc(1);
Error, (in Vector) dimension parameter is required for this form of initializer

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