How to calculate colimit with only substitution and solve? Any simple example to show the steps.

run a command string in C# by calling maple

it can run in maple if copy into maple

however return input string was not in correct format

String commandstring = "restart;with(LinearAlgebra):with(ExcelTools): filename := "0257.HK";open3 := Import(cat(cat("C://Temp//HK//Transportation//",filename),".xls"), filename, "B2:B100");high3 := Import(cat(cat("C://Temp//HK//Transportation//",filename),".xls"), filename, "C2:C100");low3 := Import(cat(cat("C://Temp//HK//Transportation//",filename),".xls"), filename, "D2:D100");close3 := Import(cat(cat("C://Temp//HK//Transportation//",filename),".xls"), filename, "E2:E100");n := 30;Round := proc(x,n::integer:=1) parse~(sprintf~(cat("%.",n,"f"),x)); end proc: t:=1; gg :=Matrix(n+1,1); ggg :=Matrix(n+1,1); for k from 0 to n do InputMatrix3 := Matrix([[close3[t+1+k] , close3[t+k], close3[t+2+k]],[close3[t+k], close3[t+2+k],0],[close3[t+2+k],0 , 0]]): InputMatrix3b := Matrix([[close3[t+2+k], close3[t+1+k] , close3[t+3+k]],[close3[t+1+k] , close3[t+3+k],0],[close3[t+3+k],0 , 0]]): InputMatrix3c := Matrix([[close3[t+3+k] , close3[t+2+k], close3[t+4+k]],[close3[t+2+k], close3[t+4+k],0],[close3[t+4+k],0 , 0]]): Old_Asso_eigenvector := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3), InputMatrix3)): Old_Asso_eigenvector2 := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3b), InputMatrix3b)): Old_Asso_eigenvector3 := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3c), InputMatrix3c)): gg[k+1,1] :=Old_Asso_eigenvector[2][1,1]; od;Round(Re(gg[1,1][1,1]));";

(g o f ) o alpha =g o (f o alpha)
restart;alpha := (1/2)*(-x-x*t1-y*t2-y*t3+sqrt(x^2+2*x^2*t1+2*x*y*t2+2*x*y*t3+x^2*t1^2+2*x*t1*y*t2+2*x*t1*y*t3+y^2*t2^2+2*y^2*t2*t3+y^2*t3^2-4*x*t4*y*t9-4*x^2*t4*t7-4*x*t4*y*t8-4*y^2*t9-4*y*x*t7-4*y^2*t8-4*y^2*t5*t9-4*y*t5*x*t7-4*y^2*t5*t8-4*y^2*t6*t9-4*y*t6*x*t7-4*y^2*t6*t8))/(x*t4+y+y*t5+y*t6);
g := -y/x;
f := (-x+sqrt(x^2-x*y-2*y^2))/(2*y+x);
subs(p=f,subs(q=f,subs(x=p,subs(y=q,g)))); # -1
g := (-x+sqrt(x^2-x*y-2*y^2))/(2*y+x);
f := x*y;
gof := subs(p=f,subs(q=f,subs(x=p,subs(y=q,g)))); # -(1/3)*(y/x+sqrt(-2*y^2/x^2))*x/y
lhsgofoalpha := subs(q= alpha,subs(p=alpha, subs(x=p,subs(y=q,gof))));
foalpha := subs(p= alpha,subs(q=alpha,subs(x=p,subs(y=q,f))));
rhsgofoalpha := subs(x= foalpha,subs(y= foalpha, g));
osys := lhsgofoalpha = rhsgofoalpha;
sys1 := subs(x=0, osys);
sys2 := subs(y=0, osys);
sys3 := subs(x=1, osys);
sys4 := subs(y=1, osys);
sys5 := subs(x=2, osys);
sys6 := subs(y=2, osys);
sys7 := subs(x=3, osys);
sys8 := subs(y=3, osys);
sys9 := subs(x=4, osys);
sys1 := subs(x=3,subs(y=2, osys));
sys2 := subs(x=5,subs(y=1, osys));
sys3 := subs(x=1,subs(y=5, osys));
sys4 := subs(x=1,subs(y=2, osys));
sys5 := subs(x=2,subs(y=5, osys));
sys6 := subs(x=5,subs(y=2, osys));
sys7 := subs(x=2,subs(y=1, osys));
sys8 := subs(x=3,subs(y=5, osys));
sys9 := subs(x=5,subs(y=3, osys));
res:=solve([sys1, sys2, sys3, sys4, sys5, sys6, sys7, sys8, sys9], {t1,t2,t3,t4,t5,t6,t7,t8,t9});
eval(osys,res);
simplify(%);
`~`[lhs](select(evalb, res));

I want to begin by saying hello! im new to the forums i hope some one can give me a push in the right direction with some of my maple homework. im sort of stuck on a few of these questions and would be greatfull for some help. 

Let .

a) Let g be the tangent line to f when x = c. Use Maple to find g as a function of c.

b) Use Maple to plot f and g(3) using view = [0..5, -25..100].

c) Define a function called plot_tan that plots both f and g(c) where f is blue and g(c) is red. Also use the same view as in part (b). Note that plot_tan is also a function of c.

d) Using your function plot_tan, the following all in one graph using the display command:

plot_tan(1), plot_tan(1.5), plot_tan(2), plot_tan(2.5), plot_tan(3), plot_tan(3.5), plot_tan(4), plot_tan(4.5), plot_tan(5).

e) Try using the option insequence = true in the display command. What does this option do? (You will need to click on the graph and play around with some buttons).

now it seems to me i have to use the point slope formula to get to a fuction g of c. thanks in advance! i hope you can help

Question

Find t1,t2,t3,...t9 in Matrix
Matrix(3, 3, {(1, 1) = 1+t1, (1, 2) = t2, (1, 3) = t3, (2, 1) = t4, (2, 2) = 1+t5, (2, 3) = t6, (3, 1) = t7, (3, 2) = t8, (3, 3) = t9})

osys := (1/2)*(-x-x*t1-y*t2-y*t3+sqrt(x^2+2*x^2*t1+2*x*y*t2+2*x*y*t3+x^2*t1^2+2*x*t1*y*t2+2*x*t1*y*t3+y^2*t2^2+2*y^2*t2*t3+y^2*t3^2-4*x*t4*y*t9-4*x^2*t4*t7-4*x*t4*y*t8-4*y^2*t9-4*y*x*t7-4*y^2*t8-4*y^2*t5*t9-4*y*t5*x*t7-4*y^2*t5*t8-4*y^2*t6*t9-4*y*t6*x*t7-4*y^2*t6*t8))/(x*t4+y+y*t5+y*t6) = (-x+sqrt(x^2-x*y-2*y^2))/(2*y+x)
sys1 := subs(x=0, osys);
sys2 := subs(y=0, osys);
sys3 := subs(x=1, osys);
sys4 := subs(y=1, osys);
sys5 := subs(x=2, osys);
sys6 := subs(y=2, osys);
sys7 := subs(x=3, osys);
sys8 := subs(y=3, osys);
sys9 := subs(x=4, osys);
solve([sys1, sys2, sys3, sys4, sys5, sys6, sys7, sys8, sys9],[t1,t2,t3,t4,t5,t6,t7,t8,t9]);

since i have only one equation osys, to find t1..t9, i substitute some values into x and y to get enough equation to solve this , however, the result is not expected below

then i try without x= 0 or y = 0 , i failed

sys1 := subs(x=3,subs(y=2, osys));
sys2 := subs(x=5,subs(y=1, osys));
sys3 := subs(x=1,subs(y=5, osys));
sys4 := subs(x=1,subs(y=2, osys));
sys5 := subs(x=2,subs(y=5, osys));
sys6 := subs(x=5,subs(y=2, osys));
sys7 := subs(x=2,subs(y=1, osys));
sys8 := subs(x=3,subs(y=5, osys));
sys9 := subs(x=5,subs(y=3, osys));
solve([sys1, sys2, sys3, sys4, sys5, sys6, sys7, sys8, sys9],[t1,t2,t3,t4,t5,t6,t7,t8,t9]);

solution : Matrix(3, 3, {(1, 1) = 2, (1, 2) = 0, (1, 3) = 0, (2, 1) = 1, (2, 2) = 1, (2, 3) = 1, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1})

 t1 = 1

t2 = 0

t3 = 0

t4 = 1

t5 = 0

t6 = 1 

t7 = 0

t8 = 0

t9 = 1

Data.xlsx

XY.mw

XYZ.mw

Hello,

I'm using the Global Optimization Toolbox to solve some examples and fit equations to a given data, finding "unknown" parameters. I generated the data on Excel, and I already know the values of these parameters.

The XY case is (there is no problem here, I just put as a example I follow):

> with(GlobalOptimization);
> with(plots);
> 
> X := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "I5:I25");
> Y := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "J5:J25");
> 
> XY := zip( (X, Y) -> [X, Y] , X, Y);
> fig1 := plot(XY, style = point, view = [.9 .. 3.1, 6 .. 40]);

> Model := A+B*x+C*x^2+D*cos(x)+E*exp(x):
> VarInterv := [A = 0 .. 10, B = 0 .. 10, C = -10 .. 10, D = 0 .. 10, E = 0 .. 10];

> ModelSubs := proc (x, val)

    subs({x = val}, Model)

    end proc;

> SqEr := expand(add((ModelSubs(x, X(i))-Y(i))^2, i = 1 .. 21));
> CoefList := GlobalSolve(SqEr, op(VarInterv), timelimit = 5000);
> 
> Model := subs(CoefList[2], Model):

I could find the right values of A, B, C, D and E. 

My problem is in the XYZ case, where I don't know how to "write" the right instruction. My last attempt was:

> with(GlobalOptimization);
> with(plots);

> X := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "Q5:Q25"); X2 := convert(X, list);
> Y := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "R5:R25"); Y2 := convert(Y, list);
> Z := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "S5:S25"); Z2 := convert(Z, list);
> NElem := numelems(X);

> pointplot3d(X2, Y2, Z2, axes = normal, labels = ["X", "Y", "Z"], symbol = box, color = red);

> Model := A*x+B*y+C*sin(x*y)+D*exp(x/y);

> VarInterv := [A = 0 .. 10, B = 0 .. 10, C = 0 .. 10, D = 0 .. 10];

> ModelSubs:=proc({x,y},val)

subs({(x,y)=val},Model)

end proc:
Error, missing default value for option(s)

> SqEr := expand(add((ModelSubs(x, y, X(i), Y(i))-Z(i))^2, i = 1 .. NElem));
> CoefList := GlobalSolve(SqEr, op(Range), timelimit = 5000);
Error, (in GlobalOptimization:-GlobalSolve) finite bounds must be provided for all variables

My actual problem involves six equations, six parameters and four or five independent variables on each equation, but I alread developed a way to solve two or more equations simultaneously.

Thanks

Does anybody know why the answer of a equation i am getting on maple is coming with "eval" written?

Example:

the answer should be a number ...

Why does it happen?

-.733448502640020+0.*I

i am investigating above numeric

when ln(-.733448502640020+0.*I);

-.3099978916+3.141592654*I

it has Pi imaginary part

then 

i try 

complex(1, exp(Pi)^3);

it return Complex(...) but not 1 + i*exp(Pi)^3

3 means 3 times come from recursively  using pattern ln(Re(ln(x) - 3.141592654*I))

3.141592654 in imaginary part appear 3 times

i use Round(Im(x), 8) during above operation

 actually i want to extract Pi imaginary part from -.733448502640020+0.*I

however, after minus exp(Pi) from it first time,

it is near the original number  -.733448502640020

is this elimination of imaginary part is just a illusion from log function?

Dear Experts,

When I run this code in maple I am facing with "Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging".

restart:
 
 unprotect('gamma');
 lambda:=5*10^5:
 mu:=0.003:
 beta:=4*10^(-10):
 delta:=0.2:
 alpha:=0.043:
 sigma:=alpha+delta:
 k:=6.24:
 gamma:=0.65:
 A[1]:=1:
 A[2]:=1:

ics := x[1](0)=1.7*10^8, x[2](0)=0,x[3](0)=400,psi[1](50)=0,psi[2](50)=0,psi[3](50)=0:

ode1:=diff(x[1](t), t)=lambda-mu*x[1](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t)*x[3](t)+delta*x[2](t),
 diff(x[2](t), t) =(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t)*x[3](t)-sigma*x[2](t),
 diff(x[3](t), t) =(1+psi[3](t)*k*x[2](t)/A[2])*k*x[2](t)-gamma*x[3](t),
 diff(psi[1](t), t) =-1+1/A[1]*beta^2*x[1](t)*x[3](t)^2*(psi[1](t)-psi[2](t))^2-psi[1](t)*(-mu+beta^2*x[3](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[1](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[3](t))-psi[2](t)*(-beta^2*x[3](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[1](t)+(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[3](t)),
> diff(psi[2](t), t) =1/A[2]*psi[3](t)^2*k^2*x[2](t)-psi[1](t)*delta+psi[2](t)*sigma-psi[3](t)*(psi[3](t)*k^2/A[2]*x[2](t)+(1+psi[3](t)*k*x[2](t)/A[2])*k),
> diff(psi[3](t), t) = 1/A[1]*beta^2*x[1](t)^2*x[3](t)*(psi[1](t)-psi[2](t))^2-psi[1](t)*(beta^2*x[1](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[3](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t))-psi[2](t)*(-beta^2*x[1](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[3](t)+(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t))+psi[3](t)*gamma;

sol:=dsolve([ode1,ics],numeric, method = bvp[midrich]);

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

Please help me to solve this equation on Maple.

Hello,

I understand that the question is not really Maple related, but I still hope for some help.

See the worksheet below. I defined a pure sine wave and determined the complex Fourier coefficients for it which I used to plot the amplitude and power spectra. It is easy to see the relations in terms of amplitude and power between the time and frequency signal.

The Fourier Transform of the sine wave logically shows the Dirac distribution, but I can't see the relation in terms of amplitude and power to the original time signal. Taking the integral of the transformed signal (A) wil result in a step of Pi at w=-1 and again at w=1. What am I missing here?

Thanks

Download 20140127MaplePrime.mw

I am using Maple worksheets in a class. I have a student who finds it difficult to spend much time at the keyboard because of a joint disorder. I am looking for alternate input methods such as Dragon or the Dictate Facility on MacBooks which might help her out. Any suggestions would be appreciated. 

Thanks,

-Maury

f:=Intat(1.0000000000000000000*(1.7969454312181156991*_f^1.2+1.80)^1.2/sqrt(-1.4974545260150964159*(8.9847271560905784954*_f^3+14.640368911168931285*_f^2+30.220202497712627297)^1.2), _f = 0);

I tried to use  value(f);  eval(f); simplify(f); expand(f), but non provide an answer, but return an integral unevaluated.

Is there a command to produce a  numerical result ?

THE FOLLOWING CODE 

restart;

A:=Matrix([[ a , b ], [ c , d ]]);

a:=1; b:=0; c:=0; d:=1;

A; 

produces differents results under MAPLE 16  linux i386 and under MAPLE 16  linux amd64

in the first case the last evalution has the following printed output:

on the second machine the printed output is

Does anybody has an explication; I thought that the "coorect behaviour was the first one since tables use last-name evalutation. But now I am puzzled.

how to decompose a matrix into time invariant and time variant 

is it possible to make time invariant and time variant template and then decompose into it

i mean decomposition can be 

 time invariant matrix + time variant matrix

or

 time invariant matrix * time variant matrix

 dsolve([Diff(f, t) = f, Diff(f,t) + g = h], f);

 dsolve([Diff(f, t) = f, Diff(f,t)*g = h], f);

where h is orthogonal matrix, f,g,h are matrix

would like to find g and f from h

can dsolve solve differential equation of matrix ? how?

dsolve([Diff(f(t), t) = f(t), Diff(f(t),t) + g(t) = h1(x)*h2(x), int(h1(x)*h2(x),x=-1..1) = 0], [f(t),g(t),h1(x),h2(x)]);

dsolve([Diff(f(t), t) = f(t), Diff(f(t),t)*g(t) = h1(x)*h2(x), int(h1(x)*h2(x),x=-1..1) = 0], [f(t),g(t),h1(x),h2(x)]);

assume x^2 + 1 is from interpolation of polynomial

pdsolve([Diff(f(t), t) = f(t), Diff(f(t),t) + g(t) = h1(x,t)*h2(x,t), h1(x,t)*h2(x,t)= x^2+1], [f(t),g(t),h1(x,t),h2(x,t)]);
pdsolve([Diff(f(t), t) = f(t), Diff(f(t),t)*g(t) = h1(x,t)*h2(x,t), h1(x,t)*h2(x,t) = x^2+1], [f(t),g(t),h1(x,t),h2(x,t)]);

these system can not be solved

hope no real number any more after decomposition and only have iinteger in I time invariant function

I am trying to get a solution to the heat equation with multiple boundary conditions.

Most of them work but I am having trouble with two things: a Robin boundary condition and initial conditions.

First, here are my equations that work:

returns a solution (actually two including u(x,y,z,t)=0).

However, when I try to add:

or

I no longer get a solution.

Any guidance would be appreciated.

Regards.

I have uploaded a worksheet with the equations...

Download heat_equation_pde.mw