Good afternoon.

I request your valuable suggestion for the above cited subject.

I here by uploading the file for your kind notice.

Hello.

given this expression

T:=unapply((1/6930)*exp(-(1/7938)*(X[4]-933)^2)*exp(-(1/6050)*(X[2]-805)^2)/((1+exp((1/50)*X[4]-(1/50)*X[2]))*Pi),X[2]);

U := unapply(sum(T(X[2]), X[4] = 0 .. 3600), X[2]):

I want to display U, but not all 3600 terms. is there anyway to simplify/reduce this sum?

kind of like geo series a+ar+ar^2+ar^3+...+ar^(n-1)=sum(ar^k,k=0..n-1) can be reduced to a*(1-r^n)/(1-r)

hello
i have a problem that you could help me
i have an expression that i want convert it to an expression according to the expression q[d] with maple
i have bellow expressions
B[d]:=(-d*w[1]+w[3])/(((-2*w[1]+w[3])^2)-((-d*w[1]+w[3])^2))
B[o]:=(-2*w[1]+w[3])/(((-2*w[1]+w[3])^2)-((-d*w[1]+w[3])^2))
A[o]:=w[1]*(alpha[o]-c[o]-t[o])+2*w[2]*e[o]
A[d]:=w[1]*(alpha[d]-c[d]-t[d])+2*w[2]*e[d]
q[o]:=B[o]*A[o]-B[d]*A[d]
q[d]:=B[o]*A[d]-B[d]*A[o]
i want simplify expression U[d] such as this one
U[d]:=w[1]*(q[d]*(alpha[d]-q[d]-d*q[o]-c[d]-t[d])-C)+w[2]*(e[d]*q[d]+e[o]*q[o])+w[3]*((1/2)*(q[d]+q[o])^2)
I'm looking to simplify U[d] according to the expression q[d]
please please help me

Hey,

Basically the problem is that when I try to derive a variable L, which is defined by a very big equation, Maple does not do the maple. But if I copy and paste the big equation it calculates everything perfectly. Could I get any insight on why is that?

The copy paste method is very space consuming.

Thanks in advance.

I have a system of pdes and solved numerically using pdsolve (numeric) command.

The system consists of four first order partial differentia equations.

for example u(x,t), R(x,t)....

what command should I give to the Maple and get the graph of u(x,t) at a specific point x_0?

For example, I need a plot for u(30,t).

Is it possible with the maple plot?

I really appreciate your help.

Thank you for reading this post. :)

Dear community,

The VectorCalculus package in Maple 18 exhibits some rather odd behaviour when calculating an integral over a 3D-domain (an elipsoid centered at (0,0,1) with length of semi-axes 2, 2, and 1) given by a 'Region'. It also reports an incorrect result when calculating the flux of a vector field through the surface of this ellipsoid.

See below for a minimal working example:

// integrate several functions over ellipsoid

int(2*x+2*y, [x, y, z] = Region(-2 .. 2, -sqrt(-x^2+4) .. sqrt(-x^2+4), -sqrt(1-(1/4)*x^2-(1/4)*y^2)+1 .. sqrt(1-(1/4)*x^2-(1/4)*y^2)+1));    ---- output: 0

int(2*z, [x, y, z] = Region(-2 .. 2, -sqrt(-x^2+4) .. sqrt(-x^2+4), -sqrt(1-(1/4)*x^2-(1/4)*y^2)+1 .. sqrt(1-(1/4)*x^2-(1/4)*y^2)+1));    ---- output: 32*Pi/3

int(2*x+2*y+2*z, [x, y, z] = Region(-2 .. 2, -sqrt(-x^2+4) .. sqrt(-x^2+4), -sqrt(1-(1/4)*x^2-(1/4)*y^2)+1 .. sqrt(1-(1/4)*x^2-(1/4)*y^2)+1));    ---- output: -32*Pi/3

Why does the integral change sign?

// Calculate flux of vector field over surface of ellipsoid

F2 := VectorField(`<,>`(x^2, y^2, z^2));

S2 := Surface(`<,>`(2*sin(t)*cos(s), 2*sin(t)*sin(s), 1+cos(t)), s = 0 .. 2*Pi, t = 0 .. Pi);

Flux(F2, S2, 'outward');   ---- output: -32*Pi/3

However, since 'z' is positive over the entire ellipsoid, by the Divergence Theorem we know the result should be positive (in fact, equal to +32*Pi/3). Changing 'outward' to 'inward' does not change the sign, by the way.

Is this a bug inside the VectorCalculus package which appears more often, or have I done something wrong?

Thank you for responding and apologies if a similar question has already been answered in another thread.

Best wishes,

QQ

I have drawn a 3d plot of a sphere in maple, but when I try to export this one in an .eps file, only the coordinate system of the plot is shown, but not the colourful plot. The export works if I use jpg and similar file types, but not with .eps, does anybody know if there is a way out of this problem?

I have a problem solving a system of PDEs.

The system of PDEs are

PDE01 := -(l^2+1^2)*(diff(v(l, t), t))+(l^2+1^2)*(diff(R(l, t), l, l))+4*l*(diff(R(l, t), l))+4*l*v(l, t)/(l^2+1^2)^(1/4)-6*R(l, t)/(l^2+1^2)+(l^2+1^2)^(1/2)*(-1.1+sqrt(.1))^2*sqrt(24)*u(l, t) = 0

PDE02 := diff(R(l, t), t) = v(l, t)

PDE03 := diff(u(l, t), t)-sqrt((1.1^2-1)/1.1^2)*(diff(u(l, t), l))-2*l*sqrt(1.1^2-1)*u(l, t)/(l^2+1^2) = 0

the initial condisions are

v(l, 0) = 0, R(l, 0) = 0, u(l, 0) = sqrt((l^2+1^2)^(1/2))*10^(-5)*exp(-(l-10)^2/.5^2)

and the BCs are

bdry00 := {((30^2+1^2)/30^2)^(1/4)*v(-30, t) = -((30^2+1^2)/30^2)^(1/2)*(D[1](R))(-30, t), ((30^2+1^2)/30^2)^(1/4)*v(30, t) = -((30^2+1^2)/30^2)^(1/2)*(D[1](R))(30, t), u(-30, t) = sqrt(30^2+1^2)*10^(-5)*exp(-40000), u(30, t) = sqrt(30^2+1^2)*10^(-5)*exp(-10000)}

to solve the system,

I enter

pde := pdsolve({PDE01, PDE02, PDE03}, {bdry00, init00}, time = t, numeric, range = -30 .. 30, timesstep = 1/60, spaceste = 1/254)

then, I failed to get the result constantly.

I tried several cases changing the initial conditions...

Can you let me know what I am doing wrong?

I have a problem with IsMatrixShape. I have in my part of formulation this matrix expression: Q^TI_bQ

While I_b is a symmetric matrix, this matrix expression is clearly symmetric. However, when I try to check this issue with IsMatrixShape command, it returns false. I am extremely confused. Can anyone help me? Thanks in advance.

I'm attempting to plot the Nyquist plot for a complex system such that Maple cannot determine the frequency limits automatically, and suggested I use 'range' to specify the frequency limits. How do you do this? For example if you have a system G=1/(s+1), how do you plot the Nyquist plot in the frequency range 0 to 1rad/s?  Thanks

Write a Maple code that performs the Gaussian elimination for an nxn matrix, converting it to an upper triangular matrix. 

(Hint: you will need to use three for .. do loops.)

Write a recursive Maple procedure, called “decToBin”, that converts an integer from decimal (base 10) to binary (base 2). Ensure that only integers are allowed as arguments to the procedure. Passing a negative integer should result in no output. Test your procedure by outputting the result of the following:
decToBin(10)
decToBin(163)
decToBin(213)
decToBin(-1)
decToBin(“A”) # should result in an “invalid input” error

Hello everyone,

I am working on a program in Maple and got stuck in exchanging limits for integrals. For example, if I have an expression of following type.

Eq:=4*Int(f(x), x=0..1/3)+Int(x*f(x), x=0..2/3);

I want to convert it in to an expression of form

4*Int(f(x),x=0..x)-4*Int(y,x=1/3..x)+ Int(x*f(x), x=0..x)- Int(x*f(x), x=2/3..x)

In short, I want to split both the integral at x but flip in limits in the second integral. I tried as follows which did not work

applyrule(Int(f::anything,y=c::numeric..d::numeric)=Int(f,y=c..x)-Int(f,y=c..x), Eq)

Please, help me!

Thank you for your time.

Hey people,

I am trying to get the following code to run, but it keeps returning an error about too many arguments

restart:with(plots):with(PDEtools):
alpha_const := 0.5:gamma_const := 2.5: D1 := 0.05: D2 := 0.002:
A := diff_table(a(x,t)):B := diff_table(b(x,t)):
Selkov[1] := A[t] = 1 - A[]*B[]^(gamma_const) + D1*A[x,x]:
Selkov[2] := B[t] = alpha_const * ( A[]*B[]^(gamma_const) - B[]) + D2 * B[x,x]:

bc[1] := D[1](a)(0,t)=0: bc[2] := D[1](b)(0,t)=0: bc[3] := D[1](a)(4*Pi,t) = 0: bc[4]:=D[1](b)(4*Pi,t)=0:

ic[1] := eval(A[],t=0)=a_0:ic[2] := eval(B[],t=0)=b_0:
case1 := eval(ic,[a_0=1,b_0=1]):
case2 := eval(ic, [a_0=piecewise((x<2*Pi+1) and (x>2*Pi-1), 0.99, 1), b_0=piecewise((x<2*Pi+1) and (x>2*Pi-1), 0.99, 1)]):

Case1Default := pdsolve({Selkov[1],Selkov[2]},{bc[1],bc[2],bc[3],bc[4],case1[1],case1[2]},numerical);

Error, (in pdsolve/sys) too many arguments; some or all of the following are wrong: [{a(x, t), b(x, t)}, {a(x, 0) = 1, b(x, 0) = 1, (D[1](a))(0, t) = 0, (D[1](a))(4*Pi, t) = 0, (D[1](b))(0, t) = 0, (D[1](b))(4*Pi, t) = 0}, numerical]

My code worked just earlier today, and now it wont. If i try to run pdsolve({Selkov[1],Selkov[2]}) it says that there is an error with general case of floats. 

You help is greatly appreciated!

I want to translate my maple code with matrice multiplication  to C code. But the command  "Multiply" cannot be translated. So I want to edit the function translation by myself. I use "AddFunction" command to create a new function  "Multiply" and want to specify its corresponding C code.

f := proc ()
local x,y;
x := Matrix([[1, 2], [3, 4]]);
y := Matrix([[1,3],[4,2]]);
Multiply(x, y);
NULL;
end proc;

LanguageDefinition:-Define("NewC", extend = "C", AddFunction("Multiply", [Matrix,Matrix]::Matrix,
proc (X, Y)
local a,b;
a := 2;
b := convert(a, string);
Printer:-Print("Mmultiply(", X);
Printer:-Print(",", Y, ")"); Printer:-Print("\n");
Printer:-Print("from", b, "to");
Printer:-Print(",", Y, "do") end proc, numeric = double));
Translate(f, language = "NewC")

But when I run it, the "Multiply" function cannot be translated.  The result is:

Warning, type signature [CodeGeneration:-Names:-ArrayType(integer,CodeGeneration:-Names:-ArrayRanges(1 .. 2,1 .. 2),CodeGeneration:-Names:-ArrayOptions()), CodeGeneration:-Names:-ArrayType(integer,CodeGeneration:-Names:-ArrayRanges(1 .. 2,1 .. 2),CodeGeneration:-Names:-ArrayOptions())] for function Multiply is not recognized
void f (void)
{
  int x[2][2];
  int y[2][2];
  x[0][0] = 1;
  x[0][1] = 2;
  x[1][0] = 3;
  x[1][1] = 4;
  y[0][0] = 1;
  y[0][1] = 3;
  y[1][0] = 4;
  y[1][1] = 2;
  Multiply(x, y);
  ;
}

I don't know why "Multiply(x,y)" cannot be translated.

If I put two "Multiply(x, y)" in the procedure, like this:

f := proc ()
local x,y;

Multiply(x, y);
x := Matrix([[1, 2], [3, 4]]);
y := Matrix([[1,3],[4,2]]);
Multiply(x, y);
NULL;
end proc;

LanguageDefinition:-Define("NewC", extend = "C", AddFunction("Multiply", [Matrix,Matrix]::Matrix,
proc (X, Y)
local a;
a := 2;
b := convert(a, string);
Printer:-Print("Mmultiply(", X);
Printer:-Print(",", Y, ")"); Printer:-Print("\n");
Printer:-Print("from", b, "to");
Printer:-Print(",", Y, "do") end proc, numeric = double));
Translate(f, language = "NewC")

THe result is:

Warning, cannot resolve types, reassigning x's type
Warning, cannot resolve types, reassigning y's type
Error, (in CodeGeneration:-IssueError) type 'Matrix' cannot be translated to target language

I don't know why type 'Matrix' cannot be translated.