I am a new user to Maple, but have used PTC's Mathcad and Prime.

I have several matrices that I need to combine both vertically and horizontally.  The command augment will combine the matrices horizontally.  I was unable to find a command to combine the matrices vertically.  I tried the stack command (Prime command).  The Maple stack command appears to have a different functionality.  Could you suggest which command would do the job?  The matrices are large and I would like to limit the number of rows and columns shown in the document.

The next step will be sorting the data. I am researching this at this time.

Thank you for the support,

David Tietje

Download onderzoek_reeks_-hoe_krijg_ik_een_partieke_symbolische_som.mw

Input:

 a := x^2;
 whattype(x);
 b := x[1]^2;
 whattype(x[1]);
 CodeGeneration[C](a);
 CodeGeneration[C](b);

Output:

Do you know why cg0 =/= x[0]*x[0]?

Hello people in MaplePrimes,

I can't understand a code with PLOT3D using GRID in it.
I hope you will give me explanation about it.

restart;
k:=[[1,2,10],[1,1,8],[0,1,5],[0,0,6]];
PLOT3D(GRID(1..2,1..3,k),
       AXESLABELS(x,y,z));

I cannot understand the correspondence between points in the graph and lists in the code such as [1,2,10], [1,1,8].

 As two ranges in GRID augments in the code are 1..2 and 1..3, x takes value from 1 to 2, and
y from 1 to 3 in the picture.
And, as k is k:=[[1,2,10],[1,1,8],[0,1,5],[0,0,6]], which means this list of lists are 4 X 3, so in the picture
as for x the interval of 1 to 2 is divided to three sections with the points of value of 0, 1/3, 2/3 and 3/3, which total number is 4.
And, as for y the interval of 1 to 3 is devided to two sections with the points of value of 1, 2 and 3, which total number is 3.

And, I cannot understand why from the grid of [1,1,8] in the code, which I think is the coodinate of (1, 1) on x-y plane, does not mean that the value of z on that point on the graph is not 8, but 1.

graph.mw

restart:

sys:={-diff(v(x,t),t)+0.5*p*diff(u(x,t),x,x)+q*u(x,t)*(u(x,t)^2+v(x,t)^2)=0,diff(u(x,t),t)+0.5*p*diff(v(x,t),x,x)+q*v(x,t)*(u(x,t)^2+v(x,t)^2)=0};
        /                      /  2         \
        |/ d         \         | d          |
sys := < |--- u(x, t)| + 0.5 p |---- v(x, t)|
        |\ dt        /         |   2        |
        \                      \ dx         /

               /       2          2\       / d         \
   + q v(x, t) \u(x, t)  + v(x, t) / = 0, -|--- v(x, t)|
                                           \ dt        /

           /  2         \                                      \ 
           | d          |             /       2          2\    | 
   + 0.5 p |---- u(x, t)| + q u(x, t) \u(x, t)  + v(x, t) / = 0 >
           |   2        |                                      | 
           \ dx         /                                      / 
eq1 := diff(u(x,t),t) = u__t(x,t):
eq2 := diff(v(x,t),t) = v__t(x,t):

sys_tmp := subs(eq1, eq2, sys):

sys_new := sys_tmp union {eq1, eq2}:

Boundary conditions:
bc :=
    u(0,t) = 2,
    v(0,t) = 0;
                 bc := u(0, t) = 2, v(0, t) = 0
Initial conditions:
ic :=
    u(x,0) = tanh(2*Pi),
    v(x,0) = tanh(2*Pi),
    u__t(x,0) = 0,
    v__t(x,0) = 0;
 
ic := u(x, 0) = tanh(2 Pi), v(x, 0) = tanh(2 Pi), u__t(x, 0) = 0, 

  v__t(x, 0) = 0
Solve the system:
pdsol := pdsolve(subs(p=1, q=0.5, sys_new), {ic, bc}, numeric);

I want to change my variables. The coding below shows the influence of the Nb and Nt on the local Nusselt number (-theta') against the convection Bi.

But now I want it to be  the influence of the Bi on the local Nusselt number (-theta') against the Nb and Nt.

Can anyone help me?

Download odeProb2.mw

Download contourintegraal_vraag1.mw

I have just come across this curious but really boring problem.
In the code snippet below, expr1 and expr2 are identical.

restart:
data := [a=1, b=2]:
convert(
  piecewise(And(x(t) > a, x(t) < b), 1, 0),
  Heaviside
):
expr1 := eval(eval(%, data),  x(t)=z):
plot(expr1, z=0..3);


convert(
  piecewise(And(z > a, z< b), 1, 0),
  Heaviside
):
expr2 := eval(%, data),:
plot(expr2, z=0..3);

But if I change the parameterization of the problem, expr2 is still correct but expr1 is not

restart:
data := [d=1.5, a=0.5]:
convert(
  piecewise(And(x(t) > d-a, x(t) < d+a), 1, 0),
  Heaviside
):
expr1 := eval(eval(%, data),  x(t)=z):
plot(expr1, z=0..3);


convert(
  piecewise(And(z > d-a, z< d+a), 1, 0),
  Heaviside
):
expr2 := eval(%, data),:
plot(expr2, z=0..3);

Where does this come from?

PS: I'm sorry not to be able loading the mw file

Hello, 

I would like to write to a file the output of the command CodeGeneration[Matlab]. I couldn't find a way to write the output. 

What I am trying to do is to generate complex symbolic equations and expressions and write them as either a function or variables in matlab. 

As an example: 

exp := [sin(theta(1)), cos(theta(1))]; 

func := unapply(exp,[theta]); 

CodeGeneration:-Matlab(func)

If i can write the output of the above command in a matlab file, it will generate a matlab function file. 

I was using the command 'writeto' but this one basically outputs every line a command written to a file instead of the terminal, which is not what I want (it will output even the warnings, I know I can silent them!). 

can you please help.. thanks. 

Hello guys,

I want to plot two functions such as x(t) and y(t) in a unique diagram as a function of each other. In a routine way, one needs to solve one of these functions as t and then input its results in others. for example, solving x(t) to find t and then input this t(x) into y(t) to have y(x). but here problem is that I cannot solve x(t) to find t and so this routine solution is not accelssible.

x(t):=1 + (3*n*(v - 1)^2*A*(t^v)^2*(1 + alpha*(v - 1)^2*A^2*(t^v)^2*ln(m^2*t^2/((v - 1)^2*A^2*(t^v)^2))/(3*n^2*m^2*t^2) + A^2*beta*(v - 1)^2*(t^v)^2/(3*n^2*m^2*t^2))*((4*A^2*alpha*t^v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + 6*t^(-v + 2)*m^2*n^2 + 4*t^v*(beta - alpha/2)*A^2*(v - 1)^2)*sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2) - 3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2))*(1 + ((4*A^2*alpha*t^v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + 6*t^(-v + 2)*m^2*n^2 + 4*t^v*(beta - alpha/2)*A^2*(v - 1)^2)*sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2) - 3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2))/(3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2))))/(2*v^2*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2)) - (3*n^2*(v - 1)^2*A^2*(t^v)^2*(1 + alpha*(v - 1)^2*A^2*(t^v)^2*ln(m^2*t^2/((v - 1)^2*A^2*(t^v)^2))/(3*n^2*m^2*t^2) + A^2*beta*(v - 1)^2*(t^v)^2/(3*n^2*m^2*t^2))*(((4*A^2*alpha*t^v*v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2))/t + 4*A^2*alpha*t^v*(v - 1)^2*(2 - 2*v)/t + 6*t^(-v + 2)*(-v + 2)*m^2*n^2/t + 4*t^v*v*(beta - alpha/2)*A^2*(v - 1)^2/t)*sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2) + (4*A^2*alpha*t^v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + 6*t^(-v + 2)*m^2*n^2 + 4*t^v*(beta - alpha/2)*A^2*(v - 1)^2)*n^2*(v - 1)^2*A^2*t^(2*v)/(sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2)*v*t) - 3*n*A*(2*A^2*alpha*t^(2*v)*v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2))/t + A^2*alpha*t^(2*v)*(v - 1)^2*(2 - 2*v)/t + 2*A^2*beta*(v - 1)^2*t^(2*v)*v/t + 6*n^2*m^2*t))/(3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2)) - (((4*A^2*alpha*t^v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + 6*t^(-v + 2)*m^2*n^2 + 4*t^v*(beta - alpha/2)*A^2*(v - 1)^2)*sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2) - 3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2))*(2*A^2*alpha*t^(2*v)*v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2))/t + A^2*alpha*t^(2*v)*(v - 1)^2*(2 - 2*v)/t + 2*A^2*beta*(v - 1)^2*t^(2*v)*v/t + 6*n^2*m^2*t))/(3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2)^2)))/(2*v^2):

y(t):=1 + ((4*A^2*alpha*t^v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + 6*t^(-v + 2)*m^2*n^2 + 4*t^v*(beta - alpha/2)*A^2*(v - 1)^2)*sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2) - 3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2))/(3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2)) - (((4*A^2*alpha*t^v*v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2))/t + 4*A^2*alpha*t^v*(v - 1)^2*(2 - 2*v)/t + 6*t^(-v + 2)*(-v + 2)*m^2*n^2/t + 4*t^v*v*(beta - alpha/2)*A^2*(v - 1)^2/t)*sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2) + (4*A^2*alpha*t^v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + 6*t^(-v + 2)*m^2*n^2 + 4*t^v*(beta - alpha/2)*A^2*(v - 1)^2)*n^2*(v - 1)^2*A^2*t^(2*v)/(sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2)*v*t) - 3*n*A*(2*A^2*alpha*t^(2*v)*v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2))/t + A^2*alpha*t^(2*v)*(v - 1)^2*(2 - 2*v)/t + 2*A^2*beta*(v - 1)^2*t^(2*v)*v/t + 6*n^2*m^2*t))/(3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2)) - (((4*A^2*alpha*t^v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + 6*t^(-v + 2)*m^2*n^2 + 4*t^v*(beta - alpha/2)*A^2*(v - 1)^2)*sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2) - 3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2))*(2*A^2*alpha*t^(2*v)*v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2))/t + A^2*alpha*t^(2*v)*(v - 1)^2*(2 - 2*v)/t + 2*A^2*beta*(v - 1)^2*t^(2*v)*v/t + 6*n^2*m^2*t))/(3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2)^2))*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2)/((4*A^2*alpha*t^v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + 6*t^(-v + 2)*m^2*n^2 + 4*t^v*(beta - alpha/2)*A^2*(v - 1)^2)*sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2) - 3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2)):

there are x(t) and y(t). I want to plot y as x, not t. so please help me.

with best

Hello people in Mapleprimes,
I haven't written in this site for a long time.

I have a question in the below program, which is to write ribbons.
For the implementation of this program, 
I wrote this.
ribbonplot5([cos, sin, cos + sin], -Pi .. Pi,numpoints=20);

In the part of pattern matching, as -Pi .. Pi above is a range, so it is OK.
But, when I changed this part to x=-Pi..Pi, an error message appears.

ribbonplot5([cos, sin, cos + sin],x=-Pi .. Pi,numpoints=20);

brings error messages:
"Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct"

In the code of ribbonplot5,  x=-Pi..Pi which is the type of name=range shoud satisfy the pattern matching, as I wrote in the first part of the program as 
ribbonplot5 := proc(Flist, r1::{range,name=range})

I cannot know why the part of the program:
 
" else
       newFlist := map(unapply, Flist, lhs(r1));
     opts := ['labels'=[lhs(r1), " "," "],
                 args[3 .. nargs]];
    ribbonplot5(newFlist,rhs(r1),op(opts)):
"

wouldn't work well.

I wish I could get an answer to this. 

Thanks in advance.

This is a program in maple9 Advanced Programming Gude p. 253

graphic_ribbonplot.mw

restart;
extend := proc(f)
     local x, y;
     unapply(f(x), x, y);
end proc:
p:=x->cos(2*x):
q:=extend(p);


ribbonplot5 := proc(Flist, r1::{range,name=range})
     local i, m, p, n, opts,newFlist;
     opts := [args[3 .. nargs]];
     if type(r1, range) then
         if not hasoption(opts, 'numpoints', 'n', 'opts')
         then n := 25
         end if; 
         m := nops(Flist);
         p := seq(plot3d(extend(Flist[i]), r1, (i-1) .. i,
                                  grid=[n, 2], op(opts)),
                       i = 1 .. m):
         plots[display](p):
     else
       newFlist := map(unapply, Flist, lhs(r1));
     opts := ['labels'=[lhs(r1), " "," "],
                 args[3 .. nargs]];
    ribbonplot5(newFlist,rhs(r1),op(opts)):
   end if:
end proc:
ribbonplot5([cos, sin, cos + sin], -Pi .. Pi,numpoints=20);

I'd like to get the simplest possible expression when using simplify. The problem is that this is all done in a program, without having the benifit of looking at the expression on the screen and trying things. So I need a method that works for large set of input all the time.

I noticed in this example that simplify did not do what I think it should have.

Given the expression -2*(x^3 + 2)/(x*(x + 1)*(sqrt(3)*I + 2*x - 1)*(sqrt(3)*I - 2*x + 1)) it can be simplified to (x^3 + 2)/(2*x^4 + 2*x) but  I had to go into many tries in order to get this final result.

Is there a better way to do this? I end up now   doing simplify(expand(numer(expr))/expand(denom(expr))) in the hope to get better simplification.  Here is an example

It would be nice if Maple simplify would just do it directly as follows in Mathematica. May be there is a an  option I am overlooking

Download simplify.mw

I drew a methane molecula and display three times because I wanted to get two-fold and three-fold symmetry axis. ,I would is that I would like to get a more exact output and doing it without clicking, it's say, using code. Can someone help me?tareaclase6.mw
 

Download tareaclase6.mw

Suppose I have a real function which is defined on these intervals [x0,x1],...[x1,xn], and on each interval it's defined differently, for example f(x):=sqrt(x) if x>=0; f(x):=1/x if x<0.

For the last example I tried my last resort to use the assuming operator the following way:

f := ((x -> sqrt(x)) assuming (0 <= x)) or ((x -> 1/x) assuming (x < 0)) plot(f, x)

But it doesn't seem to be working, how do you propose to define this function? perhaps proc?

I tried looking for an example in maple's help, but didn't find any.

Your help is appreciated.

I read that abs(v) should find the magnitude of complex number. But I find cases where it does not.

Should one then use sqrt( Re(v)^2 + Im(v)^2 ) instead or is there different command to use?  Here is an example

Download complex.mw

Here is the same thing in Mathematica:

I searched help for modulus but could not find one.

Maple 2021.2