hi i did this in maple and i get an error when i try to solve the system of equation  :

restart;
with(Student[VectorCalculus]);
with(PDEtools);with(plots);

h_f := 300;
h_a := 1000;
T_f := 1500 + 273;
T_a := 30 + 273;
k_r := 15;
k_s := 70;
Ra := 5;
Rf := 6.05;
Rc := 6;

I like using Record in Maple. It allows me to collect related variables to pass around inside one object. (Like with Pascal or Ada records or C struct).

But I find myself copying the record definition over and over everywhere I want to use the same specific record layout.

Is there a way to define specific record layout somewhere, may be as a type and give it a name, and then in each proc I want to make a variable of this record type, just tell Maple that this variable is a record of that type so I do not have to explicity define the record there each time? 

Here is a simple example to make it more clear

foo:=proc() #some proc that uses same Record layout
   local S;
   S:=Record('name','age');   
   S:-name:="joe doe 1";
   S:-age:=99;
   return S;
end proc:

boo:=proc() #another proc that wants to use same Record layout
   local S;
   S:=Record('name','age');   
   S:-name:="joe doe 2";
   S:-age:=80;
   return S;
end proc:

S1:=foo();
S2:=boo();

These proc's can be anywhere, such as inside package or module, either local or exported.

I just want to avoid having to type   S:=Record('name','age');   Each time. I want to tell Maple that a local variable is of this specific Record layout, without having to type the layout explicitly.

This way, when I add new field to this Record,  I just have to do it in one place and not in 10 places in the code. 

I think I need to add a new type? But do not know how to do this.  I hope the question is clear. If not, will add more information.

Hello everyone

I have the solution of diffusion equation from Help of maple website. I put the code here

*****************************

restart: with(plots):
 

unprotect(D);
 

alias(c[0]=c0, c[1]=c1, c[2]=c2);
PDE:=diff(C(x,t),t)=D*diff(C(x,t),x,x);
IBC:={C(x,0)=cx0, C(0,t)=ct0, D[1](C)(10,t)=0};
ct0:=1;
cx0:=0;
D:=1;
pds:=pdsolve(PDE,IBC,numeric);
L1:=[0.01, 0.1, 1, 5, 10];
L2:=[red, green, yellow, blue, magenta, black];
for i from 1 to 5 do
 pn[i] := pds:-plot(t=L1[i], color=L2[i]):
end do:
display({seq(pn[i], i=1..5)}, title=`Numerical solution at t=0.01, 0.1, 1, 5, 10`);

****************************

the code is working perfectly. But, My question is how can I found the diffusion constant (D) if I have the solution ( C(x,t) ).  Probably it should be an algorithm which use least square method to find (D) based on the data C(x,t).

I am looking for a fast and efficient algorithm if there is any.

thank you so much for your kind attentions in advance

Sincerely yours,

Amir

This ODE turns out to be a simple separable ODE. With one solution, if the ODE is rewritten.

But in its original form, Maple dsolve gives 6 complicated looking solutions with complex numbers in some of them. Even though all 6 solutions are valid.

Any one knows why Maple did that and not give the one simple solution instead? 

I used isolate to solve for y' from the original ODE. Verfiied that only one solution exist.  The ODE then became y'(x)= 3*y(x)/(2*x). Which by uniqueness theorem, should have one unique solution in some region in the RHS or in some region in the LHS that does not inculde x=0 ?

Just wondering what is going on, and why Maple did not give same simpler solution, so I can learn something new. That is all.

Download strange_ode_answer.mw

Maple 2019.1

Physics 395

Hi, I am trying to plot the phase potrait for this as follow:

s0 := 3*10^5;
d := 10^(-3);
delta := 10^4;
b := 5*10^6;
lamda := 4.16;

DEplot([diff(I(t), t) = s0 + I(t)*(-d - delta*Q(t)/(b + Q(t))), diff(Q(t), t) = -lamda*Q(t)], [I(t), Q(t)], t = 0 .. 10, I = 0 .. 100, 0, Q = 0 .. 100, 0, dirfield = 400, arrows = smalltwo, number = 2, [[0, 4, 0.1], [0, 0.2, 4.1], [0, 7, 0.2], [0, 0.2, 7]], color = red, linecolor = blue, numsteps = 100)

But, there is an error saying "Error, (in DEtools/DEplot) vars must be declared as a list, e.g. [x(t),y(t),...]". However, I did the same for other problem and worked well tho. I have no idea what the problem is for above.

When I apply the uses function with the Physics package in a procedure, the commands in this package are not restricted to the inside of the procedure, but are applied globally. See the example below:

gds := proc(LL, qi, t)

 local ta,i;  

uses Physics;

ta := sec(diff(diff(LL, diff(qi[i](t), t)), t), i = 1 .. nops(qi));

RETURN(ta) end:

sxy := diff(x(t), t)^2 + diff(y(t), t)^2:

gds(sxy, [x, y], t);

Error, (in Physics:-diff) name expected for external function
 

On the other hand, when I apply the uses function with the LinearAlgebra package in a procedure, the commands in this package are restricted to the inside of the procedure only.
dst:=proc(MM) 

local DA; 

uses LinearAlgebra;

DA:=Determinant(MM); 

RETURN(DA) end:

dst(<<1 | 2>, <3 | 4>>);

                  -2

Determinant(<<1 | 2>, <3 | 4>>);

                         Determinant(Matrix(2, 2, [[1, 2], [3, 4]]))

This could be a bug in Maple 2019?

The following differential equation:

sy := (dsolve({T*diff(y(x), x, x) + rho*omega^2*y(x) = 0, y(0) = 0, y(L) = 0}, y(x)) assuming (0 < T, 0 < omega, 0 < rho))

                                                                 sy:=y(x)=0

Maple only returns the trivial solution. Should return other expressions:
Thank you

step := t −> piecewise(t sum( (−1)∧n * step(t−n) , n=0..50);

Consider the following forced D.E. L d 2x dt2 + R dx dt + 1 C x = 200 ∗ f(t/3)

where R = 20 , C = 0.01 , L = 10 , x(0) = 10 , x 0 (0) = 0.

a. Graph the solution curve in the phase plane on Maple.

b. Graph x(t) over the interval 0 ≤ t ≤ 25 on Maple .

For the DE solution below, Maple returns only one option. I can't get the others. Can anyone help?

wW := unapply(piecewise(0 <= x and x < L/2, 0, L/2 <= x and x <= L, w[0]), x):

eq := k*diff(y(x), x$4) = wW(x):

dsolve({eq, y(0) = 0, y'(0) = 0, y''(L) = 0, y'''(L)=0}, y(x)) assuming 0 < L

          y(x) = -L*w[0]*x^3/(6*k) + L^2*w[0]*x^2/(4*k) + w[0]*x^4/(24*k)

Obrigado.
Oliveira

given an expression such as expr:=-1/2*x*(y^2-1) which in tree form will be

I can get -1/2 using op(1,expr).   I need command to return the "rest" of the right side of the tree, all of it, not matter how big.

I tried op(2..nops(expr),expr) and that returns x, y^2 - 1 

Is there a way to return directly x*(y^2-1)*etc....  so I do not have to play around with the above expression sequence?  Another option is to type

           expr/op(1,expr)

to get the right side of the tree. But this seems like a hack. Do not like to divide. worry about zero.

The same thing if the type was `+`, I want to get  the whole right side in one command.

Again, I can do  expr-op(1,expr) to get the whole right side. But this also seems like  a hack, altought not as bad as with  the * case above

Any hints on how to best do these things?

Maple 2019.1

I never used applyrule before. Seems like a good command. I was trying to tell Maple to rewrite

as

I could not find one command to do it.  Collect does not work. The only way I figure to it, is by replacing 

by a new single unused symbol, and then use collect on the symbol, then use subs again to replace the symbol with orginal  expression. like this

restart;
expr:=(x^2 - 1)/x^2*y + (x^2 - 1)/x^2;
r:=(x^2 - 1)/x^2; #this is what I want to collect
applyrule(r=Z,expr);
collect(%,Z);
subs(Z=r,%)

In the above code, if I replace applyrule by algsubs, it does not work. Why?

restart;
expr:=(x^2 - 1)/x^2*y + (x^2 - 1)/x^2;
r:=(x^2 - 1)/x^2;
algsubs(r=Z,expr);

You see, it did not replace (x^2-1)/x by Z, like applyrule does:

restart;
expr:=(x^2 - 1)/x^2*y + (x^2 - 1)/x^2;
r:=(x^2 - 1)/x^2;
applyrule(r=Z,expr);

I will learn applyrule now more to do this. I was just wondering why algsubs failed, and if applyrule is the better tool to do this. Or may be there is a better way to do this whole thing?

Maple 2019.1

I made a typo below, I did not mean to put [...] around the solution. But why Maple throws an error on this only?

restart;
ode:=diff(y(x),x) = exp(x)*sin(x)+y(x)*cot(x);
my_sol:=[sin(x)*(exp(x)+_C1)];
odetest( y(x)=my_sol,ode) assuming x::real

          Error, (in type/algext) too many levels of recursion

But on other ODE's, it works

restart;
ode:=diff(y(x),x) = y(x);
my_sol:=[_C1*exp(x)];
odetest( y(x)=my_sol,ode) assuming x::real

                [0]

I'll correct my type and remove the []. But the question is, should Maple have thrown an error? And why only on this one? Would this be considered a bug?

Removing the [] from the first example above, the error is gone and 0 is returned.

Maple 2019.1, Physics V 395 on windows 10

I'm new to Maple.

My problem is that if I input the command sqrt(3.0), for example, I get this strange result:

1.81847767202745*10^(-58) + (7.53238114626421*10^(-59))*I

The results is the same, no matter the argument of sqrt.

Also, when using ln, I get this:

-265.745524189222 + 0.785398163397448*I

Again, no matter the argument of ln, the result is the same.

What is happening?

I thought I remembed how to do this once in Maple, or asking something like this here, but may be it was something similar. But I am not able to figure it now or remember.

Given an expression, I want to find all occuranes of a pattern in it.  Not just one.  So this is like using patmatch but over and over again untill all patterns found. I'll give an example to make it easy to explain.

Given

expr := y^2*sin(1/y) + y^(3/2) + y + x*y^7;

I want to find all patterns of form y^n  so the result should be 

{y^(3/2), y^7, y^2, 1/y, y}

This below is how it is done in Mathematica, but having hard time translating this code to Maple.

The last line below does the actual repeated pattern matching. That line was not written by me. It is something from Mathematica forum at stackexchange and I use it all the time and it works well.

ClearAll[x,y,n]
expr = y^2*Sin[1/y] + y^(3/2) + y + x*y^7;
pat = y^n_.;
Last@Reap[expr /. a : pat :> Sow[a], _, Sequence @@ #2 &]

I looked at hastype also. But hastype will only tell me if the pattern is there or not. May be I did not use it right.

restart;
expr := y^2*sin(1/y) + y^(3/2) + y + x*y^7;
hastype(expr,symbol^(anything));

Gives true

I tried patmatch, but again, it only find one:

restart;
expr := y^2*sin(1/y) + y^(3/2) + y + x*y^7;
if patmatch(expr,a::anything+y^(n::anything)+b::anything,'la') then
   assign(la);
   n;
fi;

And the above is not even robust for finding one. Since I have to change the pattern again to account for multiplication/addition cases between terms. 

Is it possible to do in Maple the same thing I show in Mathematica? I am sure it is possible, but can't now find the right function in Maple.

Maple 2019.1