Problem is here how to define the local variables?

Also the formatting of the code is not ideal

There is a error , but if the local variables are good defined , it could vanish    

Download exc_set_3_task_6.mw

Hi. I am trying to solve a system of differential equations but I am having trouble understanding what I do wrong. I am a novice Maple user.

>with(PDEtools): with(LinearAlgebra): with(DifferentialGeometry): with(VectorCalculus): with(DEtools):

>_Omega_d := 1-_Omega_r

>eq1 := h1(z)*h2(z)+h2(z)*h3(z)+h1(z)*h3(z)-3*(_Omega_d*((1+z)^3)+_Omega_r*((1+z)^4)) = 0

>eq2 := h2(z)^2+h3(z)^2+h2(z)*h3(z)-1/3*(1+z)*(h2(z)*(diff(h2(z), z))+h3(z)*(diff(h3(z), z)))+_Omega_r*((1+z)^4) = 0

>eq3 := h1(z)^2+h3(z)^2+h1(z)*h3(z)-1/3*(1+z)*(h1(z)*(diff(h1(z), z))+h3(z)*(diff(h3(z), z)))+_Omega_r*((1+z)^4) = 0

>eq4 := h2(z)^2+h1(z)^2+h2(z)*h1(z)-1/3*(1+z)*(h2(z)*(diff(h2(z), z))+h1(z)*(diff(h1(z), z)))+_Omega_r*((1+z)^4) = 0

>sys := {eq2, eq3, eq4}

Equations eq1 - eq4 are my equations, but since eq1 does not have a differentiated function, I leave it out of the system, otherwise I get an error that states that I have more functions than variables.

>sys1 := subs(_Omega_r = 10^(-15), sys)

>ics := {h1(0.1e-3) = 1, h2(0.1e-3) = 1, h3(0.1e-3) = 1, (D(h2))(0.1e-3) = 4.500015, (D(h3))(0.1e-3) = 4.500015, (diff(h1(z), z))(0.1e-4) = 4.500015}

ics are my inititial conditions.

>pdsolve(sys1 union ics, {h1(z), h2(z), h3(z)}, type = numeric, generalsolution)

But when I run this, I get an error that says "Error, (in pdsolve/sys) found the independent variables {z} also present in the names of the functions of the system {}".

I have tried numerous different methods to solve this, and I get stuck every time. If anyone has any advice, I would appreciate it. I am trying to get solutions for h1(z), h2(z), h3(z) (to ultimately plot these functions versus z), if possible.

Hi, I want to use Maple to derive the eigenvectors of a 3x3 matrix A. I can obtian the 3 eigenvalues correctly by using eigenvalues(A), and the results are "u, -a+u, a+u". But after inputing eigenvectors(A), I can only get "[-a+u, 1, {r}], [a+u, 1, {r}], [u, 1, {r}]". All the 3 eigenvectors are written as {r}, I dont know why...and how can I tranform {r} into visiable results? 

I would be very appreciate if anyone could give me some help!

Hi,

I am trying to find q(t) from this 

ode1:=-diff(q(t), t) - 1.851851852*10^(-7)*q(t)*(2.042885233*10^10 - 3.517396152*10^18*(0.00001474262739*cos((1000*sqrt(1122)*t)/33) + 0.00001474262739*sin((1000*sqrt(1122)*t)/33))^2) + 9.259259260*10^(-7);

with initial condition

ics := q(0) = 2.45*10^(-12)

using

dsolve({ode1,ics})

but I cannot get the full solution. Is there any way I could find q(t)?

Thanks,

Baharm31

This is the source:

ode1.mw

Whay the command:  123! + 1 takes significantly more time than 123! only??? Moreover time(123!+1) and time(123!) are very similar and fast.

I am using Worksheet GUI.

I do not understand what I am doing wrong. I have an Object, with private variable call hint. This private variable can be seen only by other proc's inside the object as expected.

Now inside one of those other proc's, I nested a small local proc inside it.

What I want is to access the object private variable from inside this small local proc nested inside.

But not able to. I tried different combinations and nothing is working.  Here is one of many attempts. 

restart;
module my_class()
   option object;
   local hint::string:="X"; #private variable to the object
 
   export foo::static:=proc(o::my_class) #can be seen from outside
      local boo; #local proc inside proc foo

      boo:=proc(o::my_class) #local proc
          print("inside boo()");
          print(o:-hint);
      end proc;

      print("in foo(), calling local proc boo()");
      print("hint is ",o:-hint); #works OK
      o:-foo:-boo(o); #tried also o:-boo(o) and boo(o)
   end proc;
end module;

called it as

o:=Object(my_class);
o:-foo(o)

Error, (in my_class:-foo) module `my_class` does not export `boo`
 

Also tried different combinations but so far nothing worked. For example, I tried making the nested proc static, but that did not help:

restart;
module my_class()
   option object;
   local hint::string:="X"; #private variable to the object
 
   export foo::static:=proc(o::my_class) #can be seen from outside
      local boo; #local proc inside proc foo

      boo::static:=proc(o::my_class) #local proc, static
          print("inside boo()");
          print(o:-hint);
      end proc;

      print("in foo(), calling local proc boo()");
      print("hint is ",o:-hint); #works OK
      boo(o);
   end proc;
end module;

o:=Object(my_class);
o:-foo(o)

Error, (in boo) module `my_class` does not export `hint`
 

But this error do not show up, when I made boo local to the object itself (vs. local to the proc). As follows, where the nested boo() proc is moved one level higher.

restart;
module my_class()
   option object;
   local hint::string:="X"; #private variable to the object
 
   export foo::static:=proc(o::my_class) #can be seen from outside     
      print("in foo(), calling local proc boo()");
      print("hint is ",o:-hint); #works OK
      o:-boo(o);
   end proc;

   local boo:=proc(o::my_class) #local proc to the object
      print("inside boo()");
      print(o:-hint);
   end proc;
end module;

now

o:=Object(my_class);
o:-foo(o)

works. No problem and no error.

How does one call a local proc to an object? Similar to how one does it in normal non-object proc's? 

Are local proc's inside object proc's allowed? Or for an Object, only one level of nesting is allowed?

Maple 2020.1

In Maple, an expression of type `*` can have many operands. I need to break it to product of two operands only.

For example given, expr:=A*B*C, I want first_part to be A and second_part to B*C

The way I do it now is clumsy.

I first check if expression is of type `*`, then use first_part :=op(1,expr) to find the first term, then divide the expression by that first term to find the second part. second_part:=expr/first_part

second_part:=op(2..nops(expr)) does not exaclty works, since it gives me B,C instead of B*C.

What would be a good way to do this? Notice that expr:=-A is actually a `*`, where first_part:=-1 and second_part:=A. Which is OK.

restart;
expr         := A*B*C;
first_part   := op(1,expr);
second_part  := expr/first_part;

How to draw a circle transfomed by orthogonal affinity to oblique line and k ration ? Thank you.

When I create a rooted vector 

v1:=RootedVector(root=[1,Pi/4,0],[0,0,1],spherical[r,theta,phi])

and a free vector

v2:=Vector([0,2,1],cartesian[x,y,z])

and dot product them

v1.v2

it gives me 2.

But if I change v1 to 

v1:=RootedVector(root=[1,Pi/6,0],[0,0,1],spherical[r,theta,phi])

the product of v1.v2 gives me an error

"..cannot combine two rooted vectors with different points of origin"

Can anyone explain me the problem? 

Here is what I understand: 

In spherical coordinates the unit vector e_r, e_th, e_ph are functions of theta and phi. So when I call root=[1,Pi/4,0] that means r=1, theta=Pi/4 and phi=0. This uniquely defines the unit vectors in spherical coordinates and r places the vector away in the e_r direction. The [0,0,1] then attaches a vector to the point r=1, theta=Pi/4 and phi=0  with only 1 unit along the e_ph direction.

What I don't understand is the concept of origin with the free vector and the rooted vector. How changing the theta from Pi/4 to Pi/6 makes the origin "different"? 

Edit: This is part of the VectorCalculus pacakge.

Hi:

How can I solve this system with numerical method:

eq1 := diff(f_n(zeta), zeta$2)-h_n(zeta)*(diff(f_n(zeta), zeta))-f_n(zeta)^2+g_n(zeta)^2 = 0;
eq2 := diff(g_n(zeta), zeta$2)-h_n(zeta)*(diff(g_n(zeta), zeta))-2*f_n(zeta)*g_n(zeta) = 0;
eq3 := 2*f_n(zeta)+diff(h_n(zeta), zeta) = 0;
ics := f_n(0) = 0, f_n(10) = 0, g_n(0) = 1, g_n(10) = 0, h_n(0) = 0;
tnx...

Hello

Maple is dangerously close to using all available memory on my Linux machine by doing a calculation using  Grid:-Seq (Map, ..).   Is there a way to control the amount of memory used? Is numcpus a good option?   Or tasksize? 

I expect that Maple will use a large amount of memory since the calculations are performed over a rather large list of sets.  

Many thanks.

Ed

[Moderator's note: The original version of this Question mentioned using both Grid and Threads. The following 5 Replys will not make sense without knowing that Threads was mentioned.

Ed: Editing your Questions is fine, but please don't remove information that is necessary to understand the Replys and/or Answers that are already posted.--Carl Love]

Hello 

I am having equation y(x) in 5 variable c1, c2, A, R and x.

I am not able to plot graph in x and y(x) for A=1, c1 = 2.3, c2 = 2.4 and R=0,2 5,9.

Range of x: -1..1

Caption :graph of y(x) at different value of R.

Legend: R=0, R=1, R=2, R=3.

my equation is

Download Ques1.mw

I have the numeric solution of differential equation and interpolate the data points with a spline of third degree. Is there a way of differentiating the spline as a whole? Differentiating every single polynom seems awkward.

 Help me please.  How can i simulate murmuration in maple.

Hi:

How can I solve the below ODE system in Maple?

sys_ode := diff(F0(zeta), zeta, zeta)-b^2*F0(zeta)+G0(zeta)^2 = 0, diff(G0(zeta), zeta, zeta)-b^2*G0(zeta) = 0, 2*F0(zeta)+diff(H0(zeta), zeta) = 0:
ics := F0(0) = 0, G0(0) = 1, H0(0) = 0, F0(infinity) = 0, G0(infinity) = 0:

Note: b is a constant.

tnx...