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...

Hi everyone:

How can I earn the coefficients with P only in this equation? (No P^2 or P^3).

eq:=p*(diff(F1(zeta), zeta, zeta))-b^2*p*F1(zeta)+2*G0(zeta)*p*G1(zeta)+p^2*G1(zeta)^2-p*H0(zeta)*(diff(F0(zeta), zeta))-H0(zeta)*p^2*(diff(F1(zeta), zeta))-p^2*H1(zeta)*(diff(F0(zeta), zeta))-p^3*H1(zeta)*(diff(F1(zeta), zeta))-p*F0(zeta)^2-2*F0(zeta)*p^2*F1(zeta)-p^3*F1(zeta)^2+p*b^2*F0(zeta)+b^2*p^2*F1(zeta):

tnx...

Hi, 

I would like to enable/disable the Explore(plot(...), parameters=[...]) command according to some boolean value.
First idea (note that ending the previous command by : instead of ; doesn't prevent a figure to be displayed) was to encapsulated this Explore command within a conditional structure:
if T then Explore(...) end if.

But I prefered trying to define my own command by doing something like this:

EXPLORE := proc(TF::boolean)
  if TF then 
    Explore(_passed[2..-1])
  end if:
end proc:
with a call made this way:
EXPLORE(true, 'plot(a*x, x=0..1)', 'parameters=[a=-1.0 .. 1.0]');
wich ended with this error
Error, (in Explore) No parameters to explore

I also tried this without any more success:
EXPLORE := proc(TF::boolean)
  if TF then 
    Explore(_passed[1], parameters=_passed[2])
  end if:
end proc:
with a call made this way:
EXPLORE(true, 'plot(a*x, x=0..1)', [a=-1.0 .. 1.0]);
I get no more error but this warning and an inactive Explore
Warning, expecting only range variable x in expression a*x to be plotted but found name a

Can you help me to fix this?

Thanks in advance

ddesys := {diff(x(t), t, t) + 2/25*diff(x(t), t) + 4*x(t) = 1/25*diff(x(t), t, t)*piecewise(t - 6/7 < 0, cos(t - 6/7), x(t - 6/7)) + 2/3*diff(x(t), t)*piecewise(t - 6/7 < 0, cos(t - 6/7), x(t - 6/7)) + 5/2*piecewise(t - 6/7 < 0, cos(t - 6/7), x(t - 6/7)), h(t) = diff(x(t), t, t), x(0) = cos(0), z(t) = diff(x(t), t), D(x)(0) = -sin(0)}

tdsn := dsolve(ddesys, numeric):

plots[odeplot](tdsn, [[t, x(t), color = red]], 0 .. 20, labels = [t, ""]);

Hello,
I wish to make a simulation of a solution of  Neutral Delayed Differential  Equation (second order) whose initial condition is the history function cos(t) for t <0.
unfortunately Maple considers the history function as a constant and not a function, the simulation I tried to do by Maple is therefore not good.
Could somebody help me please ?

Download Free_Vibration_Euler_Bernouli_Beam_1.mw

I have tried to solve these 4 equations to get the characteristic equation and finally the solution of the PDE.  But it shows some error. Can you please help with this issue?