What is the best (easiest) way to build up a small sytem (procedures) for calculating with base4-numbers ?

...  like multiplication, ln, square, root and so on.

I was thinking about padic or convert-procedures in maple, but before I will begin with that it would be very friendly to have a hint or the opinion of a professional maple programmer.

Thanks for helping 😃

Arno

I am trying to do the integration on the picture (int1). V,omega,theta,rhotræ,ix,iy,ixy,E,R are constants. a(r),å(r),FL(r),FD(r) are splines. It seems to run forever without any error. I have tried a simpler version to figure out if the problem has to do with the splines or the arctan. They can run independently but not when combined. (int2). I use an i7 6700k. I am fine with an aproximated answer within a couple %.  

I noticed PDEtools:-Solve hangs sometimes on some input where solve does not. When I change the solver for PDEtools:-Solve to use solve, it did not hang.

This means PDEtools:-Solve default solver is something else. I did not see what it is by looking at help.

Here is an example

restart;
eq:=[1/3*(-334*I*(-4807763*I+27000*I*2^(1/2)+60*(1746675+72116445*2^(1/2))^(1/2))^(1/3)-2*(-4807763*I+27000*I*2^(1/2)+60*(1746675+72116445*2^(1/2))^(1/2))^(2/3)+56978)/(-4807763*I+27000*I*2^(1/2)+60*(1746675+72116445*2^(1/2))^(1/2))^(1/3)*v[1]-20*I*2^(1/2)*v[2] = 0, (-18000*I*2^(1/2)+33400*I-40*(1746675+72116445*2^(1/2))^(1/2)-40*(-167*I*(1746675+72116445*2^(1/2))^(1/2)+75150*2^(1/2)+10*(-4807763*I+27000*I*2^(1/2)+60*(1746675+72116445*2^(1/2))^(1/2))^(2/3)+145445)/(-4807763*I+27000*I*2^(1/2)+60*(1746675+72116445*2^(1/2))^(1/2))^(1/3))/(167*I*(-4807763*I+27000*I*2^(1/2)+60*(1746675+72116445*2^(1/2))^(1/2))^(1/3)+(-4807763*I+27000*I*2^(1/2)+60*(1746675+72116445*2^(1/2))^(1/2))^(2/3)-28489)*v[2]-20*I*2^(1/2)*t = 0];

solve(eq,[v[1],v[2]]); #OK
PDEtools:-Solve(eq,[v[1],v[2]],solver=solve); #OK
PDEtools:-Solve(eq,[v[1],v[2]]); #hangs

Maple 2021

Hey guys I need help solving the following system of trigonometric equations

invEqs := [a[3]*cos(theta[1] + theta[2] + theta[3]) + a[2]*cos(theta[1] + theta[2]) + a[1]*cos(theta[1]) = px, a[3]*sin(theta[1] + theta[2] + theta[3]) + a[2]*sin(theta[1] + theta[2]) + a[1]*sin(theta[1]) = py, theta[1] + theta[2] + theta[3] = phi]

which everything except theta[1], theta[2], theta[3] are known.

here what I came up with but no success

res := solve(invEqs, {theta[2], theta[3], sin(theta[1])})

or better be like this but no output printed

res := solve(invEqs, {theta[1], theta[3], cos(theta[2])})

thanks in advance

How to find the power series solution of a nonlinear 4th order ordinary differential equation.

>ode:=U""+c^2*U"+k*c*U"-(3U^2+a)*U''=0

where U' denotes the differential w.r.t  z and a,k,c are constants. Please help to find.

hi! is there any kind of formula for coloring functions by HUE like this

contourplot(abs(sin(x) + y^2 + y + x*I), x = -6 .. 6, y = -5 .. 5, contours = [seq(1/2^n, n = 1 .. 3), seq(2^n, n = 1 .. 5)], numpoints = 200000, thickness = 1.5, color = black);

I wonder about situation when we don't have function for example f(z)=z but f(x,y)=x+I*y and we want to use domain coloring for that. Thanks in advance.

Hi!

How do I solve a equation ln in Maple:ln.mw

Let E be a random variable of expectation mu and A an algebraic expression containing no random variable.
If E has any known Maple distribution, then  Mean(A+E) = A+mu.

But if E is an "abstract" random variable, Mean doesn't seem capable to compute the expectation of A+E.
Notional example:

restart:
with(Statistics):
E := RandomVariable(Normal(mu, sigma)):
Mean(f(x)+E)
                           f(x) + mu
E := RandomVariable(Distribution(PDF = (z -> f(z)), Mean=mu)):
Mean(f(x)+E); 
     int((f(x) + _t) f(_t), _t = -infinity .. infinity)

IntegrationTools:-Expand(%);
        f(x) (int(f(_t), _t = -infinity .. infinity)) + (int(f(_t) _t, _t = -infinity .. infinity))

Questions:

• Why does Mean not behave as expected for an abstract random variable?
• Is there a simple way to obtain the expected result (Mean (A+E) = A+mu) (maybe by completing the definition of the distribution of E, or by any other means)?

TIA

PS: I know that I can replace Mean(A+E)  by A+Mean(E)  to obtain the desired result: this is not the type of answer I look for.

PS: I know (since Carl Love showed me how long ago) that I can define a "random variable" plus an operator Expectation such that Expectation(A+E)  by A+Expectation(E) ... but it's not a way I would call simple

Expectation := proc(e::algebraic)
     local a,b;
     if not hastype(e, RV) then e
     elif e::RV then 'procname'(e)
     elif e::`+` then map(thisproc, e)
     elif e::`*` then
          (a,b):= selectremove(hastype, e, RV);
          b*thisproc(a)
     else 'procname'(e)
     end if
end proc:

#------------------------------------------------------------------------

TypeTools:-AddType(
     RV, 
     {RandomVariable, 
     'RandomVariable^posint', 
     '`*`'({RandomVariable, 'RandomVariable^posint'})
     }
):
eval(Expectation(f(x)+E), Expectation=Mean)
                           f(x) + mu

Download mod_proc.mw

Hi 😊

I have found this Code here somewhere in MaplePrimes.

I am very interested in that Procedure, but it doesn't run.

I will be very happy, to get help with that.

Thanks a lot,

Arno

Hello

When doing chemistry in Maple, I want to be able to do my calculations with units.

Maple does not support the unit [M] (molar concentration), so I have to manually type the unit as [mol/L].

That is not a problem in itself, but I have encountered som issues with Maple's own formatting of the units.

For example, in the attached document I want the output unit to be (mol/L)^(-2). However, Maple automatically formats it as

It even does the same thing in the "Maple Math" here on MaplePrimes - Here I try to type (mol/L)^(-2):

So does anyone know a way to avoid Maple's auto-formatting of the output, or is there a way to customize it so I get my desired output?

I have attached the document with some screenshots in it: chemistry_units.mw

// Frederik

primes.mw

As a result of a calculation I have a long expression. I give it a name, say, X,

X:= long expression. 

I try to use typematch to extract different parts of X and its does not work (it returns false).  

If, however, I copy and paste the long expression from the output and plug into my typematch query it works!   

It seems that copy and paste change the type of the expression. I am very confused with this. 

I have uploaded a file with the problem at the beggining.  Thank you! 
Max 
 

Hey guys, how can I apply multiplication to a sequence of matrices like A[1], A[2]...A[n] so it becomes A[1]*A[2]...*A[n] ? thanks in advance

I am investigating the history of scales and temperament in western music. I would like to be able to play a tone of a given frequency in Maple, and then a sequence of tones to make a scale, and then a collection of tones to make a chord. I found the Play command  in the online help screen for Audio Tools, but can't make it work. I don't get an error message, but neither do I get a sound. 

I am merging two separate modules  B,C to be child modules inside one main A module.

Now, I found the code breaks, because uses does not work any more.

Before merging, C module did uses B. But now this gives an error when both B,C sit inside one parent module.  An example make this easier to explain

restart;
interface(warnlevel=4);
kernelopts('assertlevel'=2):

A:=module()

   export B:=module()
     export foo:=proc()
         print("In B:-foo()");
     end proc;
   end module;

   export C:=module()
      uses B; #this cases problem
      export boo:=proc()
           foo();
      end proc;
   end module;
end module;

Error, (in A:-C) no bindings were specified or implied

Changing uses B; to uses A:-B; does not help. I get error Error, (in A:-C) `A` does not evaluate to a module

I also tried uses :-A:-B; , now this does not give error, but it does not work. i.e. when doing  A:-C:-boo() Maple does not end up calling foo() inside module B as expected.

One way to avoid all this, is not to use uses B inside the module C and do this instead

A:=module()

   export B:=module()
     export foo:=proc()
         print("In B:-foo()");
     end proc;
   end module;

   export C:=module()      
      export boo:=proc()
           B:-foo(); 
      end proc;
   end module;
end module;

But it means I have to now change lots of code inside the C module, and add an explicit B:- everywhere

This is how it was before the merging

B:=module()
   export foo:=proc()
       print("In B:-foo()");
   end proc;
end module;

C:=module()  
  uses B;    #no problem now
  export boo:=proc()
      foo();  #this now uses B:-foo() automatically due to uses.
  end proc;
end module;

The above works. Now I can do C:-boo() and it works as expected.

The question is: How to make it work after moving both C and B inside one parent module so I do not have to change lots of code? I tried many things, but can't get it to work.

Maple 2021 on windows 10

Edit

Thanks for the answers below. I think I have to change my code then either way to add a prefix to the call. I actually always use the long form of the call for everything as in module:-function() but for one function, which I use so much everywhere, using the fully qualified name would make things hard to read.  This function converts Maple expressions to Latex after some filtering. Here is an example

cat(",toX(y),"' = f_0(",toX(f),")",toX(y),"+f_1(",toX(x),")",toX(g),"^n \\tag{2}, etc.....")

Now the function toX comes from one module, the one I had uses for it. Now I have to change the above to becomes

",module_name:-toX(f),"' = f_0(",module_name:-toX(x),")",module_name:-toX(y),"+f_1(",module_name:-toX(x),")",module_name:-toX(g),"^n \\tag{2}

Since my strings are very long as it is, (program generates Latex on the fly as it runs), this will make them even longer and harder to read.

But I can change all this in the editor, using global search and replace.

I was just hoping I do not have to just because I moved the modules all into one main module. I still do not understand why Maple does not allow uses when moving the modules inside one bigger module, but I guess this is by design.

Hello

I have a couple of large lists that will be further processed.  One of the steps is to index a list using another list (a list of indices).  A short example will be something like

L:=[2,1,4,3,7,6,8,3,4,5];
ind:=[2,2,3,3,5,6,7,1,4,10];

The solution 

L1:=L[ind]:

does not seem to be a good choice since it takes longer than the following solution

L1:=Threads:-Map(w->L[w],ind):

Since I am not a Maple expert, it is very likely that is a faster solution.   

Many thanks