Is there an equivalent to Pivot Table in Excel?
I'm working on some investing data, and am using Maple to gather information from various sources and using DataFrame to combine all the data. I could export the dataframe and open in Excel or other spreadsheet and use the Pivot table to summarize the data, but is there an easy way to do all of it in Maple?

Thanks

Good evening,could you please help me to find the values of Phi[2],Phi[3],Phi[4],....

The right hand side of the for loop is the equation i need.Is this maple code correct.

rps1.mw

I would like to get a (necessary and sufficient) condition on real parameters , , and  for which there exists (at least) one non-negative solution to . 
A convenient way to formulate this is using quantifiers. Unfortunately, if I run 

QuantifierElimination:-QuantifierEliminate(:-exists([x],:-And(x>=0,9*x^4+c<9*a*(x-1)+3*b*(x^2-1)+c*x^3)));

Maple will simply output 

As an alternative method, one can execute 

RealDomain:-solve([x >= 0, 9*x**4 + c < 9*a*(x - 1) + 3*b*(x**2 - 1) + c*x**3], 'parameters' = {a, b, c});
Warning,  computation interrupted

Regretfully, this time the computation is not done in several minutes (so one may have to abort it manually). 

So, what is the proper approach to the above problem in Maple (without any a priori knowledge, if possible)?

I have doubts as to whether this is possible, but I would like to ask anyway.

For example, can

`*`(`+`(a, b), c);
                           c (a + b)

be written with composed procedures (`*`@`+`) and somehow grouped arguments (a,b) for `+` and (a+b,c) for `*`.

So far I have only come across composed procedures in parethesis applied to one expression in parenthesis.

Since the second pair of parenthesis does a function application to everything what is inside the parenthesis it seems impossible that the right most procedure is only applied to a sub-term of the expression first.

If the answer to my question is no, I want to aks a related question:

Is it possible to separate procedures calls from arguments? So, in a first part of a statement I have a sequence (or a list or a composed function) of procedures/operators and in the second part a sequence of arguments instead of a nested construct of procedure calls?

I'm running Maple 2020 on a Mac with OS 14.3.1.  Maple is not seeing current files in folders, and when it saves files, it does so with an older date.  In Settings, Maple has permission to access the Desktop, Documents, and Downloads folders, the only options that my Mac provides.

It's a bit frustrating.  Any help would be appreciated.

I am presently working on bivariate functions defined this way

C := (u, v) -> (phi@@(-1))(phi(u)+phi(v));

phi is a function of specific expression named the "generator". Both u and v are assumed to be in the closed interval [0,1].

Here is an example:

restart
phi := u -> (u^(-theta)-1)/theta:
C := (u, v) -> (phi@@(-1))(phi(u)+phi(v)):
C(u, v)
                       / (-theta)        (-theta)    \
                      | u         - 1   v         - 1|
           @@(phi, -1)| ------------- + -------------|
                       \    theta           theta    /

This definition of C is correct providing that  theta in [-1, +infinity) \ {0}.
As you can see, the display of C(u, v) contains the inverse function phi@@(-1) which Maple doesn't seem to know what to do with.

What I would like is to get rid of  phi@@(-1) and get 

C(u, v);
        (-1+u^(-theta)+v^(-theta))^(-1/theta)

The only way I found to get this is to do that:

restart
phi := u -> (u^(-theta)-1)/theta:
(phi@@(-1)) := u -> solve(phi(x)=u, x): # explicit definition of (phi@@(-1))
C := (u, v) -> simplify((phi@@(-1))(phi(u)+phi(v))) assuming theta >= -1, theta <> 0:
C(u, v);
                                         /    1  \
                                         |- -----|
                                         \  theta/
             /      (-theta)    (-theta)\         
             \-1 + u         + v        /         

As you see I have been forced to tell Maple what the inverse function of phi was.
Is there another way do get this result without writting the bold red line?

Maple knows several inverse functions (trigonometric functions for instance), but how does it know that?
As Maple does not seem to use a (f@@(-1)) := u -> solve(f(x)=u, x) like definition, does it uses a correspondence table between functions and their inverse?
If it is so can we augment it?

Thanks in advance.

PS: the ultimate goal is to do something like this Download CAC.mw  for different generators.

For the moment I have defined my own table generator <--> inverse function  as I did above with the bold red line: this works but it is not very elegant.

Hi,
I have a problem and I haven't been able to solve it yet. I want to solve an ordinary diffrential equation similar to
                                                                                                   (dphi/dxi)^2+2*V(phi)=0
and plot phi versus xi for a the following conditions:
1) V(phi)=dphi/dxi=0 at (phi=0,phi_m) and
2) dV(phi)/dphi=0 at phi=phi_m and 
3) d^2V(phi)/dphi^2=0 at both phi=0 and phi=phi_m.
How can I do this by Maple?(see the attached file)
w1.mw

I tried

interface(warnlevel=0); infolevel[all]:=0;prinlevel:=0;kernelopts('printlevel'=0);

to suppress the warnings I get from this code

restart;
f:=z^3;
z_map:=proc(f,re,im) 
  if((re>0) and (im>0) and (im<1-re))then
    eval(f,z=re+I*im);
  else
    NULL;
  end if;
end proc;
p_re:=plots:-display(seq(plot([Re('z_map(f,re,im)'),Im('z_map(f,re,im)'),im=0..1]),re=0..10,0.1)):
p_im:=plots:-display(seq(plot([Re('z_map(f,re,im)'),Im('z_map(f,re,im)'),re=0..1]),im=0..10,0.1),color=green):
plots:-display(p_re,p_im,scaling=constrained)

The reason for the warnings is clear. The input lines are too long to be plotted. However, the resulting plot is exactly what I intended. Programatically truncating the lines would make the warning disappear, but it would make the code much more complicated.

What else can be done to suppress this kind of warning.

For Mathematica  math software app,there is a plugin to use in chatGPT pro ( paid subscription ) and maybe this can be done for Maple too ? 

Haven't used the plugin for Mathematica yet, am curious about it.
Let me have the AI look at the Riemann Hypothesis :)  
Have a few books on it, but can't get through that math with all those special functions.

i have two euations including integration which has two unkwnon x1 and x2.
how can i get these equations solved, thanks for the help.

fsolve_problem.mw

For this integro-differential equation,

Equation:= int[y'(x)* (x^2)/[(x^2)-1],x)  =  (int[sqrt(y(x)])^(-2/3)

Maple is able to obtain an exact intrinsic solution

from which an exact solution can be extracted, namely,

ExtrinsicSolution:= y(x) = sqrt(3)*(-8*_C1*x^(8/3) + 12*x^2 - 3)^(3/4)

My question concerns how was this solution obtained.

Even more, specifically, 'odeadvisor' suggests converting the

equation in question to the form

ode:= y = G(x,diff(y(x),x));

However, I cannot reconcile how this can be applied to an equation which

contains two integrals. (Regretably, I am not able to directly, attach my

Maple worksheet directly on to this sheet). The situation is that after

applying 'dsolve' to the above 'Equation', Maple comes back with an

intrinsic solution which can was used to obtain the 'ExtrinsicSolution' in 

the above.  So it is the missing steps between applyingthe dsolve command

to Equation and the intrinsic solution which MS provides which, in turn, leads

to the 'Extrinsic Solution' above. I would greatly, appreciate if anyone can 

fill in the missing steps.

How to convert barycentric coordinates to cartesian ? Thank you

Is there a way to manipulate an equation so that it is in the form of (Expression of Primary Variables)*(Expression of Secondary Variables)
In the example below from Video 1: Fast Analytical Techniques for Electrical and Electronic Circuits (youtube.com), the primary variables are R1 and R2

PS. When I type ctrl-v to insert an image, I always get 2 copies.

I got the proportional symbol to work once, typing "proportional" + CRTL + Space.  Went for wlak came back and could not get it to work at all.

Does it actually work or am I imagining things?

Greetings All,

This is an application for control theory, specifially using Maple to solve control problems in the area of Interconnection and Damping Assignment Passivity Based Control (IDA-PBC).

- Assuming two variables (iL and Vo), there is a potential function that I am trying to solve for called "Ha".  I have two equations here, and I want to solve for Ha using the pdsolve() command:  

eq1 := diff(Ha(iL, Vo), iL) = rhs(result[1]);
eq2 := diff(Ha(iL, Vo), Vo) = rhs(result[2]);
pdsolve( {eq1, eq2  } );

Once I do this, Maple gives me an expression for Ha that has arbitrary functions in it (I understand where these are coming from).  So far, so good.

--> In order to get help solving for these arbitrary functions, I also want to tell Maple some constraints.  For example:

"the Hessian matrix of Ha must be positive definite"

Is there a way to do this?