MaplePrimes - Maple Posts and Questions

How is a cyclic command sequence programmed?

Alfred_F — Sat, 25 Jul 2026 15:18:20 Z

In the attached file, I would like to calculate the expressions for the function f(n,x) using a recursion for a given index range, e.g., n=3..15. I would appreciate any advice on this.

restart;

>	kernelopts(version);

(1)

>	f(1,x):=x;

(2)

>	f(2,x):=2x + 2sin(x);

(3)

>	f(n,x):=2f(n-1,x)-f(n-2,x)+2sin((n-1)*x)/(n-1);

(4)

>	f(3,x):=eval(f(n,x),n=3);

(5)

>	f(4,x):=eval(f(n,x),n=4);

(6)

Download test24c.mw

How to Import Converations from ChatGPT

ianmccr — Sat, 25 Jul 2026 14:18:57 Z

Responses from the AI assistant in Maple2026 can be copied directly into a Maple Document or Worksheet, Is there a process which allows one to similarly import a external ChatGPT conversation. I have Maple MCP configured in my ChatGPT account.

Dynamic assignment of ranking of variables in DifferentialThomas

Steven_Huang — Sat, 25 Jul 2026 11:56:41 Z

So the problem I encountered is when I try to assign ranking of variables of ODE in ThomasDecomposition, the indexed variables are not allowed. For instance, for an ODE system containing a[0], a[1], a[2] as dependent variables, if I assign:
R := Ranking([x],[a[0],a[1],a[2]])
It throws an error: due to efficiency reasons no variables of type "indexed" are allowed in the list of depended variables NULL;
This is going to be inconvenient when I have to dynamically solve ODE system within a function call, especially when the system is nonlinear and algebraically closed(no integration constants in solutions) and calling DifferentialThomas in dsolve will be slow. I want to know how to resolve this.

How to integrate a trig function with parameter?

Aliocha — Thu, 23 Jul 2026 11:42:49 Z

How to integrate this function (n::posint) :
f := (n, x) -> (1 - cos(n*x))/(1 - cos(x))

Maple is not returning a result. It seems unable to establish the connection with the Dirichlet kernel. Is there a solution that doesn't require forcing a decomposition into a sum of cosinus?

Thank you for your help.

Best regards.

Creation of difference equations

C_R — Thu, 23 Jul 2026 10:44:31 Z

In the context of numerical integration of partial differential equations I am looking for tools to create difference equations for the numerical integration of PDE's. Ideally the desired integration scheme could be given as an input.

The only command that I am aware of is the DiffEquation command from the DynamicSystems package (see ?DynamicSystems,DiffEquation) which is limited to linear time invariant systems and only provides a simple forward integration scheme.

Any insights/examples into the topic of numerical integration of pde's with Maple beyond pdsolve/numeric capabilites is very much appreciated. (I know that Maple comes with advanced numerical solvers for ODE's. MapleSim uses such solvers to integrate systems of ODE's. This seems to be, in terms of computation, close to what I am looking for.)

Creating Pi from a Single Binary Operator and the Constant 1

mcarvalho — Wed, 22 Jul 2026 22:27:36 Z

Today is Pi approximation day (22/7) and I will use that as an excuse to share my new favourite expression for Pi:

And this isn't even an approximation! Recently, continuous mathematics has found its own equivalent to the digital hardware NAND gate. In his paper “All elementary functions from a single binary operator”, Andrzej Odrzywołek demonstrated that a single functional primitive can generate the entire standard continuous spectrum of operations. In other words, every single button on a scientific calculator, from addition and subtraction to sines, cosines, and logarithms, can be built using just this one function.

This Maple Worksheet explores how the 'Exp-Minus-Log' ("EML") operator, when paired solely with the constant 1, can be systematically nested to construct basic arithmetic, constants, and complex transcendental functions within Maple.

In essence, he discovered that the binary operator EML, along with the constant 1, forms a basis for the set of standard scientific-calculator operations.

This means that functions like , and operations like or can be creating by composing EML with itself in clever ways. Some constants and functions are trivial to represent, such as EML(1,1) = e or EML(x, 1) = exp(x), others however, are not...

With a quick one-command tweak, you can get Maple to use the property of the extended reals that

And then with a simple argument about standard branches, you can construct the natural logarithm for real numbers, which immediately leads the constant zero:

You can then expand the tools in your toolbox by creating subtraction with EML, ln(x), and exp(x)

Which then expands the toolbox further by allowing for the construction unary minus from the constant 0 (since -x = 0 - x), and then addition (since a+b=a-(-b))

Since we've constructed addition, subtraction, zero and one, we can technically construct every integer! It would not be very pleasant, and by no means optimal... but you could! Here's 7 for example:

The next step to building all the standard functions is multiplication and inversion. And these use the classic trick by using the fact that x=exp(ln(x)) can help simplify:

These are compositions of exp, addition, ln, and unary minus (all functions constructed previously), which means they can be made with only EML:

It's at this point that I will leave the derivation of division (a/b) and exponentiation (a^b) as exercises for the reader, so I can skip to something a little more complex...

To go beyond the basic operators, you'll need to step into the complex domain by constructing the imaginary constant i. To do this, take ln(-1) = -i*Pi (by using the standard branch) and combine it with Euler's formula

And once again the expression on the left-hand side is made up of operations that were all previously defined, so you can compose EML to get a new constant:

And finally, it's possible to break down the expression for Pi from the start, since it's the product i*ln(-1)

By successfully extracting the mathematical constants i and Pi, I think this demonstrates the complete constructive capability of the EML operator in the complex domain. While the resulting syntax trees become exponentially deep and unoptimized for human readability, they prove that continuous operations do not require a massive, distinct toolbox. Future applications of this uniform binary structure could dramatically simplify symbolic regression and machine learning optimization models.
Ultimately, the EML operator reveals the remarkable truth that the vast complexity of scientific mathematics can be distilled down to a single, beautiful building block.

Isn't math awesome?