ecterrab

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16 years, 199 days

MaplePrimes Activity


These are replies submitted by ecterrab

@J F Ogilvie 

Take a look at what's new in Differential Equations in Maple 2021 page. That page answers - not a generic question on "number of solutions" (there are infinitely many possible ODE problems) - but what I meant by skyrocketed (informal for increase very steeply or rapidly).

In brief, the problem of 2nd order linear ODEs splits into those that admit Liovillian solutions and those that do not. In the second set, the approach is to compute hypergeometric or Heun function solutions; the corresponding standard and some original approaches were implemented in previous Maple releases.

In Maple 2021, however, we implemented something far beyond that. For example, as said on that what's new in DEs page, none of the ODE problems shown there can be solved in Maple 2020 or before, or using other computer algebra systems. At the end of the ODE section of that what's new page, you will also see seven references to the scientific literature explaining the new methods and how they extend previously existing ones.

So while It is true that the Maple ODE and PDE solvers were already state-of-the-art in previous Maple releases, in Maple 2021, regarding 2nd order linear ODEs and ODE / PDE problems that require solving that kind of problem as an intermediate step, the solving capabilities skyrocketed. This achievement is a milestone in computer algebra and differential equations.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Hi

Complementing Samir's comments, two advanced topics which are among the things that make Maple 2021 absolutely unique, state-of-the-art, are

  • We literally skyrocketed our ability to solve second order linear ODEs. With that, it also significantly increased our ability to solve higher-order linear and nonlinear ODEs, PDEs, and systems of them that require solving 2nd order linear ODEs as an intermediate step. 
  • Building on the work of Maple 2020, in the Maple 2021 Physics environmentnew, we can compute Feynman Integrals - Particle Physics - and significantly improved our ability to compute with non-commutative operators - Quantum Mechanics - also with tensors and tetrads in curved spacetimes - General Relativity.

The Maple system has acquired a maturity level in these subjects, including the LaTeX development, only possible because of people's systematic feedback, frequently on the novelties presented every week in each Maplesoft Physics Updates, which in truth it includes the differential equation and mathematical functions novelties as well. I want to thank again all of you that contributed in that way here in Mapleprimes.

 

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@vv 

The Wirtinger derivatives d/dz, d/dzbar are yes implemented in Maple. It is one of the Physics:-Setup settings (input Setup(); and you see it there in the applet). Your point about diff/abs, however, is another thing. I will take a look.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

 

@itsme 

I somehow missed your reply 5 years ago (!) Attached is the worksheet showing current output, it works fine with all daggered operators to the left, and SortProducts performing the operation as requested; this command got reworked significantly during the last 3 years.

Your worksheet reviewed: commutator_stuff_(from_2016)_reviewed.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

 

dharr is right. See also the help page for ODESolStruc

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@nm 

Without debating anything of what you are saying, I only want to point out two relevant things about debugging that you may not be aware of.

One is the MapleCloud Emacs package. It provides terrific additional debugging capabilities, using Emacs, right, not the GUI you talk about, but still a very significant step ahead concerning the default DEBUG window you mentioned.

Two: in addition to stopat(some_procedure), input debug(some_procedure), and put the DEBUG window side by side with the Maple worksheet window before starting the computation to be debugged. When the computation starts, you will see what you see in the DEBUG window and also the computation evolving one step at a time and with full typesetting. If you happen to have the code behind, in addition, input kernelopts(tracelineinfo = 2) to see the line numbers.

I only debug using "Two", and if the debugging activity is heavier, always use "One".

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

The error message is incorrect, but the expectation is a bit too. You are not showing the answer; it is in parametric form, parameter _T. There is no y(x) as you say. There is only x(_T) and y(_T). This is not a standard "implicit" solution. To test, you'd need to isolate _T in one of the equations then substitute into the other one - say to obtain a solution involving y(x). Or, differentiate both with respect to _T and somehow manage to use that to remove _T to obtain dy/dx, and from there, see if it reduces ode. Although possible, none of that is implemented.

PS: busy until the end of January.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@Preben Alsholm 

Sorry about that. End of the year, 8,000 RPM non-stop, reading too fast .. All the best @Preben Alsholm@Carl Love@mmcdara@nm !

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

 

@mthkvv 
There is still the alpha123 (large numbers) of intermediate indices appearing in the output, most of them can be changed by single greek letter indices. It is not a wrong thing, but it is something that makes readability more difficult. I will give a look at how to improve that.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@nm 

I see a lot of good ideas around; here is my version, similar to those presented. (It follows an image, at the end is the worksheet linked.)

ConstantsFirst.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

 

@vv 

Good catch, a different problem this function of no arguments C(); it is fixed in v.895, thanks.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@nm 

It makes sense to me to only implement existing notation. I have not seen "\arcsin^2 x" as you say. For reference, see this wiki page about the subject. That said, I am inclined to remove 'mixed' and maybe keep 'computer' as default. Quoting what for me are the two related key points in that wiki page,

  • To distinguish exponentiation from function composition, the common usage is to write the exponential exponent after the parenthesis enclosing the argument of the function; that is, f(x)^3 means (f(x))^3, and f(x)^(–1) means 1/f(x). 
  • For historical reasons, and because of the ambiguity resulting from not enclosing arguments with parentheses, a superscript after a function name "applied specifically to the trigonometric and hyperbolic functions" has a deviating meaning: a positive exponent applied to the function's abbreviation means that the result is raised to that power, while an exponent of −1 still denotes the inverse function​​​​​​​.

Me again, the first item is the same as saying that () has higher precedence than ^, as it is, in fact, the case in computer algebra systems. There is more on that page, but I feel the above is the essence and is what you see implemented in (Physics:-)Latex, to replace latex. The first item for computer notation and the second item (as you see it described, no parenthesis in "sin^2 x") as textbooknotation. The current value mixed reflects more my dislike of interpreting the n in "sin^n" as power while the -1 in "sin^(-1)" as composition (for inverse function), but it is tradition, and we people speak with that.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

 

@Carl Love 

Yes, but I suppose @nm used LinearAlgebra just to generate the structures (Vector and Matrix), and that is what Latex receives and translates; the translation is performed regardless of whether a package is loaded (unless the package - itself - specifies LaTeX-translation rules, as, e.g. DifferentialGeometry does, but not the case of LinearAlgebra).

That said, I also have the impression that some people think LinearAlgebra is needed to input a Vector or Matrix, and your comment helps clarifying that; likewise people frequently load PDEtools before using pdsolve, which is also unnecessary.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

@rlopez 
Wow! I didn't have that one. Fantastic tip!

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft.

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