Maple 2023: The colorbar option for contour plots does not work when used with the Explore command. See the example below.

No_colorbar_when_exploring_contour_plots.mw
 

Just installed Maple 2023 on Macbook Air M1.

Maple Tasks dosn't work :-(

/

The inverse problem of a mathematical question is often very interesting.

I'm glad to see that Maple 2023 has added several new graph operations. The GraphTheory[ConormalProduct], GraphTheory[LexicographicProduct], GraphTheory[ModularProduct] and GraphTheory[StrongProduct] commands were introduced in Maple 2023.

In fact, we often encounter their inverse problems in graph theory as well. Fortunately, most of them can find corresponding algorithms, but the implementation of these algorithms is almost nonexistent.

I once asked a question involving the inverse operation of the lexicographic product.

• https://www.mapleprimes.com/questions/235863-An-Inverse-Problem-Of-Lexicographic

Today, I will introduce the inverse operation of line graph operations. (In fact, I am trying to approach these problems with a unified perspective.)

To obtain the line graph of a graph is easy, but what about the reverse? That is to say, to test whether the graph is a line graph. Moreover, if a graph  g is the line graph of some other graph h, can we find h? (Maybe not unique. **Whitney isomorphism theorem tells us that if the line graphs of two connected graphs are isomorphic, then the underlying graphs are isomorphic, except in the case of the triangle graph K_3 and the claw K_{1,3}, which have isomorphic line graphs but are not themselves isomorphic.)

Wikipedia tells us that there are two approaches, one of which is to check if the graph contains any of the nine forbidden induced subgraphs. 

Beineke's forbidden-subgraph characterization:  A graph is a line graph if and only if it does not contain one of these nine graphs as an induced subgraph.

This approach can always be implemented, but it may not be very fast. Another approach is to use the linear time algorithms mentioned in the following article. 

• Roussopoulos, N. D. (1973), "A max {m,n} algorithm for determining the graph H from its line graph G", Information Processing Letters, 2 (4): 108–112, doi:10.1016/0020-0190(73)90029-X, MR 0424435

Or: 

•   Lehot, Philippe G. H. (1974), "An optimal algorithm to detect a line graph and output its root graph", Journal of the ACM, 21 (4): 569–575, doi:10.1145/321850.321853, MR 0347690, S2CID 15036484.

SageMath can do that: 

   root_graph()

Return the root graph corresponding to the given graph.

    is_line_graph()

Check whether a graph is a line graph.

For example, K_{2,2,2,2} is not the line graph of any graph.

K2222 = graphs.CompleteMultipartiteGraph([2, 2, 2, 2])
C=K2222.is_line_graph(certificate=True)[1]
C.show() # Containing the ninth forbidden induced subgraph.

Another Sage example for showing that the complement of the Petersen graph is the line graph of K_5.

P = graphs.PetersenGraph()
C = P.complement()
sage.graphs.line_graph.root_graph(C, verbose=False)

(Graph on 5 vertices, {0: (0, 1), 1: (2, 3), 2: (0, 4), 3: (1, 3), 4: (2, 4), 5: (3, 4), 6: (1, 4), 7: (1, 2), 8: (0, 2), 9: (0, 3)})

Following this line of thought, can Maple gradually implement the inverse operations of some standard graph operations? 

Here are some examples:

•   CartesianProduct
•   TensorProduct
•   ConormalProduct
•   LexicographicProduct
•   ModularProduct
•   StrongProduct
•   LineGraph
•  GraphPower

The moment we've all been waiting for has arrived: Maple 2023 is here!

With this release we continue to pursue our mission to provide powerful technology to explore, derive, capture, solve and disseminate mathematical problems and their applications, and to make math easier to learn, understand, and use. Bearing this in mind, our team of mathematicians and developers have dedicated the last year to adding new features and enhancements that not only improve the math engine but make that math engine more easily accessible within a user-friendly interface.

And if you ever wonder where our team gets inspiration, you don't need to look further than Maple Primes. Many of the improvements that went into Maple 2023 came as a direct result of feedback from users. I’ll highlight a few of those user-requested features below, and you can learn more about these, and many, many other improvements, in What’s New in Maple 2023.

• The Plot Builder in Maple 2023 now allows you to build interactive plot explorations where parameters are controlled by sliders or dials, and customize them as easily as you can other plots

• In Maple 2023, 2-D contour and density plots now feature a color bar to show the values of the gradations.

• For those who write a lot of code:  You can now open your .mpl Maple code files directly in Maple’s code editor, where you can  view and edit the file from inside Maple using the editor’s syntax highlighting, command completion, and automatic indenting.

• Integration has been improved in many ways. Here’s one of them:  The definite integration method that works via MeijerG convolutions now does a better job of checking conditions on parameters so that they are only applied under proper assumptions. It also tells you the conditions under which the method could have produced an answer, so if your problem does meet those conditions, you can add the appropriate assumptions to get your result.
• Many people have asked that we make it easier for them to create more complex interactive Math Apps and applications that require programming, such as interactive clickable plots, quizzes that provide feedback, examples that provide solution steps. And I’m pleased to announce that we’ve done that in Maple 2023 with the introduction of the Quiz Builder and the Canvas Scripting Gallery.
• • The new Quiz Builder comes loaded with sample quizzes and makes it easy to create your own custom quiz questions. Launch the quiz builder next time you want to author interactive quizzes with randomized questions, different response types, hints, feedback, and show the solution. It’s probably one of my favorite features in Maple 2023.

• The Scripting Gallery in Maple 2023 provides 44 templates and modifiable examples that make it easier to create more complex Math Apps and interactive applications that require programming. The Maple code used to build each application in the scripting gallery can be easily viewed, copied and modified, so you can customize specific applications or use the code as a starting point for your own work

• Finally, here’s one that is bound to make a lot of people happy: You can finally have more than one help page open at the same time!

For more information about all the new features and enhancements in Maple 2023, check out the What’s New in Maple 2023.

P.S. In case you weren’t aware - in addition to Maple, the Maplesoft Mathematics Suite includes a variety of other complementary software products, including online and mobile solutions, that help you teach and learn math and math-related courses.  Even avid Maple users may find something of interest!

I was looking at symbolically solving a second-order differential equation and it looks like the method=laplace method has a sign error when the coefficients are presented in a certain way.  Below is a picture of some examples with and without method=laplace that should all have the same closed form.  Note that lines (s6) and (s8) have different signs in the exponential than they should have (which is a HUGE problem):

Download DsolveLaplaceIssues.mw

Transfer functions are normally not used with units. Involving units when deriving transfer functions can help identify unit inconsistencies and reduce the likelihood of unit conversion errors.

Maple is already a great help in not having to do this manually. However, the final step of simplification still requires manual intervention, as shown in this example.

Download Collecting_and_expanding_units.mw

Does everyone have a good idea of ​​the work of the Draghilev method? For example, in this answer https://www.mapleprimes.com/questions/235407-The-Second-Example-Of-Finding-All-Solutions#answer291268
( https://www.mapleprimes.com/questions/235407-The-Second-Example-Of-Finding-All-Solutions )
there was a very successful attempt by Rouben Rostamian to calculate the line of intersection of surfaces without applying the Draghilev method.
Let now not 3d, but 8d. And how will the solve command work in this case? Imagine that aij ((i=1..7,j=1..8)) are partial derivatives, and xj (,j=1..8) are derivatives, as in the above example. f8 is responsible for the parametrization condition.
 

restart;
 f1 := a11*x1+a12*x2+a13*x3+a14*x4+a15*x5+a16*x6+a17*x7+a18*x8; 
 f2 := a21*x1+a22*x2+a23*x3+a24*x4+a25*x5+a26*x6+a27*x7+a28*x8; 
 f3 := a31*x1+a32*x2+a33*x3+a34*x4+a35*x5+a36*x6+a37*x7+a38*x8; 
 f4 := a41*x1+a42*x2+a43*x3+a44*x4+a45*x5+a46*x6+a47*x7+a48*x8;
 f5 := a51*x1+a52*x2+a53*x3+a54*x4+a55*x5+a56*x6+a57*x7+a58*x8; 
 f6 := a61*x1+a62*x2+a63*x3+a64*x4+a65*x5+a66*x6+a67*x7+a68*x8; 
 f7 := a71*x1+a72*x2+a73*x3+a74*x4+a75*x5+a76*x6+a77*x7+a78*x8;
 f8 := x1^2+x2^2+x3^2+x4^2+x5^2+x6^2+x7^2+x8^2-1; 
allvalues(solve({f1, f2, f3, f4, f5, f6, f7, f8}, {x1, x2, x3, x4, x5, x6, x7, x8}))

And this is how the Draghilev method works in this case.
 

restart; with(LinearAlgebra):
f1 := a11*x1+a12*x2+a13*x3+a14*x4+a15*x5+a16*x6+a17*x7+a18*x8; 
f2 := a21*x1+a22*x2+a23*x3+a24*x4+a25*x5+a26*x6+a27*x7+a28*x8; 
f3 := a31*x1+a32*x2+a33*x3+a34*x4+a35*x5+a36*x6+a37*x7+a38*x8; 
f4 := a41*x1+a42*x2+a43*x3+a44*x4+a45*x5+a46*x6+a47*x7+a48*x8; 
f5 := a51*x1+a52*x2+a53*x3+a54*x4+a55*x5+a56*x6+a57*x7+a58*x8;
f6 := a61*x1+a62*x2+a63*x3+a64*x4+a65*x5+a66*x6+a67*x7+a68*x8; 
f7 := a71*x1+a72*x2+a73*x3+a74*x4+a75*x5+a76*x6+a77*x7+a78*x8;

n := 7; 
x := seq(eval(cat('x', i)), i = 1 .. n+1):
 F := [seq(eval(cat('f', i)), i = 1 .. n)]: 
A := Matrix(nops(F), nops(F)+1):
 for j to nops(F) do for i to nops(F)+1 do A[j, i] := op(1, op(i, op(j, F))) 
end do:
           end do: 

# b[i] and b[n+1] are solutions of a linear homogeneous system and at the 
# same time they serve as the right-hand sides of an autonomous ODE.
for i to n do

 b[i] := Determinant(DeleteColumn(ColumnOperation(A, [i, n+1]), n+1)) 
                                                                     end do:
 b[n+1] := -Determinant(DeleteColumn(A, n+1)):

Only the original seven linear homogeneous equations with eight variables are needed. We solve them according to Cramer's rule, and in order to have uniqueness when solving the ODE, we use a point on the curve (according to the theory). (This point is sought in any convenient way.)
If we want to get a parameterization, then additionally, directly in dsolve, we can add the following:
 

for i to n do 
b[i] := simplify(Determinant(DeleteColumn(ColumnOperation(A, [i, n+1]), n+1))) 
end do:
b[n+1] := simplify(-Determinant(DeleteColumn(A, n+1))); 
deqs := seq(diff(x[i](s), s) = b[i]/(b[1]^2+b[2]^2+b[3]^2+b[4]^2+b[5]^2+b[6]^2+b[7]^2+b[8]^2)^.5, i = 1 .. n+1):

In an old post, vv reported a bug in simpl/max, which has been "fixed" in Maple 2018. However, it seem that such repairs are not complete enough.
For example, suppose it is required to find the (squared) distance between the origin and a point on x³ - x + y² = ⅓ which is closest to the origin. In other words, one needs to minimize x²＋y² among the points on this curve, i.e., 

extrema(x^2 + y^2, {x^3 + y^2 - x = 1/3}, {x, y}, 's'); # in exact form

Unfortunately, an identical error message appears again: 

Download tryHarder.mws

How about changing the values of parameter ?

for a from -3 by 3/27 to 3 do
    try
        extrema(x^2 + y^2, {x^3 + y^2 - x = a}, {x, y}); 
    catch:
        print(a); 
    end;
od;
                               -1
                               --
                               3 

                               -2
                               --
                               9 

                               -1
                               --
                               9 

                               1
                               -
                               9

                               2
                               -
                               9

                               1
                               -
                               3

By the way, like extrema, Student[MultivariateCalculus]:-LagrangeMultipliers also executes the Lagrange Multiplier method, but strangely, 

Student[MultivariateCalculus][LagrangeMultipliers](y^2 + x^2, [x^3 + y^2 - x - 1/3], [x, y], output = plot):

does not cause any errors.

This is about functionality introduced in Maple 2022, which however is still not well known: Integral Vector Calculus and parametrization using symbolic (algebraic) vector notation. Four new commands were added to the Physics:-Vectors package, implementing the parametrization of curves, surfaces and volumes, as well as the computation of path, surface and volume vector integrals. Those are integrals where the integrand is a scalar or vector function. The computation is done from any description (algebraic, parametric, vectorial) of the region of integration - a path, surface or volume.
 
There are three kinds of line or path integrals:

NOTE Jan 1: Updated the worksheet linked below; it runs in Maple 2022.
Download Integral_Vector_Calculus_and_Parametrization.mw

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

The search query in the new Maple Application center is broken.  There is no advanced search options and a search for mapleflow or maple flow brings up 0 results.  There should at least be one found, for example the search should have at least brought up The Liquid Volume in a Partially-Filled Horizontal Tank".

Maple, please fix.

Notation is one of the most important things to communicate with others in science. It is remarkable how many people use or do not use a computer algebra package just because of its notation. For those reasons, in the context of the Physics package, strong emphasis is put on using textbook notation as much as possible regarding input and output, including, for that purpose, as people here know, significant developments in Maple typesetting.

Still, for historical reasons, when using the Physics package, the labels used to refer to a coordinate system had been a single Capital Letter, as in X, Y, ...It was not possible to use, e.g. X', or x.

That has changed. Starting with the Maplesoft Physics Updates v.1308, any symbol can be used as a coordinate system label. The lines below demo this change.

Download new_coordinates_labels.mw

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

Following the previous post on The Electromagnetic Field of Moving Charges, this is another non-trivial exercise, the derivation of 4-dimensional relativistic Lorentz transformations,  a problem of a 3rd-year undergraduate course on Special Relativity whose solution requires "tensor & matrix" manipulation techniques. At the end, there is a link to the Maple document, so that the computation below can be reproduced, and a link to a corresponding PDF file with all the sections open.

Download Deriving_the_mathematical_form_of_Lorentz_transformations.mw

Deriving_the_mathematical_form_of_Lorentz_transformations.pdf

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

According to Wikipedia

"In computing, a programming language reference or language reference manual is
part of the documentation associated with most mainstream programming languages. It is
written for users and developers, and describes the basic elements of the language and how
to use them in a program. For a command-based language, for example, this will include details
of every available command and of the syntax for using it.

The reference manual is usually separate and distinct from a more detailed
 programming language specification meant for implementors of the language rather than those who simply use it to accomplish some processing task."

And no, Maple's Programming guide is not a Language reference manual. This is a guide to how to program in Maple. But it is not reference manual for the language itself. i.e. description of the Language itself.

Examples of Language reference manuals are

C

Original C++ 

Python

Ada

Fortran 77

and so on.

Why is there no LRM for Maple? Should there be one? I find Maple semantics sometime confusing, and many times I find how things work by trial and error. Having a reference to look at will be good. 

I know for a language as large as Maple, this is not easy to do. But it will good for Maplesoft to invest into making one.