MaplePrimes Announcement

Today we are pleased to announce the release of Maple 2018.

For many people, today is just another day in March. It’s not like the release of a new version of a software product is a world-shaking event. But for us here at Maplesoft, these first few days after the latest version of Maple is released are always a bit more special. There’s always a nervous energy whenever we release Maple and everyone else gets to see what we’ve been pouring our efforts into for the past year.

I’m not going to start this post by calling the latest version of Maple “game-changing” or “cutting edge” or any other marketing friendly platitude. I’m well aware that the latest version of Maple isn’t going to change the world.

What I would say though is that with every new release of software comes an opportunity. Every new software release is an opportunity to re-evaluate how that software has evolved to better suit your needs and requirements. So… if you've been sitting on the sidelines and watching version after version go by, assuming that it won't affect you, that's wrong! There's a lot that you could be missing out on.

The way that these release announcements usually work is that we try to amaze and astound you with a long list of features. Don’t worry, I’ll get into that in a bit. But first I wanted to walk through a simple exercise of release arithmetic.

I’ll start with one of those basic truths that has always been hiding in plain sight. The build number # for Maple 2018 is 1298750. Here at Maplesoft, every time our developers make a change to Maple this build number goes up by 1. These changes are sometimes small and sometimes very big; they can be as small as fixing a documentation typo or they can constitute implementing a major feature spread across numerous files in our source tree.

I have come to look at these build numbers in a slightly different way. I look at build numbers as representing all of the small to large sized steps our developers take to get you from one version to the next (or put another way, how many steps behind you are if you are using the older versions). With that in mind, let’s do some quick math:

If you are using Maple 2017 (2017.0 was build # 1231047), there have been 1298750 – 1231047 = 67703 steps since that release (these numerous "steps" are what built the "long list" of features below). If you’re using Maple 2016 (#1113130) this number grows to 185620. And so it goes… Maple 2015 (#1022128) = 276622 steps, Maple 18 (#922027) = 376723, Maple 17 (#813473) = 485277, you get the idea. If you’re using a really old version of Maple – there’s a good chance that we have fixed up a bunch of stuff or added something that you might find interesting in the time since your last upgrade!


Every new release of Maple adds functionality that pushes Maple into new domains, rounds out existing packages, fills gaps, and addresses common user requests. Let's explore some additions:


Clickable Math - a.k.a. math that looks like math and can be interacted with using your mouse - has evolved. What was once a collection of operations found in the right-click or main menu items or in interactive smart-popups or in many additional dialogs, has been brought together and enhanced to form the new Context Panel.

We can summarize the Context Panel as follows: Enter an expression and relevant operations that you can apply to that expression appear in a panel on the right side of your screen. Easy, right? It's a great change that unlocks a large part of the Maple library for you.

The addition of the Context Panel is important. It represents a shift in the interaction model for Maple – you’ll see more and more interaction being driven through the context panel in future releases. Already, the changes for the Context Panel permeate through to various other parts of Maple too. You’ll see an example in the Units section below and here’s another for coding applications.

The Context Panel also gives you access to embedded component properties – this makes it much easier to modify parts of your application.

There’s much more we can say about the Context Panel but in the interest of keeping this post (somewhat) concise I’ll stop there. If you are interested and want to see more examples, watch this video.


Coding in Maple - For many of us, using the Maple coding language is fundamental; it's just what we do. Whether you write a lot of procedures, or modify the start-up code for your worksheet, or put a sequence of commands in a code edit region, or include a button or slider in your application, you’ll find yourself using Maple’s code editing tools.

For Code Edit Regions and the Maple Code Editor, there’s automatic command completion for packages, commands, and even file paths.

maplemint has been integrated into the Code Editor, providing code analysis while you write your code.

mint and maplemint have been unified and upgraded. If you’ve never heard of these before, these are tools for analysing your Maple code. They provide information on procedures, giving parameter naming conflicts, unreachable code, unused parameters or variables, and more. Mint is available for use with external text files and maplemint runs directly inside of Maple.

For more, I’ve got another video.


For many engineers and scientists, units are intrinsically linked with calculations. Here's something else in Maple 2018 that will improve your everyday experience – units are now supported in many core routines such as in numeric equation solving, integration, and optimization.

Here’s a quick example of using units in the int command with some thermophysical data:

We define an expression that gives the pressure of methane as a function of the specific volume V.

P := ThermophysicalData:-Property("pressure", "methane", "temperature" = 350*Unit('K'), "density" = 1/V):
-(int(P, V = 1.0*Unit('m'^3/'kg') .. .5*Unit('m'^3/'kg'), numeric));

You'll also find unit formatting in the Context Panel.

Near and dear to my heart, data analysts also have some occasion to rejoice. Maple 2018 finally adds an Interpolate command that supports irregular data! This is one of those items that users have been requesting for a long time and I'm very happy to say that it's finally here.

Furthering the data story, there are new sources for thermochemical data as well as updates to ensure that existing datasets for thermophysical data and scientific constants are up to date.


If you're interested in protecting your content in Maple, listen up:

You can now encrypt procedures; anyone can use your code, but they can't see the source!

You can also lock your Maple documents - effectively protecting them from accidental changes or other unintended modifications.



Of course, I won't leave mathematics out of this. As always, there’s a ton of new and updated stuff here.

There's a new computational geometry package. There are improvements across all fields of mathematics including group theory, graph theory, integration, differential equations and partial differential equations. And there's a ton of new work in Physics (many of you who have been following the Physics project will already know about these).

You can recreate some of the visualizations above as follows:

Here’s an example of the new VoronoiDiagram Command:

m := LinearAlgebra:-RandomMatrix(40, 2):
ComputationalGeometry:-VoronoiDiagram(m, showpoints, symbol = solidcircle, symbolsize = 7,colorregions=ColorTools:-GetPalette("Dalton"));

Here’s another change that I’ve seen mentioned several times on MaplePrimes – the ability to control the  border of arrows:

plots:-display(plottools:-arrow([0, 0], [2, 2], 0.5e-1, .2, .1, border = false, color = "DarkGrey", legend = "A+B"),
                       plottools:-arrow([0, 0], [1, 2], .15, .3, .15, border = false, color = "Crimson", legend = "A"),
                       plottools:-arrow([1, 2], [2, 2], .15, .3, .15, border = false, color = "CornflowerBlue", legend = "B"),
                   size = [600, 400]);

You can rotate Tickmarks in plots using the rotation option. Some plots, such as those in the TimeSeriesAnalysis package, use rotation by default.

ts := TimeSeriesAnalysis:-TimeSeries([7, 23, 21, 19, 13, 46, 42, 30, 31, 26, 19, 9, 16, 26, 17, 33, 31, 46, 42, 35, 45, 30, 11, 17, 23, 20, 15, 36, 31, 55, 49, 39, 36, 28, 12, 11, 21, 23, 27, 33, 36, 49, 42, 37, 33, 45, 12, 7, 23, 32, 25, 42, 27, 52, 50, 34, 41, 40, 16, 14], frequency = monthly, startdate = "2005-09");
TimeSeriesAnalysis:-SeasonalSubseriesPlot(ts, startingperiod = 9, seasonnames = ["January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"], space = .25, size = [800, 400]);


I’ll also mention some updates to the Maple language – items that the readers of this forum will likely find useful.

Dates and Times – Maple 2018 adds new data structures that represent dates and times. There are numerous functions that work with dates and times, including fundamental operations such as date arithmetic and more advanced functionality for working with Calendars.

today := Date();

Year( today ), DayOfMonth( today ), Month( today );

Date arithmetic:

One_year_ago := today - 365*Unit(d);


Until - An optional until clause has been added to Maple's loop control structure.

Here's an example, the following code finds the next prime number after 37 and then terminates the loop.

n := 37;

do n := n+1 until



As always with these posts, we can't cover everything. This post is really just the beginning of the story. I would love to spend another couple of pages describing the inner-workings of every single improvement to Maple 2018 for you; however I'd rather you just try these features yourself, so go ahead, get out there and try out Maple 2018 today. You won't be disappointed that you did.

Featured Post


Minimize the number of tensor components according to its symmetries
(and relabel, redefine or count the number of independent tensor components)



The nice development described below is work in collaboration with Pascal Szriftgiser from Laboratoire PhLAM, Université Lille 1, France, used in the Mapleprimes post Magnetic traps in cold-atom physics


A new keyword in Define  and Setup : minimizetensorcomponents, allows for automatically minimizing the number of tensor components taking into account the tensor symmetries. For example, if a tensor with two indices in a 4D spacetime is defined as antisymmetric using Define with this new keyword, the number of different tensor components will be exactly 6, and the elements of the diagonal are automatically set equal to 0. After setting this keyword to true with Setup , all subsequent definitions of tensors automatically minimize the number of components while using this keyword with Define  makes this minimization only happen with the tensors being defined in the call to Define .


Related to this new functionality, 4 new Library routines were added: MinimizeTensorComponents, NumberOfIndependentTensorComponents, RelabelTensorComponents and RedefineTensorComponents



restart; with(Physics)


Define an antisymmetric tensor with two indices

Define(F[mu, nu], antisymmetric)

`Defined objects with tensor properties`


{Physics:-Dgamma[mu], F[mu, nu], Physics:-Psigma[mu], Physics:-d_[mu], Physics:-g_[mu, nu], Physics:-KroneckerDelta[mu, nu], Physics:-LeviCivita[alpha, beta, mu, nu]}


Although the system knows that F[mu, nu] is antisymmetric, you need to use Simplify to apply the (anti)symmetry

F[mu, nu]+F[nu, mu]

F[mu, nu]+F[nu, mu]



Simplify(F[mu, nu]+F[nu, mu])



so by default the components of F[mu, nu] do not automatically reflect the (anti)symmetry; likewise

F[1, 2]+F[2, 1]

F[1, 2]+F[2, 1]


Simplify(F[1, 2]+F[2, 1])



and computing the array form of F[mu, nu]we do not see the elements of the diagonal equal to zero nor the lower-left triangle equal to the upper-right triangle but for a different sign:

TensorArray(F[mu, nu])

Matrix(%id = 18446744078270093062)



On the other hand, this new functionality, here called minimizetensorcomponents, makes the symmetries of the tensor be explicitly reflected in its components.


There are three ways to use it. First, one can minimize the number of tensor components of a tensor previously defined. For example



Matrix(%id = 18446744078270064630)


After this, both (1.2) and (1.3) are automatically equal to 0 without having to use Simplify

F[mu, nu]+F[nu, mu]






And the output of TensorArray  in (1.6) becomes equal to (1.7).


NOTE: in addition, after using minimizetensorcomponents in the definition of a tensor, say F, all the keywords implemented for Physics tensors are available for F:



F[mu, nu] = Matrix(%id = 18446744078247910206)






F[mu, nu] = {(1, 2) = F[1, 2], (1, 3) = F[1, 3], (1, 4) = F[1, 4], (2, 1) = -F[1, 2], (2, 3) = F[2, 3], (2, 4) = F[2, 4], (3, 1) = -F[1, 3], (3, 2) = -F[2, 3], (3, 4) = F[3, 4], (4, 1) = -F[1, 4], (4, 2) = -F[2, 4], (4, 3) = -F[3, 4]}



F[`~1`, mu] = Vector[row](%id = 18446744078247885990)


Alternatively, one can define a tensor, specifying that the symmetries should be taken into account to minimize the number of its components passing the keyword minimizetensorcomponents to Define .




Define a tensor with the symmetries of the Riemann  tensor, that is, a tensor of 4 indices that is symmetric with respect to interchanging the positions of the 1st and 2nd pair of indices and antisymmetric with respect to interchanging the position of its 1st and 2nd indices, or 3rd and 4th indices, and define it minimizing the number of tensor components


Define(R[alpha, beta, mu, nu], symmetric = {[[1, 2], [3, 4]]}, antisymmetric = {[1, 2], [3, 4]}, minimizetensorcomponents)

`Defined objects with tensor properties`


{Physics:-Dgamma[mu], F[mu, nu], Physics:-Psigma[mu], R[mu, nu, alpha, beta], Physics:-d_[mu], Physics:-g_[mu, nu], Physics:-KroneckerDelta[mu, nu], Physics:-LeviCivita[alpha, beta, mu, nu]}


We now have

R[1, 2, 3, 4]+R[2, 1, 3, 4]



R[alpha, beta, mu, nu]-R[mu, nu, alpha, beta]



One can always retrieve the symmetry properties in the abstract notation used by the Define command using the new Library:-GetTensorSymmetryProperties, its output is ordered, first the symmetric then the antisymmetric properties



{[[1, 2], [3, 4]]}, {[1, 2], [3, 4]}


After making the symmetries explicit (and also before that), it is frequently useful to know the number of independent components of a given tensor. For this purpose you can use the new Library:-NumberOfIndependentTensorComponents





and besides taking into account the symmetries, in the case of the Riemann  tensor, after taking into account the first Bianchi identity this number of components is further reduced to 20.


A third way of using the new minimizetensorcomponents functionality is using Setup , so that, automatically, every subsequent definition of tensors with symmetries is performed minimizing the number of its components using the indicated symmetries



Setup(minimizetensorcomponents = true)

[minimizetensorcomponents = true]


So from hereafter you can define tensors taking into account their symmetries explicitly and without having to include the keyword minimizetensorcomponents at each definition


Define(C[alpha, beta], antisymmetric)

`Defined objects with tensor properties`


{C[mu, nu], Physics:-Dgamma[mu], F[mu, nu], Physics:-Psigma[mu], R[mu, nu, alpha, beta], Physics:-d_[mu], Physics:-g_[mu, nu], Physics:-KroneckerDelta[mu, nu], Physics:-LeviCivita[alpha, beta, mu, nu]}




C[mu, nu] = Matrix(%id = 18446744078408747598)


Two new related functionalities are provided via Library:-RelabelTensorComponents and Library:-RedefineTensorComponent, the first one to have the number of tensor components directly reflected in the names of the components, the second one to redefine only one of these components


Matrix(%id = 18446744078408729774)



Suppose now we want to make one of these components equal to 1, say C__2

Library:-RedefineTensorComponent(C[1, 2] = 1)

C[mu, nu] = Matrix(%id = 18446744078270104390)


This nice development is work in collaboration with Pascal Szriftgiser from Laboratoire PhLAM, UMR CNRS 8523, Université Lille 1, F-59655, France.





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

Featured Post

This is about the recent implementation of tensor products of quantum state spaces in the Physics package, in connection with an exchange with the Physics of Information Lab of the University of Waterloo. As usual this development is available to everybody from the Maplesoft R&D Physics webpage. This is the last update for Maple 2017. The updates for Maple 2018, starting with this same material, will begin being distributed through the MapleCloud next week.

Tensor Product of Quantum State Spaces


Basic ideas and design



Suppose A and B are quantum operators and Ket(A, n), et(B, m) are, respectively, their eigenkets. The following works since the introduction of the Physics package in Maple



Setup(op = {A, B})

`* Partial match of  'op' against keyword 'quantumoperators'`


[quantumoperators = {A, B}]


A*Ket(A, alpha) = A.Ket(A, alpha)

Physics:-`*`(A, Physics:-Ket(A, alpha)) = alpha*Physics:-Ket(A, alpha)


B*Ket(B, beta) = B.Ket(B, beta)

Physics:-`*`(B, Physics:-Ket(B, beta)) = beta*Physics:-Ket(B, beta)


where on the left-hand sides the product operator `*` is used as a sort of inert form (it has all the correct mathematical properties but does not perform the contraction) of the dot product operator `.`, used on the right-hand sides.


Suppose now that A and B act on different, disjointed, Hilbert spaces.


1) To represent that, a new keyword in Setup , is introduced, to indicate which spaces are disjointed, say as in hilbertdisjointedspaces = {A, B}.  We want this notation to pop up at some point as {`ℋ`[A], `ℋ`[B]} where the indexation indicates all the operators acting on that Hilbert space. The disjointedspaces keyword has for synonyms disjointedhilbertspaces and hilbertspaces. The display `ℋ`[A] is not yet implemented.


NOTE: noncommutative quantum operators acting on disjointed spaces commute between themselves, so after setting  - for instance - disjointedspaces = {A, B}, automatically, A, B become quantum operators satisfying (see comment (ii) on page 156 of ref. [1])




2) Product of Kets and Bras (KK, BB, KB and BK) where K and B belong to disjointed spaces, are understood as tensor products satisfying, for instance with disjointed spaces A and B,


`⊗`(Ket(A, alpha), Ket(B, beta)) = `⊗`(Ket(B, beta), Ket(A, alpha))

`⊗`(Bra(A, alpha), Ket(B, beta)) = `⊗`(Ket(B, beta), Bra(A, alpha))


while of course

Bra(A, alpha)*Ket(A, alpha) <> Bra(A, alpha)*Ket(A, alpha)





3) All the operators of one disjointed space act transparently over operators, Bras and Kets of the other disjointed spaces, for example


A*Ket(B, n) = A*Ket(B, n)

and the same for the Dagger of this equation, that is

Bra(B, n)*Dagger(A) = Bra(B, n)*Dagger(A)


And this happens automatically. Hence, when we write the left-hand sides and press enter, they are automatically rewritten (returned) as the right-hand sides.


Regarding the display of Bras and Kets and their tensor products, two enhancements are happening:



A new Setup option hideketlabel makes all the labs in kets to be hidden when displaying Kets, Bras and Bracket(s), with the indices presented one level up, as if they were a sequence of labels, so instead of

 Ket(A, m, n, l) (is displayed as)   Ket(A, m, n, l).




This is the notation used more frequently when working in quantum information. This hideketlabel option is already implemented, so entering Setup(hideketlabel = true) will result in Kets, Bras and Brackets displayed without the labels.


Tensor products formed with Bras and Kets that belong to disjointed spaces set as such using Setup are displayed with the symbol 5 in between, as in Ket(A, n)*Ket(B, n) instead of Ket(A, n)*Ket(B, n).

Tensor product notation and the hideketlabel option


The implementation of tensor products using `*` and `.`


Basic exercising with the new functionality


Related functionality already in place before these changes




[1] Cohen-Tannoudji, Diue, Laloe, Quantum Mechanics, Chapter 2, section F.

[2] Griffiths Robert B., Hilbert Space Quantum Mechanics, Quantum Computation and Quantum Information Theory Course, Physics Department, Carnegie Mellon University, 2014.


See also





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

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