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I was playing around with plotting volumes of revolution for calculus.  My opinion is that the defaults for Student[Calculus1][VolumeOfRevolution] could be improved by a couple simple changes.  My hope is that the people here can make my plots better to give Maplesoft a good idea of how to change the defaults.  

The standard code and output are





Changing the surface style to patch and the surfce colors to different colors creates a plot that I find easier to interpret.

Student[Calculus1][VolumeOfRevolution](x+2,x^2+1, x = 0..1,output=plot,volumeoptions =[color="DarkBlue",style=patch],volume2options =[color="DarkGreen",style=patch],caption="");





What do you think about getting the defaults changed?  I hope someone can give better suggestions for the plot defaults.

Perhaps you could consider a Coding theory Package.  I'm working on Coding theory at the moment.

Maple introduced "Copy as LaTeX" a few versions ago and I have used this feature exensively when it suddenly stopped working.

After som experiments I found the root cause and easy (but irritating) workaround for OSX

"Copy as LaTeX" suddenly stops working ("Copy as MathML" still works fine)

This problem appears if in “Display Setting”-tab in settings dialogue the “Input display” is set to “Maple Notation
In that case all attempts on “Copy as LaTeX” will be a null-function and not move anything at all into the copy buffer.
The “Copy as MathML” is not affected by this in the same way.

I have confirmed this on OSX both Maple 2022 and 2023

Adjusting “Display Setting”-tab in settings dialogue so that the “Input display” is set to “2-D Math” and “Apply Globally” makes it work again.
A bit annoying as a prefer the maple notation input and I cannot have this setting if I want the copy to latex to work.
in OSX this can also be fixed by removing the Maple preferences file and letting Maple restore it.
~/Library/Preferences/Maple/2023/Maple Preferences

I have been working in the building construction industry for more than 30 years, and one of the big things which has been coming up is parametric design.

While every major big software company has come up with its own package (Bentley with Generative Components, Autodesk with Dynamo), there is one software now that has won over all them - Grasshopper 3D.

Nowadays all major software products are trying to write bidirectional links to Grasshopper. Inhouse we do have Tekla on the BIM side and FEM-Design on the calculation side where both are capable to link to Grasshopper.

Grasshopper itself is also capable of running Python code, though in a reduced kind of way.

I would very much like to see Maple to have a Grasshopper link, probably achievable through Python.

At least Maplesoft should have a quick look at it, to see if this is possible or not.

MapleFlow is showing the exact same icon in the taskbar as Maple when both are open.  Be nice if they were slightly different.

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

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.

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


  •   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: 


Return the root graph corresponding to the given 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] # Containing the ninth forbidden induced subgraph.


enter image description here


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

I did not see such a post for 2023 so I am starting one.

What is your 3 top bug fixes or improvements  you would like to see in Maple 2023? 

Here are mine

  1. Fix timelimit so that it completes at or near the time requested and not hang or take 10 hrs when asked to timeout after say 30 seconds.
  2. Fix the large amount of server crashes and the many random hangs when running large computation that takes long time. i.e. Make Maple more robust.
  3. Allow the user to remove output from worksheet while it is still running (Evaluate->Remove output from worksheet)

Maple is a nice language and has many nice functions. But it is the usability part of Maple that leaves many bad impressions because of these things that should really have been fixed by now given how long  Maple software have been around.

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.

Given transfer function

H(s) = 60.*Unit('m'*'kg'/('s'^2*'A'))/(.70805*s^2*Unit('kg'^2*'m'^2/('s'^3*'A'^2))+144.*s*Unit('kg'^2*'m'^2/('s'^4*'A'^2))+0.3675e-4*s^3*Unit('kg'^2*'m'^2/('s'^2*'A'^2)))

H(s) = 60.*Units:-Unit(m*kg/(s^2*A))/(.70805*s^2*Units:-Unit(kg^2*m^2/(s^3*A^2))+144.*s*Units:-Unit(kg^2*m^2/(s^4*A^2))+0.3675e-4*s^3*Units:-Unit(kg^2*m^2/(s^2*A^2)))


Desired output (derived by hand) where the transfer function is separated in a dimensionless expression and a gain that can be attributed to units with a physical meaning in the context of an application (here displacement per voltage).

H(s) = 60.*Unit('m'/'V')/(.70805*s^2*Unit('s'^2)+144.*s*Unit('s')+0.3675e-4*s^3*Unit('s'^3))

H(s) = 60.*Units:-Unit(m/V)/(.70805*s^2*Units:-Unit(s^2)+144.*s*Units:-Unit(s)+0.3675e-4*s^3*Units:-Unit(s^3))


is(simplify((H(s) = 60.*Units[Unit](m*kg/(s^2*A))/(.70805*s^2*Units[Unit](kg^2*m^2/(s^3*A^2))+144.*s*Units[Unit](kg^2*m^2/(s^4*A^2))+0.3675e-4*s^3*Units[Unit](kg^2*m^2/(s^2*A^2))))-(H(s) = 60.*Units[Unit](m/V)/(.70805*s^2*Units[Unit](s^2)+144.*s*Units[Unit](s)+0.3675e-4*s^3*Units[Unit](s^3)))))



Units to factor out in the denominator are Unit('kg'^2*'m'^2/('s'^5*'A'^2)). Quick check:

Unit('m'*'kg'/('s'^2*'A'))/Unit('kg'^2*'m'^2/('s'^5*'A'^2)) = Unit('m'/'V')

Units:-Unit(m*kg/(s^2*A))/Units:-Unit(kg^2*m^2/(s^5*A^2)) = Units:-Unit(m/V)


simplify(Units[Unit](m*kg/(s^2*A))/Units[Unit](kg^2*m^2/(s^5*A^2)) = Units[Unit](m/V))

Units:-Unit(s^3*A/(m*kg)) = Units:-Unit(s^3*A/(m*kg))


"Simplification" attempts with the denominator

denom(rhs(H(s) = 60.*Units[Unit](m*kg/(s^2*A))/(.70805*s^2*Units[Unit](kg^2*m^2/(s^3*A^2))+144.*s*Units[Unit](kg^2*m^2/(s^4*A^2))+0.3675e-4*s^3*Units[Unit](kg^2*m^2/(s^2*A^2)))))



collect(s*(.70805*s*Units[Unit](kg^2*m^2/(s^3*A^2))+144.*Units[Unit](kg^2*m^2/(s^4*A^2))+0.3675e-4*s^2*Units[Unit](kg^2*m^2/(s^2*A^2))), Unit('kg'^2*'m'^2/('s'^5*'A'^2)))



is not effective because all units are wrapped in Unit commands. Example:




Expand does not expand the argument of Unit commands.

expand(Units[Unit](kg^2*m^2/(s^2*A^2))); lprint(%)






C1: Expanding Unit command

An expand facility could be a solution that expands a Unit command with combined units to a product of separate Unit commands.

When all units are expanded in a separate Unit command, collect or factor can be used to collect units:




collect(.70805*s*Units[Unit](kg)^2*Units[Unit](m)^2/(Units[Unit](A)^2*Units[Unit](s)^3)+144.*Units[Unit](kg)^2*Units[Unit](m)^2/(Units[Unit](A)^2*Units[Unit](s)^4)+0.3675e-4*s^2*Units[Unit](kg)^2*Units[Unit](m)^2/(Units[Unit](A)^2*Units[Unit](s)^2), [Unit('A'), Unit('kg'), Unit('m'), Unit('s')])






C2: Using the Natural Units Environment

In this environment, no Unit commands are required and the collection of units should work with Maple commands.
However, for the expressions discussed here, this would lead to a naming conflict with the complex variable s of the transfer function and the unit symbol s for seconds.


C3: A type declaration or unit assumptions on names

A type declaration as an option of commands like in

Units[TestDimensions](s*(.70805*s*Units[Unit](kg^2*m^2/(s^3*A^2))+144.*Units[Unit](kg^2*m^2/(s^4*A^2))+0.3675e-4*s^2*Units[Unit](kg^2*m^2/(s^2*A^2))), {s::(Unit(1/s))})



could help Maple in simplification tasks (in its general meaning of making expressions shorter or smaller).
Alternatively, assumptions could provide information of which "unit type" a name is

`assuming`([simplify(H(s) = 60.*Units[Unit](m*kg/(s^2*A))/(.70805*s^2*Units[Unit](kg^2*m^2/(s^3*A^2))+144.*s*Units[Unit](kg^2*m^2/(s^4*A^2))+0.3675e-4*s^3*Units[Unit](kg^2*m^2/(s^2*A^2))))], [s::(Unit(1/s))]); `assuming`([combine(H(s) = 60.*Units[Unit](m*kg/(s^2*A))/(.70805*s^2*Units[Unit](kg^2*m^2/(s^3*A^2))+144.*s*Units[Unit](kg^2*m^2/(s^4*A^2))+0.3675e-4*s^3*Units[Unit](kg^2*m^2/(s^2*A^2))), 'units')], [s::(Unit(1/s))])

Error, (in assuming) when calling 'property/ConvertProperty'. Received: 'Units:-Unit(1/s) is an invalid property'


On various occasions (beyond transfer functions) I have looked for such a functionality.


C4: DynamicSystems Package with units

C4.1: The complex variable s could be attributed to the unit 1/s (i.e. Hertz) either by default or as an option. This could enable using units within the dynamic system package which is not possible in Maple 2022. An example what the package provides currently can be found here: help(applications, amplifiergain)
The phase plot shows that the package is already implicitly assuming that the unit of s is Hertz. A logical extension would be to have magnitude plots with units (e.g. m/V, as in this example).


C4.2: A dedicated "gain" command that takes units into account and that could potentially simplify the transfer function to an expression like (2) in SI units. In such a way the transfer function is separated into a dimensionless (but frequency depended) term and a gain term with units.
This would make the transfer of transfer functions to MapleSim easy and avoid unit conversion errors.



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: 


extrema(x^2+y^2, {x^3+y^2-x = -2/(3*sqrt(3))}, {x, y})



extrema(x^2+y^2, {x^3+y^2-x = 1/3}, {x, y})

Error, (in simpl/max) complex argument to max/min: 1/36*((36+12*I*3^(1/2))^(2/3)+12)^2/(36+12*I*3^(1/2))^(2/3)


`~`[`^`](extrema(sqrt(x^2+y^2), {x^3+y^2-x = 1/3}, {x, y}), 2)

{4/3, 4/27}


extrema(x^2+1/3-x^3+x, {x^3+y^2-x = 1/3}, {x, y})

{4/3, 4/27}


MTM[limit](extrema(x^2+y^2, {x^3+y^2-x = a}, {x, y}), 1/3)

{4/3, 4/27}


Download tryHarder.mws

How about changing the values of parameter ?

for a from -3 by 3/27 to 3 do
        extrema(x^2 + y^2, {x^3 + y^2 - x = a}, {x, y}); 






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.

Any chance to have "Evaluate->Remove Output From Worksheet" become active and usable when one is still running something in the worksheet?  May be in 2023 version?

This is something that has been missing in Maple for ages.

Maple definitely slows down when the worksheet becomes full of output (from print messages) when a command has been running for long time. Now there is no way to remove the output in the worksheet until the command completes which can take hours. May be this slow down because the scrolling/writing to the worksheet slows down, and this affects how long it takes to complete as the engine is waiting for the frontend to finish writing to the worksheet?. I do not know. I just know Maple slows down when this happens.

I do not understand why Maple can't implement this. Is there a tehnical reson which will make removing current output in the worksheet not possible while a command is running?

As we head back to school, I want to take a moment to thank all the math teachers out there who take on the demanding yet overlooked task of educating our children, teenagers, and young people. 

I'm where I am today because my calculus teacher, Prof. Srinivasan, was unwavering in her belief that my classmates and I could master any math topic, including calculus. Her conviction in me gave me the confidence to believe I could 'do' math. While Prof. Srinivasan made teaching look easy, I'm acutely aware that teaching math is no easy feat. Speaking with math educators regularly, I can appreciate how challenging teaching math is today compared to a decade ago. Not only do they have to teach the subject, but they must be able to teach it in-person and online, to a group of students that may not be up to speed on the prerequisite material, and in an era where disruptive technologies vie for their student's attention. No wonder math educators are so anxious about returning to the classroom this fall!

And while I wish I could abracadabra your worries away, what I can do is offer you the opportunity to use Maple Learn, a tool built to support the utopian vision of a world where all students love math. A world where math is for everyone, not just the gifted, and the purpose of math class is to explore and marvel at the wonders of the universe, not just get to the correct answer.

Slightly more concretely, Maple Learn is a flexible interactive environment for exploring concepts, solving problems, and creating rich online math content. I've seen educators use Maple Learn to help their students: 

I’ve talked to lots of instructors, in math, and in courses like economics and physics that use math, who have lots of ideas of how to engage their students and deepen their understanding through interactive online activities. What they don’t have are the tools, programming experience, deployment platform, or time to implement their vision. Fortunately, Maple Learn makes it incredibly easy to develop and share your own content, and all you need are your ideas and a web browser. But you don’t need to start from scratch. You can choose from an extensive, constantly growing repository of ready-made, easily customizable content covering a wide range of topics. I think you’ll be pleasantly surprised by how easy it is, but since we are well aware that instructors are extremely busy people, we also have content development services that can help you transform your static content into interactive lessons.

If you haven't looked at Maple Learn, or it's been a while since you last saw it, you can visit Reinventing Math Education with Maple Learn for more information, including an upcoming webinar you might be interested in attending and a special offer on Maple Learn for Maple campuses. And if you ever want to discuss ways Maple Learn might help you, or have ideas on how to make it better, please reach out. I'm always up for good conversation. 

And for all the dedicated teachers who are taking a deep breath and heading back into the classroom this fall, thank you.


Combing a Prismatic Joint component with an Elasto Gap component does not always provide correct results. Incorrectly combined (red mass below), a force is generated although the distance between the flanges is greater than the relaxed spring length. A force is exerted (instead of no force is exerted as stated here) on the mass which leads to a smaler deflection (expected are 9.81 m).

This happened to me although I connected flange_a to flange_a and flange_b to flange_b in configruation A bellow. Configuration B works with inverted flanges and configuration C works with inverted unit vector of the prismatic joint. By reversing the direction of gravity, configuration A becomes a valid configuration and configurations B and C become invalid configurations.

It seems that in invalid configruations the value of the  flange distance s_rel can have a large magnitude but is negative in sign which generates significant forces although there is no contact of flanges.

So far for the observations.


Would a change of the contact condition

prevent invalid configurations or do we have to live with it for principal reasons that I am over looking?

If so, I don't see a foolproof method to avoid invalid configurations. Instead, I can only suggest measuring the flange distance of the Elasto Gap component as in the attached. If negative values of large amplitude occur, the configuration is invalid.

Assuming that a beginner would connect intuetively flange_a to flange_a and flange_b to flange_b, there is a chance of 50% that the configuration is invalid (A instead of C). This is too much to be acceptable, especially since verifying results in complex assemblies is often not possible.

It is worth noting that the contact condition comes from the underlying Modelica component and not from 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


Original C++ 



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.

MapleSim is a mature product. The rich component library leaves little room for improvement for wide range of applications. It is understandable that latest product releases focused on specialized toolboxes and performance improvements.

Here is what I think could be beneficial for many users, which is not related to performance, but can help improve the user experience:

  1. Crossing connection lines: A view option to render a crossing connection line with an arc at the crossing point of two connection lines of the same type. Right-click on a connection line might be enough.

    -> To avoid misinterpretations of routing in crowded model diagrams
  2. Parameters: An option to populate or reset changes in the parameter pane to the parameter default settings view and vice versa

    -> When testing or optimizing a model, sometimes changed parameters should become default values or be reset. Doing this manually is error prone and takes time.
  3. Component flip: Selecting more than one component including connection lines and applying a flip to all of them

    -> When building a model, it can happen that a nicely laid out arrangement of components needs to be mirrored or rotated in its entirety. Doing this component by component and connection by connection is a lot of work that can be saved by this option.
  4. Initial conditions: An option in the view menu to highlight components where ICs have been changed from ignore to treat as guess or to strictly enforce

    -> ICs are set for many purposes. In addition to defining ICs needed for simulations, this can include extracting equations, testing different model states, or temporarily "immobilizing" a model during assembly, to name a few. Undoing a tentative change can easily be forgotten. Combining existing models that work on their own into a new more complex model often results in an overly constrained model that either cannot be assembled or does not simulate.
    In debugging a model, ICs of all components must be individually inspected. This takes time. A quick overview that shows components where ICs are not set to ignore would be very helpful in debugging models.
  5. Undo Create subsystem: A reverse operation that inserts the contents of a subsystem into a parent subsystem.

    -> With the evolution of a model it is sometimes useful to exclude or include existing components from or to a subsystem. For this purpose, an undo create subsystem operation should preserve existing connections. A time saver.
  6. Subsystem ports: An option to align a subsystem port to the drawing grid to remove “micro” steps in connection lines

    -> For perfectionists who do not have the time to learn (and remember) how to fine-tune at the component level

    Update: MapleSim 2022.2 has subtantially improved on this. This item could be removed from the list.
  7. A history or log function of user actions changing a model, its parametrization or internal state.

    -> Often a model does not simulate at all or as desired after modifications. Restoring to a configuration that worked by undo only goes back to the last simulation performed. In such a situation, only reloading the latest file version and redoing modifications may restore the desired model, parametrization, or state. This takes time and migth be unsuccessful. A record of user actions would be a great help.
    History or log information in file format could also help MapleSim support to reproduce an error.

For me personally, reducing errors (4. > 7. > 2.) would improve the use experience much more than layouting aids (3. > 1., 5., 6.).

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