We have just released updates to Maple and MapleSim.

Maple 2020.2 includes corrections and improvements to printing and export to PDF, support for macOS 11.0, more MATLAB connectivity, resolves issues with the installation of the Maplesoft Physics Updates, and more.  We recommend that all Maple 2020 users install these updates.

This update is available through Tools>Check for Updates in Maple, and is also available from our website on the Maple 2020.2 download page, where you can also find more details.

If you are also a MapleSim user, this Maple update will be installed automatically when you update your MapleSim installation to the newly released MapleSim 2020.2. The MapleSim update also includes many updates to MapleSim, the MapleSim CAD Toolbox, specialized MapleSim libraries, MapleSim connectivity tools, and MapleSim Insight.  You will find details about new features and improvements, as well as instructions on obtaining the update, on the MapleSim 2020.2 page.

One forum had a topic related to such a platform. ( Edited: the video is no longer available.)

The manufacturer calls the three-degrees platform, that is, having three degrees of freedom. Three cranks rotate, and the platform is connected to them by connecting rods through ball joints. The movable beam (rocker arm) has torsion springs.  I counted 4 degrees of freedom, because when all three cranks are locked, the platform remains mobile, which is camouflaged by the springs of the rocker arm. Actually, the topic on the forum arose due to problems with the work of this platform. Neither the designers nor those who operate the platform take into account this additional fourth, so-called parasitic degree of freedom. Obviously, if we will to move the rocker with the locked  cranks , the platform will move.
Based on this parasitic movement and a similar platform design, a very simple device is proposed that has one degree of freedom and is, in fact, a spatial linkage mechanism. We remove 3 cranks, keep the connecting rods, convert the rocker arm into a crank and get such movements that will not be worse (will not yield) to the movements of the platform with 6 degrees of freedom. And by changing the length of the crank, the plane of its rotation, etc., we can create simple structures with the required design trajectories of movement and one degree of freedom.
Two examples (two pictures for each example). The crank rotates in the vertical plane (side view and top view)
PLAT_1.mw


and the crank rotates in the horizontal plane (side view and top view).

The program consists of three parts. 1 choice of starting position, 2 calculation of the trajectory, 3 design of the picture.  Similar to the programm  in this topic.

It would be useful if there was a category (or subcategory) of scientific domain (e.g. physics, methematics, economics...)  in which Maple is applied. Thus it would become very convinient for someone who have a question on a specific topic to find a possible answer. 

I like how the Julia community has been organised in https://discourse.julialang.org, so I would suggest to implement something similar in Maple Primes

When this question was asked here earlier, I neglected to suggest or to emphasize two further items.  Now, on revising Mathematics for Chemistry with [Maple], I recognise that I should have included these two objectives for inclusion in Maple 2021.

- an extended and improved spreadsheet with symbolic capability; I suspect that Maple was the only software for symbolic computation to include such a facility, which sadly has become deprecated, for no obvious reason.

- a much extended capability to solve integral equations; publications dating from 1976 -- i.e. before Maple! -- have shown what is possible; Maple's capabilities for differential equations might still be superior, although the competition is becoming close, so further efforts in the development of both differential and integral equations are timely and appropriate.  Related to differential equations is naturally the extension of capabilities of special functions, both to extend present functions and to produce new functions, such as those of Lame.

I created a little procedure to automatically size text areas based on content. It sizes the text area based on wraparound and tab characters, something that the autosize for the code edit region does not do. (Hint to Maple developers)

Enjoy.

    AutosizeTextArea:=proc(TextAreaName, {intMinRows::nonnegint:=5, intMinChars::nonnegint:=50, intMaxChars::nonnegint:=140})
        description "Autosizes the TextArea based on content",
                  "Parameters",
                  "1) TextAreaName__The name of the textarea",
                  "Optional Parameters",
                  "intMinRows________Minimum number of visible rows",
                  "intMinChars_______Minimum character width",
                  "intMaxChars_______Maximum character width";
        uses DocumentTools, StringTools;          
        local strLines, intLongestLine, nLines;
        strLines := Split(GetProperty(TextAreaName,'value'),"\n");
        intLongestLine := max('numelems'~(strLines));
        # Count the characters in each line (add 7 extra characters for each tab). Determine the number of lines to display each line due to wraparound, then add all these together
        #   to determine the number of rows to display.
        nLines := add(ceil~(('numelems'~(strLines) + StringTools:-CountCharacterOccurrences~(strLines, "\t")*~7)/~intMaxChars));
        SetProperty(TextAreaName, 'visibleRows', max(nLines, intMinRows), 'refresh' = true);
        SetProperty(TextAreaName, 'visibleCharacterWidth', min(max(intLongestLine, intMinChars),intMaxChars), 'refresh' = true);
    
    end proc:

A fascinating race is presently running (even if the latest results seem  to have put an end to it).
I'm talking of course about the US presidential elections.

My purpose is not to do politics but to discuss of a point of detail that really left me puzzled: the possibility of an electoral college tie.
I guess that this possibility seems as an aberration for a lot of people living in democratic countries. Just because almost everywhere at World electoral colleges contain an odd number of members to avoid such a situation!

So strange a situation that I did a few things to pass the time (of course with the earphones on the head so I don't miss a thing).
This is done with Maple 2015 and I believe that the amazing Iterator package (that I can't use thanks to the teleworking :-( ) could be used to do much more interesting things.

 

Download ElectoralCollegeTie.mw

Controlled platform with 6 degrees of freedom. It has three rotary-inclined racks of variable length:

and an example of movement parallel to the base:

Perhaps the Stewart platform may not reproduce such trajectories, but that is not the point. There is a way to select a design for those specific functions that our platform will perform. That is, first we consider the required trajectories of the platform movement, and only then we select a driving device that can reproduce them. For example, we can fix the extreme positions of the actuators during the movement of the platform and compare them with the capabilities of existing designs, or simulate your own devices.
In this case, the program consists of three parts. (The text of the program directly for the first figure : PLATFORM_6.mw) In the first part, we select the starting point for the movement of a rigid body with six degrees of freedom. Here three equations f6, f7, f8 are responsible for the six degrees of freedom. The equations f1, f2, f3, f4, f5 define a trajectory of motion of a rigid body. The coordinates of the starting point are transmitted via disk E for the second part of the program. In the second part of the program, the trajectory of a rigid body is calculated using the Draghilev method. Then the trajectory data is transferred via the disk E for the third part of the program.
In the third part of the program, the visualization is executed and the platform motion drive device is modeled.
It is like a sketch of a possible way to create controlled platforms with six degrees of freedom. Any device that can provide the desired trajectory can be inserted into the third part. At the same time, it is obvious that the geometric parameters of the movement of this device with the control of possible emergency positions and the solution of the inverse kinematics problem can be obtained automatically if we add the appropriate code to the program text.
Equations can be of any kind and can be combined with each other, and they must be continuously differentiable. But first, the equations must be reduced to uniform variables in order to apply the Draghilev method.
(These examples use implicit equations for the coordinates of the vertices of the triangle.)

Download Godel_universe_and_Tedrads.mw

H

ICs:=u(0,0) =0, D[2](u)(0,0)=1,v(0,0) =1, D[2](v)(0,0)=1,D[1](u)(0,0)=0, D[1](v)(0,0)=0. #(any ics shold be 6)

num_solution := pdsolve(sys, {ICs}, numeric);

it might the issue with ICS .. 

any valuable comments

The 2020 Maple Conference is coming up fast! It is running from November 2-6 this year, all remotely, and completely free.

The week will be packed with activities, and we have designed it so that it will be valuable for Maple users of all skill and experience levels. The agenda includes 3 keynote presentations, 2 live panel presentations, 8 Maplesoft recorded presentations, 3 Maple workshops, and 68 contributed recorded presentations.

There will be live Q&A’s for every presentation. Additionally, we are hosting what we’re calling “Virtual Tables” at every breakfast (8-9am EST) and almost every lunch (12-1 EST). These tables offer attendees a chance to discuss topics related to the conference streams of the day, as well as a variety of special topics and social discussions. You can review the schedule for these virtual tables here.

Attendance is completely free, and we’re confident that there will be something there for all Maple users. Whether you attend one session or all of them, we’d love to see you there!

You can register for the Maple Conference here.

Download The_metric_[27_37_1]_in_canonical_form.mw

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

When we plot a curve with the option  style=point  , symbols go evenly not along the length of this curve, but along the range of the independent variable. For this reason the plot often looks unattractive. Here are two examples. In the first example, the default option  adaptive=true  is used, in which Maple adds points in some places.

restart;
plot(surd(x,3), x=-2.5..2.5, style=point, scaling=constrained, symbol=solidcircle, symbolsize=8, numpoints=30, size=[800,300]);
plot(surd(x,3), x=-2.5..2.5, style=point, scaling=constrained, symbol=solidcircle, symbolsize=8, numpoints=30, adaptive=false, size=[800,300]);

The  UniformPointPlot  procedure allows you to plot curves by symbols (as for  style=point), and these symbols go from each other at equal distances, measured along this curve. The procedure uses a well-known formula for the length of a curve in two and three dimensions. The procedure parameters are clear from the three examples below.

UniformPointPlot:=proc(F::{algebraic,list},eq::`=`,n::posint:=40,Opt::list:=[symbol=solidcircle, symbolsize=8, scaling=constrained])
local t, R, P, g, L, step, L1, L2;
uses plots;
Digits:=4:
t:=lhs(eq); R:=rhs(eq);
P:=`if`(type(F,algebraic),[t,F],F); 
g:=x->`if`(F::algebraic or nops(F)=2,evalf(Int(sqrt(diff(P[1],t)^2+diff(P[2],t)^2), t=lhs(R)..x, epsilon=0.001)),evalf(Int(sqrt(diff(P[1],t)^2+diff(P[2],t)^2+diff(P[3],t)^2), t=lhs(R)..x, epsilon=0.001))):
L:=g(rhs(R)); step:=L/(n-1);
L1:=[lhs(R),seq(fsolve(g-k*step, fulldigits),k=1..n-2),rhs(R)];
L2:=map(s->`if`(type(F,algebraic),[s,eval(F,t=s)],eval(F,t=s)), L1):
`if`(F::algebraic or nops(F)=2,plot(L2, style=point, Opt[]),pointplot3d(L2, Opt[]));
end proc:

   
Examples of use:

UniformPointPlot(surd(x,3), x=-2.5..2.5, 30);

UniformPointPlot([5*cos(t),3*sin(t)], t=0..2*Pi, [color=red,symbol=solidcircle,scaling=constrained, symbolsize=8,  size=[800,400]]);

UniformPointPlot([cos(t),sin(t),2-2*cos(t)], t=0..2*Pi, 41, [color=red,symbol=solidsphere, symbolsize=8,scaling=constrained, labels=[x,y,z]]);

                             
Here's another example of using the same technique as in the procedure. In this example, we are plotting Archimedean spiral uniformly colored with 7 rainbow colors:

f:=t->[t*cos(t),t*sin(t)]:
g:=t->evalf(Int(sqrt(diff(f(s)[1],s)^2+diff(f(s)[2],s)^2), s=0..t)):
h:=s->fsolve(s=g(t), t):
L:=evalf(g(2*Pi)): step:=L/7:
L1:=[0,seq(h(k*step), k=1..6),2*Pi]:
Colors:=convert~([Red,Orange,Yellow,Green,Blue,Indigo,Violet], string):
plots:-display(seq(plot([f(t)[], t=L1[i]..L1[i+1]], color=Colors[i], thickness=12), i=1..7), scaling=constrained, size=[500,400]);

Uniform_Point_Plot.mw

A few weeks ago a television station in Toronto asked me if I’d share some tips on how parents could help their kids stay engaged with remote learning. My initial reaction was to run for the hills – appearing on live TV is not my cup of tea. However my colleagues persuaded me to accept. You can see a clip of that segment here - I’ve included it in this post because otherwise someone on the marketing team would have ;-)

My tips are based on a wide variety of experiences. My role at Maplesoft requires me to speak with educators at all levels, and remote learning has been a hot topic of conversation lately, as you can imagine. As well, in my past life (i.e. life before kids) I was a high school math tutor, and now as a parent I’m in the thick of it helping my son navigate Kindergarten remotely.

So here are my 5 tips on how parents of elementary and high-school aged children can help their kids stay engaged with remote learning. If you have other tips, including suggestions for university students, feel free to leave them in the comments sections. And if these tips help you, please let me know. It will have made the stress of my appearance on TV worthwhile!

Tip 1: Look for the positives

These are unprecedented times for kids, parents and teachers. Over the course of the last 6-7 months, learning as we’ve grown to know it has changed radically. And while the change has been incredibility difficult for everyone, it’s helpful to look for the positives that remote learning can bring to our children:

• Remote learning can help some kids focus on their work by minimizing the social pressures or distractions they may face at school.
• Older kids are appreciating the flexibility that remote learning can offer with respect to when and how they complete their work.  
• Younger kids are loving the experience of learning in the presence of mom and dad. My 4 year old thinks it’s awesome that I now know all the lyrics to the songs that he learns in school.
• As many remote learning classrooms include students from across the school board, this can provide kids with the opportunity to connect with their peers from different socio-economic backgrounds living across the city.

Tip 2: Don’t shy away from your kid’s teacher

While some kids are thriving learning from home, we know that others are struggling.

If your high school student is struggling at school, do whatever it takes to convince them to connect with their teacher. If your child is younger, make the connection yourself.

In my role, I’ve had the opportunity to work with many teachers, and rest assured, many of them would welcome this engagement.  They want our kids to succeed, but without the face-to-face classroom interaction it’s becoming increasingly more difficult for them to rely on visual cues to see how your child is doing and if they are struggling with a concept.

So I encourage you to reach out to your kid’s teacher especially if you notice your child is having difficulty.

Tip 3: Get creative with learning

Another benefit of remote learning is that it presents us with a unique opportunity to get creative with learning.

Kids, especially those in middle school and high school, now have the time and opportunity to engage with a variety of different online learning resources. And when I say online learning resources, I mean more than just videos. Think interactive tools (such as Maple Learn), that help students visualize concepts from math and science, games that allow students to practice language skills, repositories of homework problems and practice questions that allow kids to practice concepts, the list goes on.

Best of all, many content providers and organizations, are offerings these resources and tools available for free or at a substantially reduced cost to help kids and parents during this time.

So if your child is having difficulty with a particular subject or if they are in need of a challenge, make sure to explore what is available online.

Tip 4: Embrace the tech

To be successful, remote learning requires children to learn a host of new digital skills, such as how to mute/unmute themselves, raise their hands electronically, turn on and off their webcam, toggle between applications to access class content and upload homework, keep track of their schedule via an electronic calendar, etc. This can be daunting for kids who are learning remotely for the first time.

As a parent you can help your child become more comfortable with remote learning by setting aside some time either before or after class to help them master these new tools. And since this is likely new to you, there are some great videos online that will show you how to use the system your school has mandated be it Microsoft Teams, Google Classroom or something else.  

Tip 5: It’s a skill

Remember that remote learning is a skill like any other skill, and it takes time and practice to become proficient.

So remember to be patient with yourself, your kids, and their teachers, as we embark on this new journey of learning. Everyone is trying their best and I truly believe a new rhythm will emerge as we progress through the school year.

We will find our way.

Examples of mathematical models for the formation of spline curves based on polynomials of various orders that simulate certain trajectories are given.
Mathematical models of the formation of a spline curve, taking into account the extreme derivatives of the initial orders, are presented. The construction of the spline curves of the hermit and bezier of various orders, consisting of different segments, is considered. The presented models are systematic and universal, i.e. can be used to generate any polynomial curves with specified extreme derivatives of the vectors.

100_nodes_not_closed.mwExample_1.mwExample_2.mwExample_3.mwExample_4.mwExample_5.mwExample_6.mwExample_7.mw

«Формирования линий OC и бриджей по линии MAT для области с островами».OC_MAT_MA_bridge.mw

As an addition to the post.
Non-orientable surface in the sequence of orientable surfaces. In the picture we see the equations corresponding to the current surface plot.
Just entertainment.
surfaces.mw