MaplePrimes Announcement

The Joint Mathematics Meetings are taking place next week (January 16 – 19) in Baltimore, Maryland, U.S.A. This will be the 102nd annual winter meeting of the Mathematical Association of America (MAA) and the 125th annual meeting of the American Mathematical Society (AMS).

Maplesoft will be exhibiting at booth #501 as well as in the networking area. Please stop by to chat with me and other members of the Maplesoft team, as well as to pick up some free Maplesoft swag or win some prizes.

This year we will be hosting a hands-on workshop on Maple: A Natural Way to Work with Math

This special event will take place on Thursday, January 17 at 6:00 -8:00 P.M. in the Holiday Ballroom 4 at the Hilton Baltimore.


There are also several other interesting Maple related talks:

MYMathApps Tutorials

MAA General Contributed Paper Session on Mathematics and Technology 

Wednesday January 16, 2019, 1:00 p.m.-1:55 p.m.

Room 323, BCC
Matthew Weihing*, Texas A&M University 
Philip B Yasskin, Texas A&M University 


The Logic Behind the Turing Bombe's Role in Breaking Enigma. 

MAA General Contributed Paper Session on Mathematics and Technology 

Wednesday January 16, 2019, 1:00 p.m.-1:55 p.m.
Room 323, BCC
Neil Sigmon*, Radford University 
Rick Klima, Appalachian State University 


On a software accessible database of faithful representations of Lie algebras. 

MAA General Contributed Paper Session on Algebra, I 

Wednesday January 16, 2019, 2:15 p.m.-6:25 p.m.
Room 348, BCC
Cailin Foster*, Dixie State University 

Discussion of Various Technical Strategies Used in College Math Teaching. 

MAA Contributed Paper Session on Open Educational Resources: Combining Technological Tools and Innovative Practices to Improve Student Learning, IV 

Friday January 18, 2019, 8:00 a.m.-10:55 a.m.
Room 303, BCC
Lina Wu*, Borough of Manhattan Community College-The City University of New York 

An Enticing Simulation in Ordinary Differential Equations that predict tangible results. 

MAA Contributed Paper Session on The Teaching and Learning of Undergraduate Ordinary Differential Equations 

Friday January 18, 2019, 1:00 p.m.-4:55 p.m.
Room 324, BCC
Satyanand Singh*, New York City College of Technology of CUNY 

An Effort to Assess the Impact a Modeling First Approach has in a Traditional Differential Equations Class. 

AMS Special Session on Using Modeling to Motivate the Study of Differential Equations, I 
Saturday January 19, 2019, 8:00 a.m.-11:50 a.m.

Room 336, BCC
Rosemary C Farley*, Manhattan College 
Patrice G Tiffany, Manhattan College 


If you are attending the Joint Math meetings this week and plan on presenting anything on Maple, please feel free to let me know and I'll update this list accordingly.

See you in Baltimore!


Maple Product Manager

Featured Post

Overview of the Physics Updates


One of the problems pointed out several times about the Physics package documentation is that the information is scattered. There are the help pages for each Physics command, then there is that page on Physics conventions, one other with Examples in different areas of physics, one "what's new in Physics" page at each release with illustrations only shown there. Then there are a number of Mapleprimes post describing the Physics project and showing how to use the package to tackle different problems. We seldomly find the information we are looking for fast enough.


This post thus organizes and presents all those elusive links in one place, a Maple worksheet (linked at the end of this post). All the hyperlinks below are alive when you open this worksheet in Maple and those to Mapleprimes posts are alive here too. A link to this page is also appearing in all the Physics help pages in the next Maple release. Comments on practical ways to improve this presentation of information are welcome.



As part of its commitment to providing the best possible environment for algebraic computations in Physics, Maplesoft launched, during 2014, a Maple Physics: Research and Development website. That enabled users to ask questions, provide feedback and download updated versions of the Physics package, around the clock.

The "Physics Updates" include improvements, fixes, and the latest new developments, in the areas of Physics, Differential Equations and Mathematical Functions. Since Maple 2018, you can install/uninstall the "Physics Updates" directly from the MapleCloud .

Maplesoft incorporated the results of this accelerated exchange with people around the world into the successive versions of Maple. Below there are two sections


The Updates of Physics, as  an organized collection of links per Maple release, where you can find a description with examples of the subjects developed in the Physics package, from 2012 till 2019.


The Mapleprimes Physics posts, containing the most important posts describing the Physics project and showing the use of the package to tackle problems in General Relativity and Quantum Mechanics.

The update of Physics in Maple 2018 and back to Maple 16 (2012)




Physics Maple 2018 updates


Automatic handling of collision of tensor indices in products


User defined algebraic differential operators


The Physics:-Cactus package for Numerical Relativity


Automatic setting of the EnergyMomentumTensor for metrics of the database of solutions to Einstein's equations


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


New functionality and display for inert names and inert tensors


Automatic setting of Dirac, Paul and Gell-Mann algebras


Simplification of products of Dirac matrices


New Physics:-Library commands to perform matrix operations in expressions involving spinors with omitted indices


Miscellaneous improvements



Physics Maple 2017 updates


General Relativity: classification of solutions to Einstein's equations and the Tetrads package


The 3D metric and the ThreePlusOne (3 + 1) new Physics subpackage


Tensors in Special and General Relativity


The StandardModel new Physics subpackage



Physics Maple 2016 updates


Completion of the Database of Solutions to Einstein's Equations


Operatorial Algebraic Expressions Involving the Differential Operators d_[mu], D_[mu] and Nabla


Factorization of Expressions Involving Noncommutative Operators


Tensors in Special and General Relativity


Vectors Package


New Physics:-Library commands


Redesigned Functionality and Miscellaneous



Physics Maple 2015 updates






Tetrads in General Relativity


More Metrics in the Database of Solutions to Einstein's Equations


Commutators, AntiCommutators, and Dirac notation in quantum mechanics


New Assume command and new enhanced Mode: automaticsimplification


Vectors Package


New Physics:-Library commands





Physics Maple 18 updates




4-Vectors, Substituting Tensors


Functional Differentiation


More Metrics in the Database of Solutions to Einstein's Equations


Commutators, AntiCommutators


Expand and Combine


New Enhanced Modes in Physics Setup




Vectors Package


New Physics:-Library commands





Physics Maple 17 updates


Tensors and Relativity: ExteriorDerivative, Geodesics, KillingVectors, LieDerivative, LieBracket, Antisymmetrize and Symmetrize


Dirac matrices, commutators, anticommutators, and algebras


Vector Analysis


A new Library of programming commands for Physics



Physics Maple 16 updates


Tensors in Special and General Relativity: contravariant indices and new commands for all the General Relativity tensors


New commands for working with expressions involving anticommutative variables and functions: Gtaylor, ToFieldComponents, ToSuperfields


Vector Analysis: geometrical coordinates with funcional dependency

Mapleprimes Physics posts




The Physics project at Maplesoft


Mini-Course: Computer Algebra for Physicists


Perimeter Institute-2015, Computer Algebra in Theoretical Physics (I)


IOP-2016, Computer Algebra in Theoretical Physics (II)


ACA-2017, Computer Algebra in Theoretical Physics (III) 



General Relativity



General Relativity using Computer Algebra


Exact solutions to Einstein's equations 


Classification of solutions to Einstein's equations and the ThreePlusOne (3 + 1) package 


Tetrads and Weyl scalars in canonical form 


Equivalence problem in General Relativity 


Tetrads and Weyl scalars in canonical form 


Automatic handling of collision of tensor indices in products 


Minimize the number of tensor components according to its symmetries


Quantum Mechanics



Quantum Commutation Rules Basics 


Quantum Mechanics: Schrödinger vs Heisenberg picture 


Quantization of the Lorentz Force 


Magnetic traps in cold-atom physics 


The hidden SO(4) symmetry of the hydrogen atom


(I) Ground state of a quantum system of identical boson particles 


(II) The Gross-Pitaevskii equation and Bogoliubov spectrum 


(III) The Landau criterion for Superfluidity 


Simplification of products of Dirac matrices


Algebra of Dirac matrices with an identity matrix on the right-hand side


Factorization with non-commutative variables


Tensor Products of Quantum State Spaces 


Coherent States in Quantum Mechanics 


The Zassenhaus formula and the Pauli matrices 



Physics package generic functionality



Automatic simplification and a new Assume (as in "extended assuming")


Wirtinger derivatives and multi-index summation

See Also


Conventions used in the Physics package , Physics , Physics examples




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

Featured Post

Over the holidays I reconnected with an old friend and occasional
chess partner who, upon hearing I was getting soundly thrashed by run
of the mill engines, recommended checking out the ChessTempo site.  It
has online tools for training your chess tactics.  As you attempt to
solve chess problems your rating is computed depending on how well you
do.  The chess problems, too, are rated and adjusted as visitors
attempt them.  This should be familar to any chess or table-tennis
player.  Rather than the Elo rating system, the Glicko rating system is

You have a choice of the relative difficulty of the problems.
After attempting a number of easy puzzles and seeing my rating slowly
climb, I wondered what was the most effective technique to raise my
rating (the classical blunder).  Attempting higher rated problems would lower my
solving rate, but this would be compensated by a smaller loss and
larger gain.  Assuming my actual playing strength is greater than my
current rating (a misconception common to us patzers), there should be a
rating that maximizes the rating gain per problem.

The following Maple module computes the expected rating change
using the Glicko system.

Glicko := module()

export DeltaRating
    ,  ExpectedDelta
    ,  Pwin

    # Return the change in rating for a loss and a win
    # for player 1 against player2
    DeltaRating := proc(r1,rd1,r2,rd2)
    local E, K, g, g2, idd, q;

        q := ln(10)/400;
        g := rd -> 1/sqrt(1 + 3*q^2*rd^2/Pi^2);
        g2 := g(rd2);
        E := 1/(1+10^(-g2*(r1-r2)/400));
        idd := q^2*(g2^2*E*(1-E));

        K := q/(1/rd1^2+idd)*g2;

        (K*(0-E), K*(1-E));

    end proc:

    # Compute the probability of a win
    # for a player with strength s1
    # vs a player with strength s2.

    Pwin := proc(s1, s2)
    local p;
        p := 10^((s1-s2)/400);
    end proc:

    # Compute the expected rating change for
    # player with strength s1, rating r1 vs a player with true rating r2.
    # The optional rating deviations are rd1 and rd2.

    ExpectedDelta := proc(s1,r1,r2,rd1 := 35, rd2 := 35)
    local P, l, w;
        P := Pwin(s1,r2);
        (l,w) := DeltaRating(r1,rd1,r2,rd2);
        P*w + (1-P)*l;
    end proc:

end module:

Assume a player has a rating of 1500 but an actual playing strength of 1700.  Compute the expected rating change for a given puzzle rating, then plot it.  As expected the graph has a peak.


Ept := Glicko:-ExpectedDelta(1700,1500,r2):
plot(Ept,r2 = 1000...2000);

Compute the optimum problem rating



                     {r2 = 1599.350691}

As your rating improves, you'll want to adjust the rating of the problems (the site doesn't allow that fine tuning). Here we plot the optimum puzzle rating (r2) for a given player rating (r1), assuming the player's strength remains at 1700.

Ept := Glicko:-ExpectedDelta(1700, r1, r2):
dEpt := diff(Ept,r2):
r2vsr1 := r -> fsolve(eval(dEpt,r1=r)):
plot(r2vsr1, 1000..1680);

Here is a Maple worksheet with the code and computations.


After pondering this, I realized there is a more useful way to present the results. The shape of the optimal curve is independent of the user's actual strength. Showing that is trivial, just substitute a symbolic value for the player's strength, offset the ratings from it, and verify that the result does not depend on the strength.

Ept := Glicko:-ExpectedDelta(S, S+r1, S+r2):
has(Ept, S);

Here's the general curve, shifted so the player's strength is 0, r1 and r2 are relative to that.

r2_r1 := r -> rhs(Optimization:-Maximize(eval(Ept,r1=r), r2=-500..0)[2][]):
p1 := plot(r2_r1, -500..0, 'numpoints'=30);

Compute and plot the expected points gained when playing the optimal partner and your rating is r-points higher than your strength.

EptMax := r -> eval(Ept, [r1=r, r2=r2_r1(r)]):
plot(EptMax, -200..200, 'numpoints'=30, 'labels' = ["r","Ept"]);

When your playing strength matches your rating, the optimal opponent has a relative rating of


The expected points you win is


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