As generative AI develops, how will education change? How should it change? How will the Class of 2040 learn? History illuminates the impact of prior innovations on mathematics curriculum and pedagogy. What does this suggest about the future? In this talk, we will see how calculators, computers, and computer algebras have altered the way mathematics is taught and the way students learn. We are now faced by the most significant innovation of them all: generative AI. How will AI change the way mathematics is used professionally? The challenge for all of us is to envisage how AI can help students learn mathematics and statistics. Will AI change what students need to know? Will AI change what students can achieve? Will AI change how students learn?

Deborah Hughes Hallett is Professor of Mathematics at the University of Arizona and Adjunct Professor of Public Policy at Harvard. Her work is on strategies to improve the teaching of mathematics, and she is interested in promoting international cooperation between mathematicians. She co-founded the Calculus Consortium for Higher Education and started a foundation to promote innovative curriculum and pedagogy. Her work has been recognized by the Association for Women in Mathematics and the Mathematical Association of America.

Educators everywhere are grappling with a pressing question: How do we evaluate students in an age where AI tools can provide answers instantly? AI and other tools that give students quick answers with minimal effort aren’t going away. But they can be leveraged to give instructors and institutions insights into where students are struggling, which types of questions lead them to seek outside help, and which concepts remain unclear. In this session, you’ll discover what Maplesoft is doing to help turn AI from a black box into a source of clarity - making assessment more meaningful and student support more effective.

Thinking about overhauling a math or math-heavy course, or starting a new one? It’s a big job, but you can save time and effort by using Maple to develop your new course materials. And that’s true even if your students won’t be using Maple in the course, and no matter what format your materials are in. In this discussion you’ll discover many Maple features that will save you time as you prepare slides, handouts, assignments, and&more.

Philip Yasskin (Texas A&M University, USA)
Maple at SEE-Math
For the past 24 years, the Math Department at Texas A&M University has hosted its Summer Educational Enrichment in Math (SEE-Math) Program for gifted middle school Math students. Each year, we have about 50 students who learn about topics such as Platonic solids, Euler numbers, infinities, map coloring, graph theory, finite state systems, matrices, Pythagorean Theorem, Rubik's cube, group theory, rotations using augmented reality and mathematical games. The one activity which has been covered every year is making computer animations using the Maple computer algebra system. There are many programs which can make animations, but most of them use hand sketching with drag and drop to make the frames. We use Maple because it forces students to learn about coordinates in the plane, radian measure and translations, rotations, reflections and scaling. Starting from no knowledge of Maple, within two weeks, each student makes a short cartoon movie. You can see the students' movies at https://see-math.math.tamu.edu/SEE-ProgDescAct/movies.html Click on the name of a group and a student's name. I will discuss how these animations are taught. In addition, students learn about linear systems by modeling baking cookies and brownies. They learn how to represent this as a matrix multiplication equation and how to solve it by hand and by using Maple. Further, students learn about finite state machines through the Page rank algorithm, how this is represented as a probability matrix multiplication, and how to use Maple to perform this multiplication and raise the matrix to a power. They discover the steady state solutions. They also use matrices to represent rotations in 2D and 3D. Many of the participants have gone on to prestigious universities and some have helped make graphics and animations for my textbook, MYMathApps Calculus, which can be accessed at https://mymathapps.com/mymacalc-sample/. I will also show some of those animations.

John Pais (Ladue Horton Watkins High School, USA)
A Note on Expressing and Determining Subgroup Properties Using Commutators and Commutator Computations
The nilpotent and solvable group properties, both of which can be determined solely by commutator computations, are contained in a basic sequence of progressively weaker group properties, e.g. cyclic of prime order, cyclic, abelian, nilpotent, and solvable. An important application of such a stratification of group properties is its use in determining whether or not a group is simple, i.e. it does not contain any non-trivial proper normal subgroups. For example, it is a basic theorem of group theory that a simple, solvable group must be cyclic of prime order. Thus, it follows that every non-abelian solvable group is not simple. So, given a non-abelian group we can use a commutator computation to determine whether or not it is solvable, and if it is solvable then we know that it is not simple. Further, by a seminal result of Feit and Thompson, all groups of odd order are solvable and so it is not necessary to check them. In order to explore various commutator computations, given subgroups H and K of a group of complex matrices G, we have implemented the commutator subgroup [H, K] in our group theory code employing the Maplesoft™ built-in interactive matrix algebra over the complex numbers. In this talk we will illustrate the use of [H, K] as a building block construction for expressing other important and useful group properties, including: subnormal, normal, normalize, subnormal closure, normal closure, and Fitting.

In addition, we will provide examples of some of these commutator computations in the following groups of order 480 in the Magma/GAP classification: SmallGroup(480,959), SmallGroup(480,946), and SmallGroup(480,218). Finally, we will discuss the essential use of commutator representations of group properties in the proofs of subnormality related theorems such as equivalents of the Wielandt join theorem, the Wielandt minimal normal subgroup theorem, the Fitting normal coalition class theorem, and the Stonehewer solvable subnormal subgroups theorem.

Juan Ramirez (Panama)
Development of an Educational Digital Twin in Microelectronics using Maple and MapleSim to support Panama’s National Microchip Strategy
This proposal outlines the progressive development of an educational digital twin for the design and simulation of microelectronic circuits using Maple and MapleSim. The project is part of Panama’s national strategy to become a regional hub in the semiconductor industry. Led by Prof. Eng. Juan Ramirez, this initiative combines his experience as a STEAM educator and Maple Ambassador with a self-taught learning methodology supported by accessible tutorials for the Spanish-speaking community.

Willem Andriessen (HAN University of Applied Sciences Arnhem-Nijmegen, Netherlands)
Exploring the Advantages of Maple's DynamicSystems package over MATLAB's Control Toolbox in Higher Technical Education
In contemporary engineering curricula, the selection of software platforms for system modeling and control is pivotal in shaping students' understanding of complex concepts. My video presentation advocates for the integration of Maple and its DynamicSystems package in higher technical education as a pedagogically superior alternative to MATLAB and its Control Toolbox, particularly in the early stages of teaching control theory and system dynamics.

In this exercise, we compare Maple 2022.2 with MATLAB R2025b without making use of MapleSim or Simulink, respectively. Both these technologies are too advanced for control engineering education and, like AI, detrimental to the understanding of the theoretical foundations of the exceptional field of control engineering.

During this talk I would like to focus strictly on ordinary Maple versus MATLAB, specifically for the design of state-space variable feedback controllers for technical systems where the output tracks the input within a predefined way, like settling time, percentage overshoot and zero steady-state error and so on.

Tian Chen (Simon Fraser University, Canada)
A new black box algorithm for factoring multivariate polynomials in Maple
Click to read PDF Abstract

Richard Hollister (Sweet Briar College, USA)
Maple Procedures for the Quasi-triangularization of Matrix Polynomials
Click to read PDF Abstract

Samir Hamdi (University of Toronto, Canada)
Two-Point Padé Approximants for Special Functions: A Maple Implementation
Approximate closed-form representations of functions play a vital role in both science and engineering. In this research work, we present a Maple-based implementation of two-point Padé approximants for functions with known formal power series expansions at both the origin and infinity. By combining these expansions with nonlinear sequence transformations, we achieve accurate evaluations of the functions across the entire positive real axis using only a few terms from each series.

The method is illustrated using MAPLE with several transcendental and integral functions commonly encountered in mathematical statistics, including the Fresnel integral, Dawson's integral, Euler’s integral, elliptic integrals, the error function, and the cumulative normal distribution function. Our results demonstrate the practical utility and versatility of the two-point Padé approach in constructing efficient approximations over wide domains.

Rashid Barket (Coventry University, UK)
Tree-Based Deep Learning for Ranking Symbolic Integration Algorithms
Symbolic indefinite integration in Computer Algebra Systems such as Maple involves selecting the most efficient algorithm from multiple available methods: when such methods succeed the results are mathematically equivalent but can have dramatically different presentations. This selection has been traditionally made with only minimal consideration of the problem instance, leading to inefficiencies. In this work, we introduce a novel machine learning approach leveraging tree-based deep learning models to rank symbolic integration algorithms based on output complexity for individual problem instances. We demonstrate that representing mathematical expressions as tree structures significantly enhances model performance compared to traditional sequence-based representations. Through extensive experiments on a diverse dataset generated by six distinct data generators, we show that our two-stage classifier and ranking framework significantly improves upon Maple’s built-in method selector, achieving nearly 90% accuracy on predicting the optimal answer for the hold-out test set. Furthermore, we demonstrate that our tree transformer model exhibits robust generalisation capabilities via experimentation on out-of-distribution benchmarks from an independently produced dataset, substantially outperforming prior binary classification approaches. Our findings underscore the importance of data representation and problem framing in symbolic computation tasks, and we anticipate that our methodology will generalise effectively to similar mathematical software optimisation problems.

Do you have a question for Dr. Laurent Bernardin, Maplesoft’s CEO? Now is your chance! This Ask Me Anything session is your chance to ask him about anything you would like to hear his thoughts on.

Michael Monagan (Simon Fraser University, Canada)
Mathematical Experiments for Mathematics Majors
Click to read PDF Abstract

Asia Majeed and Alexandre Cavalcante (OISE University of Toronto, Canada)
A Pedagogical Study of Maple Learn's Effect on Mathematical Thinking in Introductory Calculus
This presentation examines the role of Maple Learn, a digital mathematics environment, in developing mathematical thinking among first-year calculus students at a large university in Toronto. While digital tools are widely used in mathematics education, few studies have rigorously explored how specific technologies like Maple Learn function as pedagogical instruments to support conceptual understanding and engagement in calculus.

Building on a pilot study conducted last year with various groups of undergraduate students, this year’s research involves three newly designed instructional activities focused on functions, derivatives, and integration. These activities are not only learning opportunities but are also used as intentional instruments for data collection. Each activity is carefully constructed to prompt students to use Maple Learn’s dynamic and visual functionalities to explore concepts, articulate reasoning, and reflect on their understanding.

We are collecting data through students' work within Maple Learn, observational notes, and surveys following each activity. These instruments are aligned with our three research objectives: (1) to explore how Maple Learn’s features support mathematical thinking; (2) to investigate how these features interact with calculus content in academic and applied contexts; and (3) to understand students' experiences and perceptions of integrating Maple Learn into their learning practices.

By analyzing how students engage with the activities, we aim to understand the affordances and limitations of Maple Learn in enhancing mathematical thinking. This work contributes to digital pedagogy by positioning technological tools not just as delivery mechanisms, but as interactive instruments that shape the learning experience and support research-informed instructional design.

William Bauldry (ASU, USA)
An Enigma Simulator
We present a Maple-based Enigma Coding Machine simulator. The simulator can be used for cryptography courses or historical demonstrations of the work of Marian Rejewski and Alan Turing.

Patrick Mills (Texas A&M University - Kingsville, USA)
Advancing Student Educational Processes in Transport Phenomena Using Maple
Transport Phenomena is considered one of the most important core courses in chemical engineering graduate education amongst other core courses, such as applied mathematics for chemical engineers,advanced thermodynamics, chemical and catalytic reaction engineering, advanced process dynamics and control, and separation processes. The subject matter generally covers the derivation, development and application of both the microscopic and macroscopic equations that describe the conservation of momentum, energy and mass for physical systems encountered in chemical engineering with increasing degrees of complexity. It also provides an essential entry point for engineering applications involving multiphase flows, such as those that are based on gas-liquid, gas-solid, liquid-liquid, gas-liquid-solid, gas-liquid-liquid-solid systems. Common topics for each conservation principle include key aspects of the governing transport parameter and associated mechanisms of transport (viscosity, thermal conductivity, and diffusivity), the equations of change, distributions for velocity, temperature, or concentration for laminar and turbulent flow, and interphase transport. Developing a firm grasp of the subject is often viewed as a rite of passage in graduate education since it bridges the gap between the unit operations approach for process analysis with more fundamental approaches. The latter is needed for detailed analysis and design of emerging engineering systems that involve the interaction of various multiphysics (1).

The landmark textbook entitled Transport Phenomena was written by Bird et al. (2) and first released in 1960 with a revised second edition appearing in 2007 (3). Approximately thirty or so textbooks have been subsequently written on the subject by various authors (4). Experience in teaching Transport Phenomena to MS and PhD graduate students for the past 15 years using the BSL text has provided the impetus for incorporating both the symbolic and numerical capabilities of Maple into the course materials. In its current form, the text does not integrate any computer-aided approaches and is primarily focused on the manual derivation of closed-form expressions for fluid velocity profiles, temperature profiles, and/or specie concentration profiles and associated derived quantities for steady-state operation in one space dimension. A few chapters extend this approach to unsteady-state behavior or two-space dimensions for each of the conservation principles. Once a given problem is defined in terms of the governing conservation equations and associated boundary conditions, students expend notable energy on deriving the closed-form solution. Consequently, developing insight into the effect of various system parameters on the problem physics is limited unless additional steps are taken to develop limiting forms of the solution and to graphically illustrate the dependent variable(s) as a function of the independent variable(s) and model parameters.

This presentation will summarize efforts on how the symbolic and numerical functionalities of MAPLE™ provides a transformative approach to learning transport phenomena. It is shown through selected examples how MAPLE™ can be used to derive the governing conservation laws and generate solutions to basic to advanced problems, thereby allowing better insight into the underlying physicochemical phenomena versus a conventional manual approach. More importantly, the student knowledge gained from using this approach is carried forward into other advanced courses and also their research, which provides a platform for accelerated knowledge development and advanced skill-set development. Development of a reference text that would serve as useful addition to the classic BSL text and its extensions to other topics where MAPLE™ is employed as the computational engine is highlighted.

By analyzing how students engage with the activities, we aim to understand the affordances and limitations of Maple Learn in enhancing mathematical thinking. This work contributes to digital pedagogy by positioning technological tools not just as delivery mechanisms, but as interactive instruments that shape the learning experience and support research-informed instructional design.

References
1. Agi, Damian T., Kyla D. Jones, Madelynn J. Watson, Hailey G. Lynch, Molly Dougher, Xinhe Chen, Montana N. Carlozo, and Alexander W. Dowling. Computational toolkits for model-based design and optimization, Current Opinion in Chemical Engineering, 43 (2024): 100994.
2. Bird, R. B., Stewart, W. E., and Lightfoot, E. N. Transport Phenomena, First Edition, John Wiley & Sons, 1960.
3. Bird, R.B., Stewart, W.E. and Lightfoot, E.N., Transport Phenomena (Revised Second ed.). John Wiley & Sons, 2007.
4. 30 Best Books on Transport Phenomena, https://www.sanfoundry.com/best-reference-books-introduction-transport-phenomena/, Last accessed on July 23, 2025.

Daulet Nurahmetov (Astana International University, Kazakhstan)
On well-posed boundary value problems for the 2nd order nonhomogeneous differential equations
In this talk, we consider on L_2 (0;1) the internal boundary value problem. We show a connection of the two-point, three-point and boundary value problem with integral term in the boundary conditions with the internal boundary value problem (1) - (3). Main result of this talk is connected by Otelbaev’s theorem (see, [1, 2]). Some general result on the punctured interval [0,c)∪(c,1] was published in [3]. Symbolic calculations were carried out in the Maple computer mathematics system.

References
1. Otelbaev, M.; Shynybekov, A.N. On well-posed problems of Bicadze-Samarskii type. (English. Russian original) Sov. Math., Dokl. 26, 157-161 (1982); translation from Dokl. Akad. Nauk SSSR 265, 815-819 (1982).
2. Kokebaev, B.K.; Otelbaev, M.; Shynybekov, A.N. On questions of extension and restriction of operators. (English. Russian original) Sov. Math., Dokl. 28, 259-262 (1983); translation from Dokl. Akad. Nauk SSSR 271, 1307-1310 (1983).
3. Kanguzhin, B.K., Nurakhmetov, D.B. Boundary value problems for 2nd order non-homogeneous differential equations with variable coefficients. Journal of Xinjiang university (Natural Science Edition). 28, no.1, 2011. Pp. 47-56.

Patrick Mills (Texas A&M University – Kingsville, USA)
On the Utility of Maple for Mathematical Analysis of Tracer Models in Biomedical and Chemical Engineering
The origin of tracer methods occurred in 1911 when the Hungarian radiochemist George De Hevesy, who was later awarded the Nobel Prize in 1943 for the development of radioactive tracers, made an unsuccessful attempt to separate radioactive lead from stable lead (Feld and De Roo, 2000). Twelve years later in 1923, his landmark publication included experimental results that quantified dose-dependent lead uptake in plants and that radioactive lead can be displaced by stable lead (Niese, 2017). This research provided the starting basis for development of a wide array of tracer methods over the next 100 years in nuclear medicine (Hoberück et al., 2023). Scientists and engineers have subsequently leveraged this broad knowledge platform on the use of radioactive isotopes in medicine to both develop and apply both inert and reacting tracer methods across a wide range of other technologies with the goal of developing models that describe fluid mixing and transport processes (Deleersnijder et al., 2022; Nauman and Buffham, 1983). Some examples of these applications include the measurement of blood flow, perfusion, and capillary permeability of the microcirculation by contrast-enhanced MRI (Sourbron and Buckley, 2011; Weinstein and Duduković, 1975), flow visualization inside various process conduits (Deleu et al., 2021), flow phenomena and specie transport in hydrological systems (Evans, 1983), dispersion of pollutants in soils (Wang et al., 2022), and modeling of the plume dispersion in the atmosphere (Brunner et al., 2023). Other applications of tracer methods among an extensive list include the study of mechanisms of catalytic reactions (Kiani and Wachs, 2024), measurement of transport and rate parameters in porous media (Gruen et al., 2023), and modeling the fluid of fluids through various continuous-flow process systems (Levenspiel, 2011). In all cases, the tracer method requires the introduction of a well-defined input disturbance in the system inlet stream or streams, such as a pulse, ramp, staircase, or step-input in concentration, with time-resolved monitoring of the resulting system response at the system outlet(s) or at points in between. In most cases, a model is developed that describes the system output response for the given input disturbance. However, some system quantification can be obtained on a model-free basis.

The models that are used to relationships between the tracer input-output responses are usually a single or system of either ordinary or partial differential equations. When compartmental models are used, a banded system of ODE’s can occur (Le Nepvou De Carfort et al., 2024). Discrimination between various models can be performed using a number of methods, such as the method of moments or parameter estimation in the Laplace, frequency, or time-domain. Maple™ is particularly useful for solving the various forms of tracer model equations that are encountered since they are usually linear in the tracer concentration so the inttrans package can be utilized to determine the required tracer output responses to an assumed tracer input forcing function in either the Laplace or frequency domain. The expressions for the first few moments of the tracer response can be readily generated using the Taylor series expansion around s = 0.

The primary objective of this presentation is to illustrate, through a few examples, how the various features of Maple™ can be used to develop solutions to various models that are used to describe the tracer output responses for several biomedical-related and chemical engineering applications, and to discriminate between these models using experimental tracer response data as the basis. Of particular interest is the analysis of tracer responses involving multi-environment, multiphase systems where the tracer can undergo exchange between one or more flowing phases and possibly a stagnant phase (Aris, 1982; Hanratty and Duduković, 1990; Sourbron and Buckley, 2011). In addition, derivation of useful tracer probability distributions is also illustrated, such as the exit age distribution E(t), the cumulative age distribution F(t), the internal age distribution I(t), the entering life expectation distribution GE(t) and internal life expectation distribution GI(t), and the intensity function (t). The ability of Maple™ to efficiently perform the required mathematical operations that are not practical using conventional manual means is also highlighted.

References:

Aris, Rutherford, 1982, Residence time distribution with many reactions in several environments, in Residence Time Distribution Theory in Chemical Engineering (Edited by A. Petho et al.), pp. 2340. Verlag Chemie, Weinheim.

Anderson, David H. Compartmental Modeling and Tracer Kinetics. Vol. 50. Springer Science and Business Media, 2013.

Brunner, Dominik, Gerrit Kuhlmann, Stephan Henne, Erik Koene, Bastian Kern, Sebastian Wolff, Christiane Voigt et al. Evaluation of simulated CO2 power plant plumes from six high-resolution atmospheric transport models. Atmospheric Chemistry and Physics 23, no. 4 (2023): 2699-2728.

Deleersnijder, Eric, Inga Monika Koszalka, and Lisa V. Lucas. Tracer and Timescale Methods for Passive and Reactive Transport in Fluid Flows. MDPI-Multidisciplinary Digital Publishing Institute, 2022

Deleu, R., Frazao, S. S., Poulain, A., Rochez, G., & Hallet, V. (2021). Tracer Dispersion through Karst Conduit: Assessment of Small-Scale Heterogeneity by Multi-Point Tracer Test and CFD Modeling. Hydrology, 8(4) (2021):168.

Evans, G. V. Tracer techniques in hydrology.The International Journal of Applied Radiation and Isotopes 34.1 (1983): 451-475.

Feld, Michael and Michel De Roo Geschichte der Nuklearmedizin in Europa. Schattauer, 2000.

Gruen, R., Pan, F., Turuelo, C. G., & Breitkopf, C. (2023). Transient studies of gas transport in porous solids using frequency response method–A conceptual study. Catalysis Today, 417, 113838.

Hanratty, Peter J., and Milorad P. Duduković. Detection of flow maldistribution in packed‐beds via tracers." AIChE Journal 36.1 (1990): 127-131.

Hoberück, Sebastian, Klaus Zöphel, Martin G. Pomper, Steven P. Rowe and Andrei Gafita. One hundred years of the tracer principle. Journal of Nuclear Medicine 64, no. 12 (2023): 1998-2000.

Kiani, Daniyal, and Israel E. Wachs. Practical considerations for understanding surface reaction mechanisms involved in heterogeneous catalysis. ACS Catalysis14.22 (2024): 16770-16784.

Le Nepvou De Carfort, Johan, Tiago Pinto, and Ulrich Krühne. An automatic method for generation of CFD-based 3D compartment models: Towards real-time mixing simulations. Bioengineering 11.2 (2024): 169.

Levenspiel, Octave. Tracer Technology: Modeling the Flow of Fluids. Vol. 96. Springer Science & Business Media, 2011.

Nauman, E. Bruce and Buffham, B.A., Mixing in Continuous Flow Systems, Wiley, New York, 1983.

Niese, S. The Nobel Laureate George de Hevesy (1885-1966) - Universal genius and father of nuclear medicine. SAJ Biotechnol 5 (2017): 102.

Sourbron, S. P., and David L. Buckley. Tracer kinetic modelling in MRI: Estimating perfusion and capillary permeability. Physics in Medicine & Biology 57.2 (2011): R1.

Wang, Chaozi, Geng Liu, Coy P. McNew, Till Hannes Moritz Volkmann, Luke Pangle, Peter A. Troch, Steven W. Lyon, Minseok Kim, Zailin Huo, and Helen E. Dahlke. Simulation of experimental synthetic DNA tracer transport through the vadose zone. Water Research, 223 (2022): 119009.

Weinstein, H., and M. P. Dudukovic, Tracer methods in the circulation. Topics in Transport Phenomena, Hemisphere Publishing Corporation (1975).

Babatunde Gbadamosi (Abiola Ajimobi Technical University, Nigeria)
Smart Campus Health Monitoring and Response: A Maple-Based Predictive Modelling Framework for Infectious Disease Control
This submission includes a Maple-based simulation framework designed for smart campus health monitoring and predictive disease control. The central component is a modified SEIR (Susceptible–Exposed–Infectious–Recovered) model, which has been implemented in Maple 2025. The model dynamically simulates the progression of an infectious disease on a university campus, accounting for environmental factors, real-time interventions, and data variability. It integrates a suite of Maple tools including `DEtools[dsolve]` for differential equation solving, `plots[odeplot]` for time-series visualization, and `Optimization[NLPSolve]` for deriving optimal control strategies.

A user-interactive dashboard has been developed using `DocumentTools` and embedded Maple components to allow decision-makers to adjust key parameters such as contact rate, compliance, and intervention intensity and instantly observe their effects on the reproduction number, infection peak, and control costs. This solution supports health administrators and educators by combining mathematical rigor with practical usability. Included in the submission is the Maple worksheet containing all model equations, parameter settings, visualizations, and the GUI interface for live interaction.

Rosario Rubio (U. Nebrija, Madrid, Spain)
Addressing, with the concourse of Maple, diverse open issues dealing with the manifold and subtle concept of geometric locus.
This submission includes a Maple-based simulation framework designed for smart campus health monitoring and predictive disease control. The central component is a modified SEIR (Susceptible–Exposed–Infectious–Recovered) model, which has been implemented in Maple 2025. The model dynamically simulates the progression of an infectious disease on a university campus, accounting for environmental factors, real-time interventions, and data variability. It integrates a suite of Maple tools including `DEtools[dsolve]` for differential equation solving, `plots[odeplot]` for time-series visualization, and `Optimization[NLPSolve]` for deriving optimal control strategies.

Yet, as we will show in our presentation, with the concourse of Maple and through quite involved examples, there are still many different, not well settled, issues involved in the locus computation. For example:

-	How to deal with symbolic locus, i.e. with locus defined in the context of geometric constructions with arbitrary (parametric) coordinates, and how to deal with the corresponding specialization for numerical values of the coordinates of the basic points of the same construction? Should we first specialize and then compute the locus or, conversely, first compute the generic locus and then specialize? Will both approaches yield the same output?
-	Should we consider, in the EliminationIdeal protocol that is usually associated to locus computation, the parameters as variables or as elements of the field of coefficients? Will both approaches yield the same output?
-	Should we eliminate over the coordinates of the locus point, or over a set of independent variables of the ideal describing the geometric construction where the locus point stands in? Will both approaches yield the same output?
-	In what sense will we “discover” geometric statements by looking for the locus of some point in a construction that verifies a certain constraint? A trivial example: we would like to “discover” how are the triangles ABC such that AC=BC. Thus, we look for the locus of C such that AC=BC and we learn that placing C in such locus, namely, in the perpendicular to AB by the midpoint of AB, the required property holds. Does this approach hold in general?

In our communication we will present some Maple worksheets to exemplify how we are currently working in these issues, aiming towards our final research goal: to state a fully symbolic algorithmic approach to locus computation.

Laureano Gonzalez Vega (CUNEF Universidad, Spain)
Deriving Closed Formulae for the Relative Position of Two Conics
Detecting the collision or overlap of two conics in the plane is of interest to robotics, CAD/CAM, computer animation, etc., where conics are often used for modelling (or enclosing) the shape of the objects under consideration. We present an efficient method to determine the relative position of two conics in terms of the sign of several polynomial expressions derived from the coefficients of the implicit equations defining the considered conics. The main advantage of this approach relies on the fact that we do not require to compute the intersection points of the two considered conics and it is especially useful when the two conics depend on one or several parameters (for example, when the two conics are moving).

We follow here an approach similar to the one presented in [1] (two conics), [2] (ellipse and parabola) or [1] and [3] (two ellipses) but we reduce the number of sign conditions in some of the cases and complete the proofs. The problem considered here can be presented as a quantifier elimination problem over the reals, since we are looking for conditions on the coefficients of the equations defining the considered conics in order they produce a prescribed geometric configuration. The bridge between the problem at hand and quantifier elimination is the characteristic equation of the pencil defined by the two considered conics since the properties of its real roots will determine each geometric configuration.

For example, we obtain that the ellipse M and the parabola N have four points of intersection iff D>0, I_4<0 and I_5<0 where D is the discriminant of det(M+xN) (the characteristic equation of the pencil defined by M and N) and I_4 and I_5 are rational functions of the entries of the matrices defining M and N. The use of Maple here has been essential to derive and manipulate these expressions but critical when trying to reduce the number of sign conditions.

This is a joint work with Jorge Caravantes, Gema Maria Diaz-Toca and M. Fioravanti.

References
[1] M. Alberich-Carramiñana, B. Elizalde, F. Thomas: New algebraic conditions for the identification of the relative position of two coplanar ellipses. Computer Aided Geometric Design 54, 3548, 2017.
[2] M. Chen, X. Hou, X. Qiu: An explicit criterion for the positional relationship of an ellipse and a parabola. IEEE International Conference on Systems, Man and Cybernetics (SMC 2008), 825829, 2008.
[3] J. Caravantes, G.M. Diaz-Toca, M. Fioravanti, L. Gonzalez-Vega: Solving the interference problem for ellipses and ellipsoids: New formulae. J. of Comp. and App. Math., 407, 114072, 2022.
[4] Y. Liu, F. Chen: Algebraic Conditions for Classifying the Positional Relationships Between Two Conics and Their Applications. J. Comput. Sci. Technol., 19, 665673, 2004.

Bahia Si Lakhal (University of Science and Technology Houari Boumediene, Algeria)
Using Partial Differential Equations with Maple in General Relativity
Maple Software facilitates the resolution of partial differential equations in general relativity. As an application I will focus on some simple cases of solving Einstein equations

Son Ho (Celtic Engineering, Inc., USA)
Double Compound-Simple Pendulum
Among the most popular amusement park rides, pendulum rides utilize their oscillatory motion which in turn results in varying accelerations to provide thrilling experiences. This study considers a pendulum ride consisting of a guest-carrying gondola attached to one end of an arm through a pin joint. The other end of the arm is attached to a fixed pivot point through another pin joint. This system can be idealized as a double pendulum consisting of two single pendula: a compound one and a simple one. The study is performed in a Maple document. First, a baseline case of a simple pendulum is considered. Its equation of motion is derived based on Newtonian mechanics as typically presented in engineering textbooks. The equation of motion and initial conditions are implemented symbolically and solved numerically in Maple for the solutions of pendulum angle, angular velocity, angular acceleration, and reaction force at the pivot point. The obtained solutions are plotted as well as evaluated at selected times for visual and numerical verification. Exact period of large-angle nonlinear oscillation is also evaluated using textbook analytical formula and compared against period value evaluated based on the numerical solutions. This baseline study is to confirm that the mathematical model of the simple pendulum is implemented correctly in Maple. Then, Lagrangian mechanics is used to derive the equation of motion for the same simple pendulum. This is to establish the workflow in Maple to implement the Lagrangian mechanics approach and to verify that it results in the same equation of motion as one discussed previously. Next, the Lagrangian mechanics workflow is extended to derive the equations of motion for the double compound-simple pendulum under consideration. Lastly, a parametric study is performed for the effects of the initial angle of the gondola to the solutions of the double pendulum.

If you want to show the work you’ve done in Maple to someone else, or even refer back to it yourself days or weeks after you did it, you are going to want to transform that worksheet full of computations into an effective communication tool that is easily read and understood. In this session, we will show tools and share tips that will help you transform your work into polished documents, and explore some of the different ways you can share those documents once they are done. Topics will include effective use of tables, choosing the best option for blocks of code, export tools, and more.

Maple 2025 included a Technology Preview of an AI-powered tool that helps you create Maple documents, and work on this new tool has continued since then. Now is your chance to get a look at how this tool has evolved, explore potential uses, and share your ideas on directions for further development.