11,890 research outputs found
Can Computer Algebra be Liberated from its Algebraic Yoke ?
So far, the scope of computer algebra has been needlessly restricted to exact
algebraic methods. Its possible extension to approximate analytical methods is
discussed. The entangled roles of functional analysis and symbolic programming,
especially the functional and transformational paradigms, are put forward. In
the future, algebraic algorithms could constitute the core of extended symbolic
manipulation systems including primitives for symbolic approximations.Comment: 8 pages, 2-column presentation, 2 figure
Computation in Classical Mechanics
There is a growing consensus that physics majors need to learn computational
skills, but many departments are still devoid of computation in their physics
curriculum. Some departments may lack the resources or commitment to create a
dedicated course or program in computational physics. One way around this
difficulty is to include computation in a standard upper-level physics course.
An intermediate classical mechanics course is particularly well suited for
including computation. We discuss the ways we have used computation in our
classical mechanics courses, focusing on how computational work can improve
students' understanding of physics as well as their computational skills. We
present examples of computational problems that serve these two purposes. In
addition, we provide information about resources for instructors who would like
to include computation in their courses.Comment: 6 pages, 3 figures, submitted to American Journal of Physic
Solving second-order linear ordinary differential equations by using interactive software
Differential equations constitute an area of great theoretical research and applications in several branches of science and technology. The scope of this work is to present new software that is able to show all the steps in the process of solving a linear second-order ordinary differential equation with constant coefficients.info:eu-repo/semantics/publishedVersio
LevelScheme: A level scheme drawing and scientific figure preparation system for Mathematica
LevelScheme is a scientific figure preparation system for Mathematica. The
main emphasis is upon the construction of level schemes, or level energy
diagrams, as used in nuclear, atomic, molecular, and hadronic physics.
LevelScheme also provides a general infrastructure for the preparation of
publication-quality figures, including support for multipanel and inset
plotting, customizable tick mark generation, and various drawing and labeling
tasks. Coupled with Mathematica's plotting functions and powerful programming
language, LevelScheme provides a flexible system for the creation of figures
combining diagrams, mathematical plots, and data plots.Comment: LaTeX (RevTeX), 10 pages, associated files available from
http://wnsl.physics.yale.edu/levelschem
Computing generalized inverses using LU factorization of matrix product
An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4} -inverses and
the Moore-Penrose inverse of a given rational matrix A is established. Classes
A(2, 3)s and A(2, 4)s are characterized in terms of matrix products (R*A)+R*
and T*(AT*)+, where R and T are rational matrices with appropriate dimensions
and corresponding rank. The proposed algorithm is based on these general
representations and the Cholesky factorization of symmetric positive matrices.
The algorithm is implemented in programming languages MATHEMATICA and DELPHI,
and illustrated via examples. Numerical results of the algorithm, corresponding
to the Moore-Penrose inverse, are compared with corresponding results obtained
by several known methods for computing the Moore-Penrose inverse
Aligator.jl - A Julia Package for Loop Invariant Generation
We describe the Aligator.jl software package for automatically generating all
polynomial invariants of the rich class of extended P-solvable loops with
nested conditionals. Aligator.jl is written in the programming language Julia
and is open-source. Aligator.jl transforms program loops into a system of
algebraic recurrences and implements techniques from symbolic computation to
solve recurrences, derive closed form solutions of loop variables and infer the
ideal of polynomial invariants by variable elimination based on Gr\"obner basis
computation
Symbolic Manipulators Affect Mathematical Mindsets
Symbolic calculators like Mathematica are becoming more commonplace among
upper level physics students. The presence of such a powerful calculator can
couple strongly to the type of mathematical reasoning students employ. It does
not merely offer a convenient way to perform the computations students would
have otherwise wanted to do by hand. This paper presents examples from the work
of upper level physics majors where Mathematica plays an active role in
focusing and sustaining their thought around calculation. These students still
engage in powerful mathematical reasoning while they calculate but struggle
because of the narrowed breadth of their thinking. Their reasoning is drawn
into local attractors where they look to calculation schemes to resolve
questions instead of, for example, mapping the mathematics to the physical
system at hand. We model the influence of Mathematica as an integral part of
the constant feedback that occurs in how students frame, and hence focus, their
work
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