Computer algebra systems | Algebra education

Computer algebra system

A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of "computer algebra" or "symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials. Computer algebra systems may be divided into two classes: specialized and general-purpose. The specialized ones are devoted to a specific part of mathematics, such as number theory, group theory, or teaching of elementary mathematics. General-purpose computer algebra systems aim to be useful to a user working in any scientific field that requires manipulation of mathematical expressions. To be useful, a general-purpose computer algebra system must include various features such as: * a user interface allowing a user to enter and display mathematical formulas, typically from a keyboard, menu selections, mouse or stylus. * a programming language and an interpreter (the result of a computation commonly has an unpredictable form and an unpredictable size; therefore user intervention is frequently needed), * a simplifier, which is a rewrite system for simplifying mathematics formulas, * a memory manager, including a garbage collector, needed by the huge size of the intermediate data, which may appear during a computation, * an arbitrary-precision arithmetic, needed by the huge size of the integers that may occur, * a large library of mathematical algorithms and special functions. The library must not only provide for the needs of the users, but also the needs of the simplifier. For example, the computation of polynomial greatest common divisors is systematically used for the simplification of expressions involving fractions. This large amount of required computer capabilities explains the small number of general-purpose computer algebra systems. Significant systems include Axiom, Maxima, Magma, Maple, Mathematica, and SageMath. (Wikipedia).

Computer algebra system
Video thumbnail

Systems of linear equations -- Elementary Linear Algebra

This lecture is on Elementary Linear Algebra. For more see http://calculus123.com.

From playlist Elementary Linear Algebra

Video thumbnail

What is linear algebra?

This is part of an online course on beginner/intermediate linear algebra, which presents theory and implementation in MATLAB and Python. The course is designed for people interested in applying linear algebra to applications in multivariate signal processing, statistics, and data science.

From playlist Linear algebra: theory and implementation

Video thumbnail

Algebra for Beginners | Basics of Algebra

#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten

From playlist Linear Algebra

Video thumbnail

Linear Algebra Full Course for Beginners to Experts

Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis may be basically viewed as the application of l

From playlist Linear Algebra

Video thumbnail

Linear Algebra: Systems of Linear Equations

Learn the basics of Linear Algebra with this series from the Worldwide Center of Mathematics. Find more math tutoring and lecture videos on our channel or at http://centerofmath.org/

From playlist Basics: Linear Algebra

Video thumbnail

Systems of equations: algebra and geometry

This is part of an online course on beginner/intermediate linear algebra, which presents theory and implementation in MATLAB and Python. The course is designed for people interested in applying linear algebra to applications in multivariate signal processing, statistics, and data science.

From playlist Linear algebra: theory and implementation

Video thumbnail

Learn Algebra 7 : Systems of Equations

New Video Everyday at 1 PM EST!!! [ Click Notification Bell ] In this video I focus on Systems of Equations. A system of equations is 2 or more equations with the same set of variables. In solving a system of equations we find those variable values that satisfy every equation. I was aske

From playlist Learn Algebra

Video thumbnail

Linear Algebra for Computer Scientists. 1. Introducing Vectors

This computer science video is one of a series on linear algebra for computer scientists. This video introduces the concept of a vector. A vector is essentially a list of numbers that can be represented with an array or a function. Vectors are used for data analysis in a wide range of f

From playlist Linear Algebra for Computer Scientists

Video thumbnail

Roberto La Scala, Università di Bari

Roberto La Scala, Università di Bari Ciphers and difference equations

From playlist Spring 2021 Online Kolchin Seminar in Differential Algebra

Video thumbnail

Sergey Yurkevich - How to Conjecture and Prove that the Generating Function of the Yang-Zagier (...)

In a recent paper Don Zagier mentions a mysterious integer sequence $(a_{n})_{n\geq0}$ which arises from a solution of a topological ODE discovered by Marco Bertola, Boris Dubrovin and Di Yang. In my talk I show how to conjecture, prove and even quantify that $(a_{n})_{n\geq0}$ actually ad

From playlist Combinatorics and Arithmetic for Physics: special days

Video thumbnail

Sonia Rueda 7/7/14 Part 1

Title: Sparse Resultant Formulas for Differential Polynomials

From playlist Spring 2014

Video thumbnail

What We've Learned from NKS Chapter 12: The Principle of Computational Equivalence [Part 2]

In this episode of "What We've Learned from NKS", Stephen Wolfram is counting down to the 20th anniversary of A New Kind of Science with [another] chapter retrospective. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or th

From playlist Science and Research Livestreams

Video thumbnail

Thomas Dreyfus, Université de Strasbourg

May 17, Thomas Dreyfus, Université de Strasbourg Computing the difference Galois group of order 3 equations

From playlist Spring 2022 Online Kolchin seminar in Differential Algebra

Video thumbnail

Matrix Ansatz and Algebraic Bethe Ansatz for the Exclusion Process by Kirone Mallick

PROGRAM URL : http://www.icts.res.in/program/NESP2015 DATES : Monday 26 Oct, 2015 - Friday 20 Nov, 2015 VENUE : Ramanujan Lecture Hall, ICTS Bangalore DESCRIPTION : This program will be organized as an advanced discussion workshop on some topical issues in nonequilibrium statstical phys

From playlist Non-equilibrium statistical physics

Video thumbnail

Seminar on Applied Geometry and Algebra (SIAM SAGA): Elisa Gorla

For more information, see our website: http://wiki.siam.org/siag-ag/index.php/Webinar Date: Tuesday, September 14 at 11:00am Eastern time zone Speaker: Elisa Gorla, University of Neuchâtel Title: Multivariate cryptography and the complexity of polynomial system solving Abstract: T

From playlist Seminar on Applied Geometry and Algebra (SIAM SAGA)

Video thumbnail

Minicourse: Deformations of path algebras of quivers with relations. Lecture III

The minicourse consists of 4 lectures. Lecturers: Severin Barmeier and Zhengfang Wang Path algebras of quivers with relations naturally occur throughout representation theory and algebraic geometry — for example in the representation theory of finite-dimensional algebras, as the coordin

From playlist Minicourse: Deformations of path algebras of quivers with relations, JTP New Trends in Representation Theory

Video thumbnail

Thomas Scanlon

Parameter identifiability through canonical bases In joint work with Alexey Ovchnnikov, Anand Pillay, and Gleb Pogudin we study the problem of whether and how parameters in input-output equations may be recovered from experiments. Specifically, we relate the problem to a problem in the mo

From playlist DART X

Video thumbnail

Is the universe geometric or algebraic? by Minhyong Kim

EINSTEIN LECTURES DATE: 21 December 2018, 15:00 to 16:00 VENUE: Christ University, Main Auditorium, Hosur Road, Bengaluru - 29 In recent years, I have heard distinguished physicists ask this question with increasing frequency and urgency. In this lecture, I will try to convey to the audi

From playlist Einstein Lectures

Video thumbnail

Computer Basics: What Is a Computer?

Computers are all around us, and they play an important role in our lives. But what exactly is a computer? We're going to answer that question and give you an overview of some of the different types of computers you might use. 0:00 Intro 0:22 Ones and zeros 0:39 Hardware and software 1:0

From playlist Starting out with Technology

Related pages

Differential equation | Signal processing | Euclidean algorithm | Satisfiability modulo theories | Schoonschip | Reduce (computer algebra system) | HP 49/50 series | Rational number | Symbolic integration | Mathematical software | Gamma function | Limit (mathematics) | Schwartz–Zippel lemma | Elementary mathematics | SageMath | Xcas | Trigonometric functions | Diophantine equation | Padé approximant | Complex number | Polynomial greatest common divisor | Algebraic modeling language | Knuth–Bendix completion algorithm | Constraint satisfaction | Chinese remainder theorem | MATLAB | HP Prime | TI-Nspire series | AP Calculus | List of computer algebra systems | Exponential function | Floating-point arithmetic | MATHLAB | Artificial intelligence | Integer | Comparison of numerical-analysis software | Buchberger's algorithm | Series (mathematics) | TI-89 series | Matrix (mathematics) | Derive (computer algebra system) | Bessel function | Limit of a function | Applied mathematics | Algebraic number | Magma (computer algebra system) | Polynomial | Automated theorem proving | Special functions | Formula editor | Gosper's algorithm | Substitution (algebra) | Risch algorithm | Berlekamp's algorithm | Group theory | Landau's algorithm | Erable | Macsyma | MuMATH | Computer algebra | Canonical form | Gröbner basis | Interval arithmetic | Riemann zeta function | Quantifier elimination | Elementary function | Factorization | Cantor–Zassenhaus algorithm | Greatest common divisor | Gaussian elimination | Error function | Maple (software) | Arbitrary-precision arithmetic | Cylindrical algebraic decomposition | Maxima (software) | Number theory | Integral | Axiom (computer algebra system) | Experimental mathematics | Graph of a function | Algorithm