Download e-book for iPad: Computer Algebra and Symbolic Computation: Elementary by Joel S. Cohen

By Joel S. Cohen

ISBN-10: 1568811586

ISBN-13: 9781568811581

Computing device Algebra and Symbolic Computation: straight forward Algorithms presents a scientific process for the algorithmic formula and implementation of mathematical operations in laptop algebra programming languages.

The perspective is that mathematical expressions, represented by way of expression timber, are the knowledge items of laptop algebra courses, and through the use of a couple of primitive operations that examine and build expressions, we will be able to enforce many easy operations from algebra, trigonometry, calculus, and differential equations.

With at the least necessities, this booklet is available and important to scholars of arithmetic, desktop technological know-how, and different technical fields. The publication features a CD with the complete, searchable textual content and implementations of all algorithms in Maple, Mathematica, and MuPad programming languages.

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Additional info for Computer Algebra and Symbolic Computation: Elementary Algorithms

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The term pseudo-language is used to emphasize that MPL is not a real CAS language that has been implemented on a computer. Although MPL is similar in spirit to real computer algebra languages, it is less formal and utilizes both mathematical symbolism and ordinary English when appropriate. The reader should have little difficulty following discussions in MPL. The reader may wonder, why introduce another algorithmic language? Why not use the programming language associated with a particular CAS? 29 30 2.

Logical operators and expressions. An MPL logical expression is one constructed using logical constants (true and false), relational expressions, and identifiers combined together with one or more of the logical operators and, or, and not. As with algebraic expressions, parentheses are used to alter the structure of an expression. Examples include (true and false) or true, not (p and q), 0 ≤ x and x ≤ 1. 2 (see pages 97-99). 1. = < <= > >= && || ! 6. Relational operators, logical constants, and logical operators in Maple, Mathematica, and MuPAD.

Use a CAS system to find the antiderivative 1/ cos5 (x) dx. Verify the result with a CAS by differentiation and simplification. 5. The following integral is given in an integral table 1 √ dx = −arcsin (x + 1) x 1−x 1+x , x > 0. 11) (a) Evaluate the integral with a CAS. ) (b) Is it possible to use a CAS to show that the antiderivative obtained in part (a) differs by at most a constant from the one given by the integral table? 24 1. Introduction to Computer Algebra 6. Consider the six equations with six unknowns {x1 , x2 , y1 , y2 , z1 , z2 }: a = b = c = r sin(θ) cos(φ) = m1 x1 + m2 x2 , m1 + m2 m 1 y1 + m 2 y2 , m1 + m2 m 1 z1 + m 2 z2 , m1 + m2 x1 − x2 , r sin(θ) sin(φ) = y1 − y2 , r cos(θ) = z1 − z2 .

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Computer Algebra and Symbolic Computation: Elementary Algorithms by Joel S. Cohen

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