By Joel S. Cohen

Mathematica, Maple, and related software program applications offer courses that perform refined mathematical operations. utilising the guidelines brought in machine Algebra and Symbolic Computation: simple Algorithms, this booklet explores the appliance of algorithms to such equipment as computerized simplification, polynomial decomposition, and polynomial factorization. This publication comprises complexity research of algorithms and different contemporary advancements. it truly is well-suited for self-study and will be used because the foundation for a graduate direction. retaining the fashion set by means of basic Algorithms, the writer explains mathematical tools as wanted whereas introducing complex tips on how to deal with complicated operations.

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**Extra resources for Computer Algebra and Symbolic Computation: Mathematical Methods **

**Example text**

34) p= 2n+2 3 must also reduce to an integer. 35) where the last expression is obtained by dividing the denominator R1 = 2 into each of the coeﬃcients of 3 p − 2. 35) q = must also reduce to an integer. 36) and the process terminates since the denominator of 2 q is the remainder R2 = 1. 34). 33) x = 5 · 2 + 4 = 3 · 4 + 2 = 14. 32). Notice that there are inﬁnitely many solutions to the remainder equations because each integer q gives a distinct solution. The approach described in the last example gives an algorithm for the solution of two remainder equations.

The Map Operator The Map operator provides another way to apply an operator to all operands of the main operator of an expression. Let u be a mathematical expression with n = Number of operands(u) ≥ 1, and let F (x) and G(x, y, . . , z) be operators. The MPL Map operator has the two forms Map(F, u) and Map(G, u, y, . . , z). The statement Map(F, u) returns a new expression with main operator Kind(u) and operands F (Operand(u, 1)), . . , F (Operand(u, n)). The statement Map(G, u, y, . . , z) returns an expression with main operator Kind(u) and operands G(Operand(u, 1), y, .

The MPL operator Variables(u) selects a set of generalized variables so that the coeﬃcients of all monomials in u are rational numbers. For example, Variables(4x3 + 3x2 sin(x)) → {x, sin(x)}. 8. 9. Many more operators are deﬁned in later chapters. 5. 8. The polynomial operators in Maple, Mathematica, and MuPAD that are most similar to those in MPL. ) 13 14 1. Background Concepts MPL Return(u) Operand list(u) Absolute value(u) |u| Max({n1 , . . , nr }) Algebraic expand(u) Numerator(u) Denominator(u) Derivative(u, x) Maple RETURN(u) [op(u)] abs(u) Mathematica Return[u] Apply[List,u] Abs[u] MuPAD return(u) [op(u)] abs(u) max(n1 , .