By Jack-Michel Cornil, Philippe Testud, T. Van Effelterre

MAPLE is a working laptop or computer algebra procedure which, due to an intensive library of refined features, permits either numerical and formal computations to be played. till lately, such structures have been merely to be had to expert clients with entry to mainframe pcs, however the fast development within the functionality of private pcs (speed, reminiscence) now makes them available to the vast majority of clients. the most recent types of MAPLE belong to this new iteration of platforms, permitting a transforming into viewers of clients to get to grips with computing device algebra. This paintings doesn't got down to describe the entire probabilities of MAPLE in an exhaustive demeanour; there's already loads of such documentation, together with wide on-line aid. in spite of the fact that, those technical manuals supply a mass of knowledge which isn't constantly of serious support to a newbie in desktop algebra who's searching for a short method to an issue in his personal speciality: arithmetic, physics, chemistry, and so forth. This ebook has been designed in order that a scientist who needs to exploit MAPLE can locate the knowledge he calls for quick. it's divided into chapters that are principally self reliant, each being dedicated to a separate topic (graphics, differential equations, integration, polynomials, linear algebra, ... ), permitting each one person to pay attention to the capabilities he fairly wishes. In every one bankruptcy, intentionally uncomplicated examples were given as a way to absolutely illustrate the syntax used.

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**Additional resources for An Introduction to Maple V**

**Example text**

58 l f:= (x-a)(x-b)(x-e) collect(f ,x); f := X3 + (-a - b - c) x 2 + (a e + a b + be) x - a be If Expr is a polynomial expression in several "unknowns", and if var _1, vaL2, ... vaLp are unknowns or objects of type function, then evaluating collect (Expr, [var _1, var _2, ... 59 > f:=expand«x-a)*(x-b)*(x-c)); [ f := x 3 - x 2 e - x 2 b + x b e - a x 2 + a x e + a b x - abc > collect(f,[a,b]); [ ((x - c) b - x 2 + X c) a + (_x 2 + X c) b + x 3 - x 2 e [> collect(f, [b,a]); (( x - e)a - x 2 + X c) b + ( _x 2 + X c) a + x 3 - x2 e Adding distributed as a third parameter results in grouping together of terms of the same degree with respect to the "unknowns" in the list.

46 [> simplify(") ; r cos (X) 4 5 + 4" simplify«x-6)-(1/3)+sqrt(4)); In the last example, (x 6 )1/3 is not transformed into x 2 since these quantities are not equal for all complex values of x. Using Particular Simplification Rules The rules simplify uses to transform expressions can turn out to be unsuitable in some cases. For example, with trigonometric expressions the function simplify systematically replaces sin(x)2 with 1- cos (x? as indicated in the table page 29. 47 [> simplifyCu); sin(x)2 - COS(X)2 sin(x)2 COS(X)4 - 2COS(X)2 +1 To obtain sin(x)4, which looks simpler than the expression returned in the previous example, one may use simplify while imposing simplification rules other than the ones defined in MAPLE's kernel.

When several simplification options are used, they must be separated by commas, with symbolic appearing last. 30 2. Introduction Example using simplify ( ... ,symbolic) without options. 43 > f:=Cx-a)-b+Cu-2+2*u+1)-(1/2)+8-(1/3); [ f := (Xa)b + J U 2 + 2 U + 1 + 8 1 / 3 l g:=simplifyCf,symbolic); 9 := X(a b) +u +3 One can verify that the expressions of f and g in the previous example are not equal for every value of the variable u. 44 r r u:=-3: 'f'=f; 'g'=g; 9= x(ab) Note: The use of apostrophes in the previous example prevents the evaluation of the left-hand-sides of the equalities, providing more informative output.