By Jack-Michel Cornil, Philippe Testud, T. Van Effelterre
MAPLE is a working laptop or computer algebra method which, due to an intensive library of subtle capabilities, permits either numerical and formal computations to be played. until eventually lately, such structures have been in basic terms on hand to expert clients with entry to mainframe pcs, however the swift development within the functionality of non-public desktops (speed, reminiscence) now makes them obtainable to the vast majority of clients. the newest types of MAPLE belong to this new iteration of platforms, permitting a becoming viewers of clients to familiarize yourself with machine 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 large on-line aid. even though, those technical manuals supply a mass of data which isn't constantly of serious aid to a newbie in computing device algebra who's searching for a short technique to an issue in his personal speciality: arithmetic, physics, chemistry, and so forth. This publication has been designed in order that a scientist who needs to take advantage of MAPLE can locate the data he calls for quick. it's divided into chapters that are mostly autonomous, every one being dedicated to a separate topic (graphics, differential equations, integration, polynomials, linear algebra, ... ), permitting every one consumer to pay attention to the features he relatively wishes. In every one bankruptcy, intentionally basic examples were given which will totally illustrate the syntax used.
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Extra info for An Introduction to Maple V
1/ COS(X)2 sin(x)2 -+ l-cos(x)2 -+ cos(x)2 cos(2x) + sin(x)2 and similarly for the hyperbolic expressions By default, simplify ( ... ,symbolic) carries out all these transformations . • If one wishes simplify ( ... ,symbolic) to carry out only some among the transformations summarized in the table above, one or several of the options listed in the left column of the table may be used. Only the simplifications from the corresponding lines will then be carried out . • When several simplification options are used, they must be separated by commas, with symbolic appearing last.
It doesn't expand or factor a polynomial on its own initiative. (x-y)(x 2 +xy+y2) x 3 _ y3 • It simplifies () , but not x-y x-y • It doesn't simplify an expression like sin 2 (x) + cos 2 (x). 31 restart; r > sin(x)-2+cos(x)-2; [ sin(x)2 + COS(X)2 MAPLE thus only carries out the bare mllllmum of transformations on its own initiative and the user must explicitly request any simplifications required. To do this, MAPLE provides transformation functions such as expand, factor, normal, simplify, convert, combine, ....
73 restart reinitializes the variables restart: L l Q:=ax2+1 g:=unapply(Q,x); 9 := X -; a x2 +1 Similarly, if P is an expression in the free variables x and y, the evaluation of unapply (p , x, y) returns the function that maps (x, y) onto P. 74 l h:=unapply(R,x,y); h := (x, y) -; x 2 + xy + y2 Conversely, if f is a function in one variable and if g is a function in two variables, then f (x) and g (x, y) are expressions with which one can compute just as with any expression that has been typed in or returned as the result of a computation.