Download e-book for kindle: Maple 7 Programming Guide by Monagan M.B., Gedes K.O., Heal K.M.

By Monagan M.B., Gedes K.O., Heal K.M.

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Map( f, p ); f(79 x71 ) + f(56 x63 ) + f(49 x44 ) + f(63 x30 ) + f(57 x24 ) + f(−59 x18 ) Thus, you can map abs directly onto the polynomial. > map( abs, p ); 79 |x|71 + 56 |x|63 + 49 |x|44 + 63 |x|30 + 57 |x|24 + 59 |x|18 Then use coeffs to find the sequence of coefficients of that polynomial. 36 • Chapter 1: Introduction > coeffs( % ); 79, 56, 49, 63, 57, 59 Finally, find the maximum. > max( % ); 79 Hence, you can calculate the height of a polynomial with this oneliner. > p := randpoly(x, degree=50) * randpoly(x, degree=99); p := (77 x48 + 66 x44 + 54 x37 − 5 x20 + 99 x5 − 61 x3 ) (−47 x57 − 91 x33 − 47 x26 − 61 x25 + 41 x18 − 58 x8 ) > max( coeffs( map(abs, expand(p)) ) ); 9214 Exercise 1.

Maple creates the local variables of a procedure each time you call the procedure. Thus, local variables are local to a specific invocation of a procedure. If you have not written many programs you might think that one level evaluation of local variables is a serious limitation, but in fact code which requires further evaluation of local variables is difficult to understand, and is unnecessary. Moreover, because Maple does not attempt further evaluations, it saves many steps, causing procedures to run faster.

By applying the formula repeatedly, the problem eventually reduces to evaluating ex , which is simply ex . The following procedure uses integration by parts to calculate the integral xn ex dx , by calling itself recursively until n = 0. > > > > IntExpMonomial := proc(n::nonnegint, x::name) if n=0 then return exp(x) end if; x^n*exp(x) - n*IntExpMonomial(n-1, x); end proc: IntExpMonomial can calculate > x5 ex dx. 4 Computing with Formulæ • 39 You can simplify this answer by using the collect command to group the terms involving exp(x) together.

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