utopia [1]% maple |\^/| Maple V Release 2 (University of Victoria) ._|\| |/|_. Copyright (c) 1981-1992 by the University of Waterloo. \ MAPLE / All rights reserved. MAPLE is a registered trademark of <____ ____> Waterloo Maple Software. | Type ? for help. % Maple computes with arbitrarily large numbers > 2^1000; 107150860718626732094842504906000181056140481170553360744375038837035105112493\ 612249319837881569585812759467291755314682518714528569231404359845775746985748\ 039345677748242309854210746050623711418779541821530464749835819412673987675591\ 65543946077062914571196477686542167660429831652624386837205668069376 > n := 10; n := 10 > sum( k, k=1..n ); 55 > sum( k, k=1..m ); 2 1/2 (m + 1) - 1/2 m - 1/2 > expand("); 2 1/2 m + 1/2 m > simplify("); 2 1/2 m + 1/2 m % A sample procedure; remember means memoize > T := proc(n) > option remember; > if n = 0 then 1 else 2*T(n-1)+1 fi; > end: > > T(10); 2047 > rsolve( f(m) = 2*f(m-1)+1, f ); m m f(0) 2 + 2 - 1 > rsolve( {f(0)=0, f(m) = 2*f(m-1)+1}, f ); m 2 - 1 > rsolve( {L(0)=1, L(m) = L(m-1)+m}, L ); (m + 1) (1/2 m + 1) - m > simplify("); 2 1/2 m + 1/2 m + 1 utopia [1]% /package/maple/bin/maple |\^/| Maple V Release 2 (University of Victoria) ._|\| |/|_. Copyright (c) 1981-1992 by the University of Waterloo. \ MAPLE / All rights reserved. MAPLE is a registered trademark of <____ ____> Waterloo Maple Software. | Type ? for help. > plotsetup(postscript); Warning, plotoutput set to postscript.out by default > with(plots); [animate, animate3d, conformal, contourplot, cylinderplot, densityplot, display, display3d, fieldplot, fieldplot3d, gradplot, gradplot3d, implicitplot, implicitplot3d, loglogplot, logplot, matrixplot, odeplot, pointplot, polarplot, polygonplot, polygonplot3d, polyhedraplot, replot, setoptions, setoptions3d, spacecurve, sparsematrixplot, sphereplot, surfdata, textplot, textplot3d, tubeplot] > tubeplot({[10*cos(t),10*sin(t),0,t=0..2*Pi, > radius=2+cos(7*t),numpoints=120,tubepoints=24], > [0,10+5*cos(t),5*sin(t),t=0..2*Pi, > radius=1.5,numpoints=50,tubepoints=18]}, scaling=CONSTRAINED); bytes used=1116652, alloc=917336, time=1.40 bytes used=2196984, alloc=1638100, time=2.63