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Maxima, Maple, and Mathematica: the Summary

Before going any further, let us summarise in Table 2.1 what we have glimpsed of Maxima, Maple, and Mathematica so far.

Table 2.1: Comparison between some Maxima, Maple, and Mathematica commands
  Maxima Maple Mathematica
limit limit(x-7,x,3); limit(x-7,x=3); Limit[x-7,x->3]
expand expand((a+b)^3); expand((a+b)^3); Expand[(a+b)^3]
factor factor(%); ezgcd(num, denom); factor(%); normal(%); Factor[%]
solve solve(a*x^2=4,x); solve(a*x^2=4,x); Solve[a x^2==4,x]
3D plots plot3d(sin(x*y),[x,-2,2],[y,-1,1]); plot3d(sin(x*y),x=-2..2,y=-1..1); Plot3D[Sin[x y],{x,-2,2},{y,-1,1}]
    display set_plot_option([plot_format,gnuplot]); plotsetup(x11); Display["math.eps", %, "EPS"]
    environment plot_options; plotsetup(); $DisplayFunction
integral integrate(x^2*sin(alpha*x),x,0,beta); int(x^2*sin(alpha*x),x=0..beta); Integrate[x^2 Sin[alpha x],{x,0,beta}]
integer factor   ifactor(%); FactorInteger(%)
square root sqrt(3); sqrt(3); Sqrt[3]
numerical ev(%,numer); evalf(%); N[%,10]
substitution ev(%,x=1,y=2); or at(%,[x=1,y=2]); eval(%,[x=1,y=2]); ReplaceAll[%,{x->1,y->2}]
sum sum((1+i)/(1+i^4),i,1,10); sum((1+i)/(1+i^4),i=1..10); Sum[(1+i)/(1+i^4),{i,1,10}]
    delayed 'sum((1+i)/(1+i^4),i,1,10); Sum((1+i)/(1+i^4),i=1..10); use :=
product product((i^2+3*i-11)/(i+3),i,0,10); product((i^2+3*i-11)/(i+3),i=0..10); Product[(i^2+3*i-11)/(i+3),{i,0,10}]
    delayed 'product((i^2+3*i-11)/(i+3),i,0,10); Product((i^2+3*i-11)/(i+3),i=0..10); use :=
infinity INF infinity Infinity
complex %I I I
  rectform(%); convert(%,rect);  
  polarform(%); convert(%,polar);  
  realpart(%); Re(%); Re[%]
  imagpart(%); Im(%); Im[%]
  abs(%); abs(%); Abs[%]
  carg(%); argument(%); Arg[%]
trigonometry trigsimp(%); trigrat(%); simplify(%); Simplify[%], TrigSimp[%], TrigReduce[%]
  trigexpand(%);   TrigExpand[%]
    other trigrat(%);   TrigFactor[%]
functions f(x):=x^2+1/2; or define(f(x),x^2+1/2); f:=x->x^2+1/2; or f:=unapply(x^2+1/2,x); f[x_]=x^2+1/2 or f=Function[x,x^2+1/2]
derivatives diff(f(x),x,2); diff(f(x),x&2); D[f[x],{x,2}]
    delayed 'diff(f(x),x,2); Diff(f(x),x&2); use :=
arrays array([x, y], 300); x := array(1..300); Array[x, 300]
split expression pickapart(%, 4); addressof(%); FullForm[%];
    disassemble(%); [[3]]
    pointto(a[2]); ReplacePart[Out[32], Expand[Out[54]], 1]
terminator ; or $ ; newline or ;
range [x,-2,2] x=-2..2 {x,-2,2}
times * * space or *
last result % % %
assignment : := =
equality = = ==

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Next: A Lawyer's View of Up: The Playsome Threesome: Maxima, Previous: Fitting, the Lessons
Zdzislaw Meglicki