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

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]` `rhs(solutions[2]);` terminator `;` or `\$` `;` newline or `;` range `[x,-2,2]` `x=-2..2` `{x,-2,2}` times `*` `*` space or `*` last result `%` `%` `%` assignment `:` `:=` `=` equality `=` `=` `==`

Next: A Lawyer's View of Up: The Playsome Threesome: Maxima, Previous: Fitting, the Lessons
Zdzislaw Meglicki
2001-02-26