(*^
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Advanced Topic: Symbolic Computation
:[font = text; inactive; preserveAspect]
Perform symbolic computations:
Generate permutations of list {a,b,c}:
:[font = input; preserveAspect]
Permutations[{a,b,c}]
:[font = text; inactive; preserveAspect]
Transform list to simple flat list:
:[font = input; preserveAspect]
Flatten[%]
:[font = text; inactive; preserveAspect]
Find positions of element b in above list:
:[font = input; preserveAspect]
Position[%,b]
:[font = text; inactive; preserveAspect]
Calculate {1, 1 ¥ a, 1 ¥ a ¥ b, ...} given above list as {a,b,c,...}:
;[s]
7:0,0;16,1;17,0;23,1;24,0;27,1;28,0;70,-1;
2:4,13,9,Times,0,12,0,0,0;3,18,13,Symbol,0,12,0,0,0;
:[font = input; preserveAspect]
FoldList[Times, {1}, %]
:[font = text; inactive; preserveAspect]
Give and plot list of the results of applying cos to x, 0 through 3 times:
:[font = input; preserveAspect]
NestList[ Cos, x, 3]
:[font = input; preserveAspect]
Plot[ Evaluate[%], {x,0,1}]
:[font = text; inactive; preserveAspect]
Apply the map f(n)=n2 to each element on the first level in {a,b,c,d}:
;[s]
3:0,0;20,1;21,0;71,-1;
2:2,13,9,Times,0,12,0,0,0;1,21,13,Times,32,12,0,0,0;
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Map[f, {a,b,c,d}]
:[font = text; inactive; preserveAspect]
Apply the map f(x)=1+x2 to each element on the first level in {a,b,c,d}:
;[s]
3:0,0;22,1;23,0;73,-1;
2:2,13,9,Times,0,12,0,0,0;1,21,13,Times,32,12,0,0,0;
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Map[ Function[x, 1 + x^2], {a, b, c, d} ]
:[font = text; inactive; preserveAspect]
Define function f(n) and enerate a list of all expressions which match form f(k) used in the evaluation of f(4):
:[font = input; preserveAspect]
f[0] = f[1] = 1; f[n_] := f[n-1] + f[n-2]
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Trace[ f[4], f[_] ]
^*)