What's wrong with using R?

Alec

`&/`:=(a,b)->b(a):

int(sin(x),x=0..Pi)&/evalf;

                                  2.

int(sin(x),x=0..Pi/4)&/evalf[20];

                        0.29289321881345247560

123456789 &/ifactor;
                            2
                         (3)   (3803)  (3607)

In general, the parentheses may be necessary (because one can't set priorities of new operators in Maple)

(x^4+4)&/factor;
                      2              2
                    (x  - 2 x + 2) (x  + 2 x + 2)

((x+1)^2) &/expand;
                              2
                             x  + 2 x + 1

Alec

For example,

Student:-Calculus1:-RiemannSum(sin(x),x=0..Pi/4,
output=sum,method=right);
                              / 10            \
                              |-----          |
                              | \        i Pi |
                      1/40 Pi |  )   sin(----)|
                              | /         40  |
                              |-----          |
                              \i = 1          /

evalf(%);

                             0.3205106625

int(sin(x),x=0..Pi/4.);

                             0.2928932188

Alec

Why not? End your expression with : evalf(%);

For example,

sin(2)+sin(3): evalf(%);

                             1.050417435

Alec

Click right button on the launch.ini in Windows explorer, select Properties, then Security. Click Edit and add write permissions for yourself.

Alec

1.  Type the equation in the worksheet, using / for over and right arrow to return back from it.
2. With mouse pointer over the equation, click the right mouse button and select Manipulate Equation

Then, in the first case, do "Group terms on the left side", then "Clear denominators", then "Add 85 to equation", then "Multiply equation by 1/96".

In the second case, "Clear denominators" and "Multiply equation by -1"

Alec

What do you mean by base 5?

Alec

Here is the implementation of the wikipedia's Method 1,

fBm:=proc(H,t)
local X,G,s,v,n;
uses Statistics, LinearAlgebra;
n:=Count(t);
X:=RandomVariable(Normal(0,1));
G:=Matrix(n,(i,j)->(t[i]^(2*H)+t[j]^(2*H)-abs(t[i]-t[j])^(2*H))/2);
s:=LUDecomposition(G,method=Cholesky);
v:=Sample(X,n);
s.v^%T
end;

t here is a list or a Vector of t₁, t₂, ..., t_n. For example,

t:=[$1..100]:
S:=fBm(0.75,t);

                       [ 100 Element Column Vector ]
                  S := [ Data Type: float[8]       ]
                       [ Storage: rectangular      ]
                       [ Order: Fortran_order      ]

plot(t,S);

Alec

It works for any H from 0 to 1.

The correlation matrix is always positive (semi)-definite, even if some of its elements are negative.

Alec

Wikipedia article has 2 methods of fBm simulation (at the end.) The first one can be easily programmed in Maple. Did you try it?

Alec

Try that with y*x instead of yx.

Alec

I almost suggested to read the help page ?plot,details , but then read it myself and found it rather confusing. Also, with a typo - plot([expr1, expr2, t=c..d) at the beginning of the Using the Parametric Form section, should contain ]  close to the end, plot([expr1, expr2, t=c..d]). Not surprising that people have problems understanding that.

Alec

Set infolevel to something like

infolevel[all]:=10;

If that is not enough, printlevel also can be increased,

printlevel:=100;

or

printlevel:=1000;

Alec

Here is an example of a procedure creating a midi (type 0) file from a list of integers from 0 to 7,

midi0:=proc(f,L)
local m,n,c;
n:=nops(L);
c:=[60, 62, 64, 65, 67, 69, 71, 72];
m:=[77, 84, 104, 100, 0, 0, 0, 6, 0, 0, 0, 1, 0, 128, 77, 84, 114, 107, 
ListTools:-Reverse(convert(2^32+7*n+5,base,256))[2..-1][], 
0, 144, c[L[1]+1], 96,
seq([129,0,c[L[i]+1],0,0,c[L[i+1]+1],96][],i=1..n-1),
129,0,c[L[-1]+1],0,0,255,47,0];
writebytes(f,m);
close(f)
end;

It works as midi0("filename.mid",listname). For example,

L := [3,2,1,2,3,3,3,2,2,2,3,5,5];

midi0("mymidi.mid",L);

Alec

PS See also my blog entry with slightly modified procedure, allowing to change the instrument from the default (piano), to a guitar, a violin, etc. -Alec

The simplest way, probably, is to write a midi file in binary. Maple can be used for that.

The Skytopia crash course (written by Daniel White) rather clearly explains how the resulting midi file should look.

Alec