Hi all,

I am after some advice on how to extract a value from a proc.

February 18 2010
hlee08 8
f := (k-1)^(p-1)/k; p := 1.99; maximize(f, k = 2 .. infinity, location);
this is the problem... and it's working fine... but.. how do i make k take on only integer values?

I have only found rand() which gives me integer values and I need to generate (a lot of) random rational numbers.

The boundary (0,2) doesn't really matter but I do need the numbers to at least go up to 2. Else any rational will do.

Thankyou.

Situation: I have multiple lists of the form [i$i=1..n,0$k] , where n is a positive integer and k is a nonegative integer.

Desired result: For each list, produce a list of permutations of the list (as you would receive from combinat[permute]) such that in each permutation, the nonnegative integers in the list appear in ascending order from left to right and no two nonnegative integers are adjacent to one another.

Here is a simple sequcnce of commands that execute without a problem:

restart;

eq1 := 5+3*x=0:

eq2 := 2+7*x-3*y-5*x*y=0:

x:=solve(eq1,x):

y:=solve(eq2,y):

lprint('x'=x,'y'=y);

x = -5/3, y = 29/16

If I put the commands into a procedure there are problems:

I'm plotting some random points along a curve but I'm not sure of a couple of things so I have a few questions.

Using a simple curve like x for example. First I'll choose some random numbers, 100, between -8 and 8, but I also want a couple of decimal points otherwise random integer values will only give me a maximum of 17 points. So is the best way to do that like this?

with(plots):

a:=[seq((rand(-800..800)(i))/100,i=1..100] # These will be my x point values;

A MaplePrimes member recently asked me how to sort two sets, using the permutation of one to sort the other. For example, given the list

L1 := [3+I, I, 2, -1, 5, 4]:

sort it according to its magnitude and then permute the second list

L2 := [a, b, c, d, e, f]:

in the same manner.

Greetings all
restart;
f := x->x^4:
assume(n::integer):
an := 1/Pi*int(f(x)*cos(n*x),x=-Pi..Pi):
FaN1 := sum(an*cos(n*x),n=1..N);
FaN2 := Sum(an*cos(n*x),n=1..N);
On Maple 13, FaN1 and FaN2 are very different representations of this series. However, on Maple 11 they are the same (same as FN2 on Maple 13).
How can I persuade Maple 13 to convert FaN2 to FaN1 ?
Also, how can I persuade Maple 11 to convert aFN1 to FaN2 ?

So it appears that using subscripts in Maple is not a good idea.
I ran into this problem for the first time yesterday, and is documented here:
http://www.mapleprimes.com/forum/drivenharmonicoscillatoramplitudephaseangle#comment-32780
And now it seems I've run into it again. Or possibly I have made a mistake ;)
This is part of an implementation of Newton-Cotes method of numerical integration:
restart:
NCcoef := proc(N::integer)
# procedure returns the Newton-Cotes coefficients for an
# appoximation with N+1 points
local a,c,p,h,B,LH,RH,eq,seqeq,seqco:
h := B/N:

The first question: Is it possible in a procedure to combine datatypes ie

zz:=proc( X:: Matrix(datatype = [integer[2], float[8], float[8] ] ))

The second question : If we assume that q is a floating number is convert( q, rational) the

best way to convert a float to a integer ?

My goal: given G(z,w), find the polynomial, P(n), in the partial derivatives of G(z,w) over the integer such that

d^n z/ dw^n = P(n) / Gz^(2n-1) where Gz= partial derivative of G with respect to z.

Step 1. Differentiate G(z(w),w) w.r.t w n times. Formulae are known for doing that (Mishkov, Tsoy-Wo Ma),

test := proc(x::integer, {y::posint:=1}, {z::posint:=1}, $)
printf("%a\n", 'procname'(args));
if x > 100 then
procname(x-y-z-1, 'y'=10); # not working (nor ''y'', uneval(y), evaln(y) etc.)
elif x < 100 then
procname(x-1, args[2..nargs]); # working
else
NULL;
fi;
end:
test(1000);
Error, (in test) invalid input: too many and/or wrong type of arguments passed to test; first unused argument is 1 = 1

Is there a method to work with Reals or Complex modulo Integers (need not

to be modulo a discrete group, circle or torus is fine for me)?

Where the residue class is represented in the unit interval or square (as

the command modp does in the finite case)?

What I have in mind is to modify 'argument' to 'argument modulo 2*Pi', but

mod is for integer cases.

I've created a Maple help page, saved in a small hdb file, that describes the hierarchy of Maple's numerical types. Insert it into the path assigned to ?libname. Access the help page with ?numer-hier. To make it compact, I took some liberties with the notation. Here is what it looks like

In the blog MRB Constant-D I noticed a peculiar outcome to several sets of equations involving f(n) = sin((a+b*floor(n))*Pi/M), where M is a constant to be explored, b is a number to be found and a is a "starting value" that causes f(n) ~= -1, 0 or 1.