how to convert a function to transition matrix?

how to convert a differential system to transition matrix?

Hi everybody and thank you all in advanced.

I tried this:

1. convert([a,b],`*`) # this worked
2. convert([a,b],`/`) # this gives an error
3. map(`/`,a,b) # this worked

Questions:

1. How can I make code for point (2) work? Apparently `/` is not an option for convert.
2. I was looking for a function that divide two symbols, something like divide(a,b) and outputs a/b for some simple
3. programing purposes but find no one. (a,b) could be numbers, could be trig functions or polynomials.
   
   Of course, you can just input a/b or lis[i]/lis[i+n], but a knowledgeable answer to this will cast light over Maple’s ways and my wrong ways.

Let be the sequence (an) so that a1 = 1, a(n+1) = 5*a(n) + sqrt(k*a(n)^2 -8), for all n >=1. I know that, the answer is k = 24.  How can I choice number k so that the sequence is an integer sequence?

I am trying to export the data list to .dat but i received that error. New with coding and Maple.

restart;
a := sin(x^(1/3))+sin(x)^(1/3);
                      / (1/3)\         (1/3)
                   sin\x     / + sin(x)     
b := diff(a, x);
                     / (1/3)\                
                  cos\x     /      cos(x)    
                  ----------- + -------------
                      (2/3)             (2/3)
                   3 x          3 sin(x)     
output := fopen("Ospino.dat", WRITE);
for x by .5 to 50 do fprintf(output, "%f\t %f\t \n", x, b) end do;
Error, (in fprintf) number expected for floating point format
fclose(output);
 

add(q[k],k=1..5)

I'd like to be able to display a general result such as

q_1 + q_2 + ... + q_n

ideally maple would do all the special stuff for me, e.g., somehow I could do

add(q[k],k=1..2..n)

but I can't even seem to get a nice output manually that doesn't involve a lot of printing code.

Hi

Can maple compute the following integral

Integral ( z^(-0.5), z in M) where  M is the lower half-unit circle from +1 to -1

Many thanks

How I can apply the condition or assuming (a>0) in ?

I want to have a plot according to the attached figure.

Download plot 

Normally the wheel mouse will scroll a file like it does in just about every other program... but when the mouse is over a code edit region it does nothing ;/ As one is scrolling with the wheel and a code edit region pops up this breaks the flow and requires hoops, I don't like hoops!

Seems most mouse funcitons do not work well in the region. Just trying to select and drag doesn't scroll the region.

I was writing in a maple document when suddently all the text and equations collapsed into a single line at the top, making it unreadable and unusuable. I was not able to restore a previous backup of the file, however i did manage to salvage a smaller part of the document. Both files are included. 
corrupted.mw 
what_i_managed_to_save.mw

ModularSquareRoot can't handle a really big n because of the factorization problem. But I would like to know if there is any other function than can use as parameters the factorization of n.

I already have an algorithm that does that for n=pq with p, q primers, and could generalize it, but I was wondering whether there was a built-in function that does that.

The Folium of Descartes (see the wikipedia page about this curve) is an algebraic curve defined by the equation 𝑥 ^3 + 𝑦 ^3 − 3𝑎𝑥𝑦 = 0, where 𝑎 is a constant. You will need the information on this wikipedia page in order to plot the following graphs. plot them for 𝑎 = 1,  Graph the curve with 𝑎 = 1 using the command implicitplot in the range of −3 ≤ 𝑥 ≤ 3 and −3 ≤ 𝑦 ≤ 3. (which i have already done)

However i am unable to Add a plot of the line 𝑥 + 𝑦 + 𝑎 = 0 on the same graph but dashed and with a different color (set numpoints as 10000).

Does global optimization toolbox has randomization option it gives same value every time

In addition to defining a function in a standard way, a fast and convenient way to turn a formula (an expression) into a function is to use unapply command (check Maple help center for this command). The following items are about defining functions. 

1. Define a function midpoint, which returns the average of two arguments given on input. For example, midpoint(2,3) returns 2.5, midpoint(a,b) returns 𝑎+𝑏2. 
2. b) For two positive natural numbers 𝑎 and 𝑏 we can define the least common multiple lcm(𝑎,𝑏) via their greatest common divisor gcd (𝑎,𝑏), i.e.: lcm(𝑎,𝑏) = 𝑎𝑏gcd (𝑎,𝑏). When 𝑎 and/or 𝑏 are zero, lcm(𝑎; 𝑏)=0. Use the arrow operator and piecewise to define the function my_lcm which returns the least common multiple of two natural numbers. 
3. c) The quadratic formula allows to write the roots of 𝑝 = 𝑎𝑥2+𝑏𝑥+𝑐 explicitly in terms of 𝑎,𝑏, and 𝑐. 

 Define a piecewise function of 𝑥 so that the value of the function is 0, if 𝑥<−(𝑟1+ 𝑟2+𝑟3) or 𝑥>𝑟1+ 𝑟2+𝑟3, and it is equal to the area of confined region if −(𝑟1+ 𝑟2+𝑟3)<𝑥<𝑟1+ 𝑟2+𝑟3. 

a) Given real values 𝑟1,𝑟2,𝑟3>0, consider the curve of the positive part of the circle with radius 𝑟1+ 𝑟2+𝑟3 and center at the origin and three semi-circles below with radii 𝑟1,𝑟2,𝑟3 so that they are arranged from left to right like the following graph. Define proper functions and plot this graph in Maple for 𝑟1=10,𝑟2=2,𝑟3=8.