## Solving an equation - the age old newbie problem...

Hi all

I have spend too much time trying to figure out why Maple won't solve this equation explicitly. Here is the code:

assume(0 <= s, 0 <= w, 0 <= t, 0 <= h):

diff(((w-s)^(1-t)-1)/(1-t)+(((1+r)*s)^(1-t)-1)/((1+h)*(1-t)), s);

solve(%, s)

It returns:

-(w-s)^(1-t)/(w-s)+1/(1+h)*((1+r)*s)^(1-t)/s

RootOf((w-_Z)^(1-t)*_Z+(w-_Z)^(1-t)*_Z*h-((1+r)*_Z)^(1-t)*w+((1+r)*_Z)^(1-t)*_Z)

## Difference between ratpoly and taylor...

Cheers!

Here is what I have done in Maple 11:

st:=taylor(sin(x),x=0,10):

sint:=convert(st,polynom)

sinr:=convert(taylor(sin(x),x=0,10,ratpoly))

plot([sin(x),sint,sinr],x=-6..6,-2..2,color=[red,navy,gold])

My question is how theoraticly do you convert a series into a rational polynom?

Mario

## Greatest common divisor...

I'm trying to find the greatest common divisor of two functions with characteristic=7:

with(Algebraic):
GreatestCommonDivisor(x^4+x^3+4*x^2+4*x+5,x^3+x^2+5*x+5,'characteristic'=7);

This gives the answer as (x+4) which is a common divisor but it is not the greatest. From working by hand, I've found that (3x+5) is the gcd.

Why is maple giving the wrong answer?

## Newton Rhapson - this one...

I decided to repost this as the previous one went crazy.......

I'm trying to construct an iterative procedure NR1(f,x0,N) where f is a function, x0 is an initial estimate (which can be complex) and N the number of iterates.

Given:  xk+1=xk - f(xk)/f'(xk), k=0,1,2....,

Now for example by defining f:= x-> x^2-2 and inputting x0=1 and N=10 i should be able to check that my procedure calculates sqrt(2) correctly.

This is what i've got so far.....

## [Problem] Java Virtual Machine Launcher...

hi, i am new to this and when i start up maple 11 i get the following error : "Java Virtual Machine Launcher,  Could not create the java virtual machine"

i hope there is a solution to this because i have searched everywhere and i cant get the solution.

thanks

## Newton-Rhapson procedure...

I'm trying to construct an iterative procedure NR1(f,x0,N) where f is a function, x0 is an initial estimate (which can be complex) and N the number of iterates.

Given:  xk+1=xk - f(xk)/f'(xk), k=0,1,2....,

Now for example by defining f:= x-> x^2-2 and inputting x0=1 and N=10 i should be able to check that my procedure calculates sqrt(2) correctly.

This is what i've got so far.....

## Matrices...

Hi i'm trying to figure out how to write a procedure for creating a NxN matrix with conditions. The conditions for M[ij] are as follows:

a if j>i+1, c if i>j+1 and b otherwise.

So far this is what i've come up with but i've tied myself into a mental loop and cant seem to figure this out. I know it's really simple and that's what is frustrating me the most.

## analytical solution with Maple...

I am trying to solve the following equation with maple

g:=t->(-l*a^2*t+l*a^2*r^(-1/(a-1))*(A*l)^(-1/a)*(1-t)^(-1/a)*exp(1/(a-1))*t-l*a^2*r^(-1/(a-1))*(A*l)^(-1/a)*(1-t)^(-1/a)*exp(1/(a-1))+l*a^2-l*a-2*l*a*r^(-1/(a-1))*(A*l)^(-1/a)*(1-t)^(-1/a)*exp(1/(a-1))*t+2*l*a*r^(-1/(a-1))*(A*l)^(-1/a)*(1-t)^(-1/a)*exp(1/(a-1))+l*t*a-a*r^(-1/(a-1))*(A*l)^(-1/a)*(1-t)^(-1/a)*exp(1/(a-1))+l*t*r^(-1/(a-1))*(A*l)^(-1/a)*(1-t)^(-1/a)*exp(1/(a-1))-l*r^(-1/(a-1))*(A*l)^(-1/a)*(1-t)^(-1/a)*exp(1/(a-1))+r^(-1/(a-1))*(A*l)^(-1/a)*(1-t)^(-1/a)*exp(1/(a-1)))*exp(-1/(a-1))/(t-1)/a;

## Derivative Help...

How do I find the derivative dy/dx of:

x+ y= 3xy

I think I use the Sum Rule for the LHS and the Product Rule for the RHS.  Where I am confused is how to treat the y on the LHS.  Do you change it to 3y and then solve the whole thing for y?, or do you keep dy/dx*y and then solve the whole thing for dy/dx?

Any thoughts?

## Coprimes...

How does one create the set of all positive integers less than and coprime to 66?

I created a set of integers from 1-66: L := {seq(i, i = 1 .. 66)}, then try define coprime66 as follws, coprime66 := isprime(igcd(L, 66)),  to get a set of the coprimes but i get an error.

I've tried op(L) but this doesn't work either. What am i doing wrong?

Does anybody know of a way to change the direction of an axis label in a plot without going back to the code and re-plotting? In the file I am working with that code has been deleted. It is possible to change the wording, font etc. of the labels, but I cannot find a way to change their directions. This becomes very annoying when I have a long label title on the y-axis, as my plot gets scrunched. Any help would be greatly appreciated. Thanks. -Evan

## Generating Function from List...

Greetings. Using the sequence command, I can generate a list of numbers.

>seq(1/(n^2+1), n=1..10);

1/2, 1/5, 1/10, 1/17, 1/26, 1/37, 1/50, 1/65, 1/82, 1/101

Given the list of numbers above, how does one derive

1/(n^2+1)

This is a specific example.  I am looking for a general case.  I scanned the genfunc and gfun packages, but I must be missing something.

Regards,

Georgios Kokovidis

## Calling external C code on Max OS X (XCode)...

Has anyone ever written procedures in C that can be called from Maple on MAC OS X? I have looked at the WRAPPER help page and given it a go but I am completely lost. I have compiled the example C code from the WRAPPER page with XCode as a "shared library" but when I try to define it in maple I get the following error: