Suppose I have a real function which is defined on these intervals [x0,x1],...[x1,xn], and on each interval it's defined differently, for example f(x):=sqrt(x) if x>=0; f(x):=1/x if x<0.

For the last example I tried my last resort to use the assuming operator the following way:

f := ((x -> sqrt(x)) assuming (0 <= x)) or ((x -> 1/x) assuming (x < 0)) plot(f, x)

But it doesn't seem to be working, how do you propose to define this function? perhaps proc?

I tried looking for an example in maple's help, but didn't find any.

Your help is appreciated.

How can factorise a polynomial with complex roots, without showing their numerical values of the roots, but only their symbolical value.

For example I have:

factor(x^4 - x^2 + x - 1)

and it shows me the following factorisation: (x-1)(x^3+x^2+1) but I want to also factorise x^3+x^2+1 but the roots should be displayed symbolically without numerical values of these roots. Then how to implement this task?

In the book I am reading it's stated to use factor(x^4-x^2+x-1, I), but it doesn't seem to be working.

How do I find with maple's help  for which parameter m does the equation:

x^2+2*m*x-6*x=m^3 have one of its roots equal to the square of the other root?

Thanks!

I have the following equations which I want to plot the curves of them by maple's:

1. |x+2|+|y|=3

2. |y|-|x|=2.

How to implement this task in maple?

thanks!

I have some algebraic expression which I want to expand.

I used the ExpandSteps command to show me the steps, but I guess I used it incorrectly.

Attached below the file with the commands.

It should be expanded to -\Delta*\sin^2(\theta), but I want maple to show me the steps.

ExpandSteps.mw
 

Download ExpandSteps.mw