Is there a way to send Command to Mathematica, or Maple, or Maxima?

[eEniquEe]

Hi,

I'm currently on a Mathematical Project from my University. The project is about using Newton's method to estimate solution to a system of equations, which involves taking the determinant of a matrix, and the first partial derivative of a multi-variable, and evaluate it at a specific point. >.<

I think this can be programmed in AutoIT. However, finding the derivatives, and the determinant may be very time-consuming. So I'm thinking about making use of other mathematical programmes, say Mathematica, Maple, or Maxima (this one is free). Those programmes can calculate complicated mathematical expressions in, like a blink. So, my idea is to send the command to one of these programmes to tell it to do the work for me, then send the result to my programme.

I don't know if anyone here's familiar with those programmes? Is it possible to do what I want? If it isn't possible, is there any other way of doing that? I have searched for Mathematica, derivative in the forum, but I haven't found what I'm looking for.

Thanks guys a lot,

And, have a good day,

[eEniquEe]

It has been a day past... Can anyone help me with this?

Or can anyone suggest me some other way of doing this? I'm just so stuck...