[scilab-Users] transforming the polynomial variable

[Samuel Gougeon]

Hi,

Sam Mathew <sam at cctech.co.in> a écrit :

> Given a polynomial function, how can one find another polynomial function
> which is obtained by translating the variable by a constant parameter.
>
> For e.g., if,
> Velocity = 2 + 3*x + 5*x^2,
>
> if the origin is shifted to say, (2,3), in the positive direction, i.e., x
> is to be replaced by x-2; is there a built-in function for finding the
> Velocity function (in polynomial form) in the new coordinate system?

Let
Velocity = poly([2 3 5],"z","coeff")
  Velocity  =
                2
     2 + 3z + 5z

Then :
NewVelocity = horner(Velocity,%z-2)

-->NewVelocity = horner(Velocity,%z-2)
  NewVelocity  =
                  2
     16 - 17z + 5z

// %z is a predefined variable. If you prefer "x", do first
x = poly(0,"x")


> Is it possible to extend it to polynomials in two variables?

Yes, with some work. But it is not yet available in Scilab itself
(maybe in an external module. Likely through Maxima)

> Is it possible to also perform such transformations if a function is of two
> variables x and y, and the coordinate axes undergo different transformations
> (translation, rotation, etc.).

It could be, whether the polynomial could be applied to a
matrix (it can) in a matrix way. But it is not the case :
horner() works on a matrix only in a element-wise way.

Regards
Samuel