Polynome


This HTML page describes the different parameters you can find in the mde - Polynome formula. For further explanations or just suggestions, you may contact me at mdessur@hotmail.com.

I would also mention that English is not my first language. So, I would appreciate comments on how to better this text from that point of view. Thanks.


The formula

This formula is based on

a) the polynomial equation of the third degree we have learnt at high school :

y = a1*x3 + a2*x2 + a3*x + a4

b) a variation of the Moebius transform :

y = a1*x3 + a2*x2
         a3*x + a4

c) a variation of the Newton formula for resolution of polynomial equations :

y = a1*x3 + a2*x2 + a3*x + a4
      3*a1*x2 + 2*a2*x + a3

The formula parameters let you choose between these three equations, their coefficients (a1, a2, a3, a4) and the power of each term. You can also apply functions to some of the terms.

Here are the particular parameters used in this formula and not described elsewhere:
 
Variation This is the parameter you use to select one among the three equations.
Choices True polynome (default), Pseudo Moebius, Pseudo Newton

 
A1, A2, A3, A4 These are the coefficients of the equations above.
Choices You may choose any complex number.
Comments The default is 1 (one) for each of them.

 
Power 1, Power 2, Power 3 These are the powers of the terms of the equations.
Choices You may choose any complex number.
Comments In the equations above, the powers are straight numbers, but you can change them for other numbers with these parameters. To make the match, the default values correspond to these numbers above.
So, the default is 3 (three) for Power 1, 2 (two) for Power 2 and 1 (one) for Power 3.

 
First Function, Second function, Third Function These are function you can use to apply to some of the terms.
Choices You may choose any available function.
Comments The First Function is applied to the term using A1 as coefficient, the Second Function is applied to the term using A2 as coefficient and the Third Function is applied to the term using A3 as coefficient.
So, the default are Ident which means no function applied. 

This formula uses also the Coordinates Parameter Toolbox, the Barnsley Parameters Toolbox, the Odd-Even Parameters Toolbox, the Epsilon Range Parameter Toolbox, the Bailout Parameters Toolbox and the Function Application (new) Toolbox.