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.
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.