Polynomial objets
How to enter a poly ?
you have two possibilities :
- by using the ' delimitor
entering '1 3 7' means : polynomial 1 + 3*X + 7*X2
- as a list, with convertion
Entering {1 3 7} and use the function {}->poly to convert your list into a poly
in every case you don't have to enter the X, you just need to enter factors.
Please note that polynomial are entered and displayed with lowest power first.
Basic Operations
Allowed operations are :
- + (and -) to add two poly, or a poly with a number..
ex : '1 1' '0 2' + gives '1 3'
- * to multiply two poly
ex :
'1 1' '0 2' * gives '2 1 2'
- / to divide two poly.
ex : '1 0 2 1' '1 1' / gives : [ '-1 1 1' '2'], please see how the result is given : into a vector, second item is the rest.
Valuation
the function PEVAl valuate a poly with a value taken from the stack.
example : '1 0 1' 4 PEVAL returns 17
this is because P(x)=1 + x2. P(4)=1+42=1+16=17.
Complex
you can works with complex in you polynomials.
exemple : '(1;1) 0 (0;1)' is the poly P(z)=1+i+i*X2.
And, obviouly, you can valuate it also with complex numbers... P(1+i)=-1+i.
Finding Roots
use the Roots function to find roots of a poly.
example '-1.6 5.9 -6 0.7 1' Roots returns { -3.2 1 0.5 1 } witch are the roots.
Roots are always given in a list.
The list may be empty if :
There are no root (ex : poly P(x)=1+x2)
roots are too hard to find (*)
(*) RPNEnh may not return all roots, serveral numerical methods are used together to find roots, I didn't notify any problem, if RPNEnh forgot to give you a root that you know, please inform me.
Methods used : Slope analysis, Sign changes analysis, home-made methods...
Polynomial drawing
You can draw a poly with function PolyDraw, a new screen will appears.
In this screen, you can move (use arrow keys) and zoom (use +/- keys)
Other functions
You can build a poly from these roots, use the function Roots->poly.
roots must be in a list.