(48S) Polynomial tools

[f16falcona46]

I like PROOT and its associated programs, but the HP 48S doesn't have them. I wrote some replacements, except I just realized there's an assembly version of PROOT that also works with the 48S. Darn.

But here they are, in all their unoptimized...er...glory?

Given a polynomial a_n x^n + a_n-1 x^n-1 + ... + a_0
Write it as a vector [a+n a_n-1 ... a_0], inserting zeroes where the coefficient of that power is zero. This is what I have called a "polynomial vector", although I'm not sure if there's a better term.

PVAL: Evaluates a polynomial specified by the vector in level 2 at the x-value in level 1.
PCOF: Generates a vector describing a polynomial with the roots given in a vector in level 1. This polynomial will always have leading coefficient 1.
TOL: Describes the difference that the result can be from the true root, or the difference that the polynomial's x-value can be from zero. Whichever one it is is not assured. This value must be positive, and values can be stored in it.
LAGUERRE: Executes Laguerre's method on the polynomial given in the vector on level 1, replacing it with a solution vector. Complex solutions can also be found.
SYNTHDIV: Executes synthetic division on the polynomial vector in level 2 by the factor (x-Level 1). The last number in the solution vector is the remainder.
DERIV: Returns a polynomial vector which is the derivative of the polynomial vector in level 1.
QD: Uses the quadratic formula to find the solutions of the quadratic polynomial vector in level 1.
RDCE: Same as SYNTHDIV, but throws the remainder away, since it is assumed to be 0.
NRMLZE: Divides a polynomial vector by its leading coefficient.
FROOT: Given a solution vector in level 2, and a polynomial vector in level 1, will append all solutions of the polynomial to the solution vector.
JOINVEC: Used by FROOT to join two vectors together.


(not sure if I'm posting in the right place)

I might get around to making these faster if I have time from schoolwork, but I don't think I will write these in System RPL, since I want these to be immediately portable between the various RPL calculators.

EDIT: Just realized "DERIV" means people using HP49 will have to modify this. Sorry...


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