(48S) Polynomial tools

03032015, 11:49 PM
(This post was last modified: 03032015 11:51 PM by f16falcona46.)
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(48S) Polynomial tools
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_n1 x^n1 + ... + a_0 Write it as a vector [a+n a_n1 ... 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 xvalue 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 xvalue 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 (xLevel 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... PTOOL.txt (Size: 2.11 KB / Downloads: 22) 

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