#----------------------------------------------------------------------
# Program to explore polynomials
#
# Copyright (C) April 23, 2018 -- Dr. William T. Verts
#
# A polynomial is a list of coefficients
# 4x^3 -3x^2 + 2x -5  would be stored as [-5, 2, -3, 4]
# The position of the coefficient is the power of x
#
# How do you handle cases where the result has extra zeroes in the
# high-order coefficients?  Such as [4,-2,4,6,1,0,0,0], which
# should be "normalized" to [4,-2,4,6,1].  How might you handle
# cases where the result is a float but a whole number such as 4.0?
# Do you change that to an int or leave it as a float?  Finally,
# how do you print out a polynomial so it LOOKS like a polynomial?
#----------------------------------------------------------------------

def addPoly(P0,P1,P2=[],P3=[]):       # P0,P1,P2,P3 are polynomials, returns a polynomial
    Answer = [0] * max(len(P0), len(P1), len(P2), len(P3))
    for I in range(len(P0)): Answer[I] = Answer[I] + P0[I]
    for I in range(len(P1)): Answer[I] = Answer[I] + P1[I]            
    for I in range(len(P2)): Answer[I] = Answer[I] + P2[I]            
    for I in range(len(P3)): Answer[I] = Answer[I] + P3[I]            
    return Answer
    
def subtractPoly(P0,P1,P2=[],P3=[]):  # P0,P1,P2,P3 are polynomials, returns a polynomial
    Answer = [0] * max(len(P0), len(P1), len(P2), len(P3))
    for I in range(len(P0)): Answer[I] = Answer[I] + P0[I]
    for I in range(len(P1)): Answer[I] = Answer[I] - P1[I]            
    for I in range(len(P2)): Answer[I] = Answer[I] - P2[I]            
    for I in range(len(P3)): Answer[I] = Answer[I] - P3[I]            
    return Answer
    
def multiplyPoly(P0,P1):              # P0 and P1 are polynomials, returns a polynomial
    Length = len(P0) + len(P1)
    Answer = [0] * Length
    for I in range(len(P0)):
        for J in range(len(P1)):
            Answer[I+J] = Answer[I+J] + P0[I] * P1[J]            
    return Answer
    
def dividePoly(P0,P1):                # P0 and P1 are polynomials, returns a polynomial
    # Division is ugly
    return
    
def integratePoly(P,C=0):             # P is a polynomial, returns a polynomial
    # But calculus isn't too bad!
    return
    
def differentiatePoly(P):             # P is a polynomial, returns a polynomial
    # But calculus isn't too bad!
    return