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# It contains rountines used to create and manipulate ##
# polynomials for WeBWorK ##
# ##
# Copyright 2002 Mark Schmitt ##
# Version 1.1.2 ##
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# In the current version, there is no attempt to verify that correct arrays are being passed to the routines.
# This ought to be changed in the next incarnation.
# It is assumed that arrays passed to the routines have no leading zeros, and represent the coefficients of
# a polynomial written in standard form using place-holding zeros.
# This means $array[0] is the leading coefficient of the polynomial and $array[$#array] is the constant term.
#
# The routines were written based on the needs of my Honors Algebra 2 course. The following algorithms have been
# coded:
# Polynomial Multiplication
# Polynomial Long Division
# Polynomial Synthetic Division (mainly as a support routine for checking bounds on roots)
# Finding the least positive integral upper bounds for roots
# Finding the greatest negative integral lower bounds for roots
# Descartes' Rule of Signs for the maximum number of positive and negative roots
# Stringification : converting an array of coefficients into a properly formatted polynomial string
# Polynomial Addition
# Polynomial Subtraction
# # Takes two arrays of polynomial coefficients representing # two polynomials and returns their sum. #
# # Takes two arrays of polynomial coefficients representing # two polynomials and returns their difference. #
# # Accepts two arrays containing coefficients in descending order # returns an array with the coefficients of the product #
# # Performs synthetic division on two polynomials returning # the quotient and remainder in an array. #
# # Performs long division on two polynomials # returning the quotient and remainder #
# # Accepts a reference to an array containing the coefficients, in descending # order, of a polynomial. # # Returns the lowest positive integral upper bound to the roots of the # polynomial. #
# # Accepts a reference to an array containing the coefficients, in descending # order, of a polynomial. # # Returns the greatest negative integral lower bound to the roots of the # polynomial #
# # Accepts an array containing the coefficients of a polynomial # in descending order # Returns a sting containing the polynomial with variable x # Default variable is x #
# # Accepts an array containing the coefficients, in descending order, of a # polynomial # Returns the maximum number of positive and negative roots according to # Descartes Rule of Signs # # IMPORTANT NOTE: this function currently does not accept coefficients of # zero. #