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Home Current UR courses Visitor page Intro to WeBWorK WeBWorK 2 Twiki WW Community Grant Support & awards Discussion group Problem library Write/modify problems Create & manage course Tutorial on running a course HowTos FAQ WeBWorK2 FAQ Software Download How to Install WW server Feedback Site Map Change preferences Change password	Prev | Next | pod PGpolynomialmacros.pl DESCRIPTION ValidPoly(@PolynomialCoeffs) PolyAdd(@Polyn1,@Polyn2) PolySub(@Polyn1,@Polyn2) PolyMult(~~@coefficientArray1,~~@coefficientArray2) (@quotient,$remainder) = SynDiv(~~@dividend,~~@divisor) (@quotient,@remainder) = LongDiv($dividendref,$divisorref) UpBound(~~@polynomial) LowBound(~~@polynomial) PolyString(~~@coefficientArray,x) ($maxpos,$maxneg) = Descartes(~~@poly) PGpolynomialmacros.pl DESCRIPTION ########################################################## # It contains rountines used to create and manipulate ## # polynomials for WeBWorK ## # ## # Copyright 2002 Mark Schmitt ## # Version 1.1.2 ## ########################################################## # 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 ValidPoly(@PolynomialCoeffs) PolyAdd(@Polyn1,@Polyn2) # # Takes two arrays of polynomial coefficients representing # two polynomials and returns their sum. # PolySub(@Polyn1,@Polyn2) # # Takes two arrays of polynomial coefficients representing # two polynomials and returns their difference. # PolyMult(~~@coefficientArray1,~~@coefficientArray2) # # Accepts two arrays containing coefficients in descending order # returns an array with the coefficients of the product # (@quotient,$remainder) = SynDiv(~~@dividend,~~@divisor) # # Performs synthetic division on two polynomials returning # the quotient and remainder in an array. # (@quotient,@remainder) = LongDiv($dividendref,$divisorref) # # Performs long division on two polynomials # returning the quotient and remainder # UpBound(~~@polynomial) # # Accepts a reference to an array containing the coefficients, in descending # order, of a polynomial. # # Returns the lowest positive integral upper bound to the roots of the # polynomial. # LowBound(~~@polynomial) # # Accepts a reference to an array containing the coefficients, in descending # order, of a polynomial. # # Returns the greatest negative integral lower bound to the roots of the # polynomial # PolyString(~~@coefficientArray,x) # # Accepts an array containing the coefficients of a polynomial # in descending order # Returns a sting containing the polynomial with variable x # Default variable is x # ($maxpos,$maxneg) = Descartes(~~@poly) # # 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. # File path = /ww/webwork/pg/macros/PGpolynomialmacros.pl <| Post or View Comments |> Prev | Next | pod
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