""" polystuff.py (Python 3.x) For a curriculum segment when we're not yet wanting to build user-defined classes. showpoly -- return an evaluable string with x the variable evalpoly -- return a numeric result given an evaluable string and x's value multipoly -- return the product of two polynomials as a tuple of tuples """ from operator import itemgetter def showpoly(A): """ Return a close-to-classic polynomial as an evaluable Python string literal, given a sequence of tuples for input (see multipoly below). Some prettifying. >>> p1 = ((4,2),(-4,1),(-7,0)) >>> showpoly(p1) '4 * x**2 - 4 * x**1 - 7' """ terms = [] for coeff, exp in sorted(A, key=itemgetter(1), reverse=True): terms.append( "{sign} {coeff}{var}".format( sign = "+" if coeff > 0 else "-", coeff = abs(coeff), var = ' * x**{}'.format(exp) if exp>0 else "" )) ans = " ".join(terms) if ans[0] == "+": # prettify ans = ans[1:].strip() return ans def evalpoly(strpoly, x): """ Evaluates a polynomial string literal for a given x value >>> p1 = ((4,2),(-4,1),(-7,0)) >>> thestring = showpoly(p1) >>> thestring '4 * x**2 - 4 * x**1 - 7' >>> evalpoly(thestring, 10) 353 """ return eval(strpoly, {"x":x}) def multipoly(A, B): """ Multiply two polynomials, represented as sequences of tuples e.g.: 3*x**3 + 2*x**2 - x - 1 would be ((3,3),(2,2),(-1,1),(-1,0)) with internal pairs in any order (term order is arbitrary) >>> p1 = ((1,1),(-1,0)) >>> p2 = ((1,1),(1,0)) >>> multipoly(p1,p2) [(-1, 0), (1, 2)] >>> p1 = ((4,2),(-4,1),(-7,0)) >>> p2 = ((1,1),(3,0)) >>> multipoly(p1,p2) [(-21, 0), (-19, 1), (8, 2), (4, 3)] """ results = [] termsAB = [] # Cartesian product of terms in poly A and poly B # multiply coefficients, add exponents for termA in A: for termB in B: termsAB.append(( termA[0] * termB[0], # coefficients termA[1] + termB[1] # exponents )) # find maximum exponent degree = max([term[1] for term in termsAB]) # collect like terms (same exponent) for exp in range(degree+1): # from 0 to degree inclusive newterm = ( sum([term[0] for term in termsAB if term[1] == exp]), exp) if newterm[0] != 0: results.append(newterm) return results def _test( ): import doctest doctest.testmod() if __name__ == '__main__': _test()