# # This program evaluates polynomials. It first asks for the coefficients # of a polynomial, which must be entered on one line, highest-order first. # It then requests values of x and will compute the value of the poly for # each x. It will repeatly ask for x values, unless you the user enters # a blank line. It that case, it will ask for another polynomial. If the # user types quit for either input, the program immediately exits. #
# Need some string services, and some standard system services. import string, sys
# # Function to evaluate a polynomial at x. The polynomial is given # as a list of coefficients, from the greatest to the least. def polyval(x, coef): '''Evaluate at x the polynomial with coefficients given in coef. The value p(x) is returned.'''
sum = 0 while 1: sum = sum + coef # Add the next coef. coef = coef[1:] # Done with that one. if not coef: break # If no more, done entirely. sum = sum * x # Mult by x (each coef gets x right num times)
# # Function to read a line containing a list of integers and return # them as a list of integers. If the string conversion fails, it # returns the empty list. If the input line is the word 'quit', then # it exits the program (which is actually accomplished with an exception). # Other exceptions are passed on. def readints(prompt): '''Read a line of integers and return the list of integers.'''
# Read a line line = input(prompt) if line == 'quit': sys.exit(0)
# Go through each item on the line, converting each one and adding it # to retval. retval = [ ]; for s in str.split(line): try: retval.append(int(s)) except ValueError: # On conversion failure, whine and return empty list. print('Conversion of', s, 'failed.') return 
# # Create a string of the polynomial in sort-of-readable form. def polystr(p): # Get the exponent of first coefficient, plus 1. exp = len(p)
# Go through the coefs and turn them into terms. retval = '' while p: # Adjust exponent. Done here so continue will run it. exp = exp - 1
# Strip first coefficient coef = p p = p[1:]
# If zero, leave it out. if coef == 0: continue
# If adding, need a + or -. if retval: if coef >= 0: retval = retval + ' + ' else: coef = -coef retval = retval + ' - '
# Add the coefficient, if needed. if coef != 1 or exp == 0: retval = retval + str(coef) if exp != 0: retval = retval + '*'
# Put the x, if we need it. if exp != 0: retval = retval + 'x' if exp != 1: retval = retval + '^' + str(exp)
# For zero, say that. if not retval: retval = '0'
# # Run until some kind of endfile. try: # Repeat until an exception or quit gets us out. while 1: # Read a poly until it works. An EOF will except out of the # program. while 1: poly = readints('Enter a polynomial coefficients: ') if poly: break print('Try again.')
# Read and evaluate x values until the user types a blank line. # Again, and EOF will except out of the pgm. while 1: resp = input('Enter x value or blank line: ') if resp == 'quit': sys.exit(0) if not resp: break try: x = int(resp) except ValueError: print("That doesn't look like an integer. Please try again.") else: print('p(x) =', polystr(poly)) print('p(' + str(x) + ') =', polyval(x, poly))
except (EOFError, KeyboardInterrupt): # Exit without error for EOF or ^C. Print a blank line to clear after # any prompt. print()
This uses several of the things we have discussed up to now.