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Ruby Example Code |

More List Ops | poly.rb |

# # 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. # # # 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) sum = 0 coef = coef.clone # Don't want to destroy the original while true sum += coef.shift # Add and remove the next coef break if coef.empty? # If no more, done entirely. sum *= x # This happens the right number of times. end return sum end # # Function to read a line containing a list of integers and return # them as an array of integers. If the string conversion fails, it # throws TypeError. If the input line is the word 'quit', then it # converts it to an end-of-file exception def readints(prompt) # Read a line print prompt line = readline.chomp raise EOFError.new if line == 'quit' # You can also use a real EOF. # Go through each item on the line, converting each one and adding it # to retval. retval = [ ] for str in line.split(/\s+/) if str =~ /^\-?\d+$/ retval.push(str.to_i) else raise TypeError.new end end return retval end # # Take a coeff and an exponent and return the string representation, ignoring # the sign of the coefficient. def term_to_str(coef, exp) ret = "" # Show coeff, unless it's 1 or at the right coef = coef.abs ret = coef.to_s unless coef == 1 && exp > 0 ret += "x" if exp > 0 # x if exponent not 0 ret += "^" + exp.to_s if exp > 1 # ^exponent, if > 1. return ret end # # Create a string of the polynomial in sort-of-readable form. def polystr(p) # Get the exponent of first coefficient, plus 1. exp = p.length # Assign exponents to each term, making pairs of coeff and exponent, # Then get rid of the zero terms. p = (p.map { |c| exp -= 1; [ c, exp ] }).select { |p| p[0] != 0 } # If there's nothing left, it's a zero return "0" if p.empty? # *** Now p is a non-empty list of [ coef, exponent ] pairs. *** # Convert the first term, preceded by a "-" if it's negative. result = (if p[0][0] < 0 then "-" else "" end) + term_to_str(*p[0]) # Convert the rest of the terms, in each case adding the appropriate # + or - separating them. for term in p[1...p.length] # Add the separator then the rep. of the term. result += (if term[0] < 0 then " - " else " + " end) + term_to_str(*term) end return result end # # Run until some kind of endfile. begin # Repeat until an exception or quit gets us out. while true # Read a poly until it works. An EOF will except out of the # program. print "\n" begin poly = readints("Enter a polynomial coefficients: ") rescue TypeError print "Try again.\n" retry end break if poly.empty? # Read and evaluate x values until the user types a blank line. # Again, an EOF will except out of the pgm. while true # Request an integer. print "Enter x value or blank line: " x = readline.chomp break if x == '' raise EOFError.new if x == 'quit' # If it looks bad, let's try again. if x !~ /^\-?\d+$/ print "That doesn't look like an integer. Please try again.\n" next end # Convert to an integer and print the result. x = x.to_i print "p(x) = ", polystr(poly), "\n" print "p(", x, ") = ", polyval(x, poly), "\n" end end rescue EOFError print "\n=== EOF ===\n" rescue Interrupt, SignalException print "\n=== Interrupted ===\n" else print "--- Bye ---\n" end

This program reads and evaluates polynomials. The arithmetic uses integers, though it could be adapted easily enough to used floats outside the exponent values.

Polynomials are read in as a list of coefficients. The number of
values determines the order. The main program is a double loop,
the outer reading polynomials, and the inner reading *x* values.
The user can enter any number of polynomials, and, for each, evaluate
them at any number of domain values. Either loop is ended by entering
a blank line. An EOF will halt the program directly.

A couple of novelties and notables:

- The
`polyval`

function takes an*x*value and a list of coefficients representing the polynomial and evaluates it at*x*. The evaluation loop is destructive, so the function begins by cloning the array so the original is un-damaged. The clone method, as you might imagine, makes a copy of the object. - The built-in
`readline`

function is the same as`gets`

, except it raises the end-of-file exception. Ruby gives you a choice to use exceptions or not. - This program makes some use of the list operations. In particular,
the
`polystr`

method which converts the polynomial to a string for printing uses`map`

and`select`

. The`map`

converts the list of coefficients to a list of pairs, coefficient and exponent, then`select`

eliminates the zero terms. - When the user enters a bad polynomial, the program raises a
`TypeError`

. The reading loop catches this with a`rescue`

, then issues a`retry`

to allow the user to reenter the polynomial. The`retry`

used in a`rescue`

block simply starts the`begin`

block over from the beginning.

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