indeedthe approach of summing components can be extended to any object whose binary representation can be viewed as -tuple ( , , - of for examplegiven integersfor we can then form hash code for as any floating point numberwe can sum its mantissa and exponent as long integersand then apply hash code for long integers to the result polynomial hash codes the summation hash codedescribed aboveis not good choice for character strings or other variable-length objects that can be viewed as tuples of the form ( , , - )where the order of the ' is significant for exampleconsider hash code for character string that sums the ascii (or unicodevalues of the characters in this hash code unfortunately produces lots of unwanted collisions for common groups of strings in particular"temp and "temp collide using this functionas do "stop""tops""pots"and "spota better hash code should somehow take into consideration the positions of the ' an alternative hash codewhich does exactly thisis to choose nonzero constanta and use as hash code the value ak- ak- - - mathematically speakingthis is simply polynomial in that takes the compo nents ( , , - of an object as its coefficients this hash code is therefore called polynomial hash code by horner' rule (see exercise - )this poly nomial can be written as - ( - ( - ( ( ax ))intuitivelya polynomial hash code uses multiplication by the constant as way of "making roomfor each component in tuple of values while also preserv ing characterization of the previous components of courseon typical computerevaluating polynomial will be done using the finite bit representation for hash codehencethe value will periodically over flow the bits used for an integer since we are more interested in good spread of the object with respect to other keyswe simply ignore such overflows stillwe should be mindful that such overflows are occurring and choose the constant so that it has some nonzerolow-order bitswhich will serve to preserve some of the information content even as we are in an overflow situation we have done some experimental studies that suggest that and are particularly good choices for when working with character strings that are english words in factin list of over , english words formed as the union