dictionary - Multiplying polynomials in Python with the use of dictionaries -

i have written little class initializer takes argument dictionary. following dictionary {2:3, 4:5, 6:7} translates polynomial 3x^2 + 5x^4 + 7x^6 keys of dictionary exponents , values coefficients.

i have managed implement comparison of 2 polynomials in class using eq method , can add them. here code:

class polynomial(object): def __init__(self, polynom = {}):     self.polynom = polynom     self.poly_string = self.nicepolynom(polynom) #just method make output nice  def __str__(self):     return self.poly_string # debugging purposes  def coefficient(self, exponent):     """     small function returns coefficient of corresponding exponent      i.e. if our polynomial p = 3x^9 p.coefficient(9) return 3     """     try:         return self.polynom[exponent]     except keyerror:         pass   def __add__(self,other):     """     overloading + operator      not elegant solution understandable.      check first if our exponent present in both polynomials     if present in 1 , symmetric case, adding result     dictionary add     """     add = {}      exponent in self.polynom:         if exponent in other.polynom:             add[exponent] = self.polynom[exponent] + other.polynom[exponent]      exponent in self.polynom:         if exponent not in other.polynom:             add[exponent] = self.polynom[exponent]      exponent in other.polynom:         if exponent not in self.polynom:             add[exponent] = other.polynom[exponent]     return add  def __mul__(self, other):      mult = {}      exponent1 in self.polynom:         exponent2 in other.polynom:             mult[exponent1 + exponent2] = self.coefficient(exponent1) * other.coefficient(exponent2)      return mult 

the crucial step , main problem during multiplication want make use of addition. absolutely new oop , don't see how can initialize polynom object on can perform addition arithmetic.

if multiply polynomial @ moment getting correct exponents, besides initial , end term, coefficients way off.

here's 1 approach might work:

for exponent1 in self.polynom:     exponent2 in other.polynom:         this_exponent = exponent1 + exponent2         this_coeff = self.coefficient(exponent1) *  other.coefficient(exponent2)         try:             mult[this_exponent] += this_coeff         except keyerror:             mult[this_exponent] = this_coeff 

that is, update coefficient of new power, , catch exception raised first time power encountered initialize dictionary @ corresponding exponent key. (this more "pythonic" if..else clause if care such things).