Question

please answer this question in python 3

For this lab, you must define a class called Polynomial. This class definition must include the following methods: ._init_0- the initialiser for the class ._str_0- returns a formatted string representation of a Polynomial object add_term) - adds a new term (coefficient and exponent) to the Polynomial .addo-modifies the existing Polynomial by adding another one to it ._add_0-returns a new Polynomial object that is the sum of two polynomials scale) - scales a Polynomial object by multiplying each coefficient by a factor evaluate0 - evaluates a Polynomial object for a given x-value .get_degree0-returns the degree of the Polynomial object collapse) reduces the Polynomial object to a single term Background A polynomial is a mathematical expression that is the sum of a series of terms that each consist of a variable (we will use x) which is taken to a given power and multiplied by a given coefficient. For example, the following are two different polynomials 2x4 +x2- 7x +13 x3-5x21 For this lab you will be defining a class called Polynomial that can be used to represent polynomials in our programs. When a Polynomial object is first created it contains no terms, and thus has the corresponding value 0. You can add terms to a Polynomial object by calling the add_termO method. Each term consists of a coefficient (which should be non-zero) and an exponent. Each exercise in the lab will build progressively on the previous exercise to show how a class is developed The collapse method The collapse() method reduces a Polynomial object to a single term. It does this by adding together all of the coefficients to produce a coefficient sum, and adding together all of the exponents to produce an exponent sum. The single term then just consists of the coefficient sum and the exponent sum. For example p1- Polynomial( pl.add_term(1, 10) p1.add_term(2, 0) pl.add term (3, -1) p1.add term(4, -2) p1.add_term(5, -3) p1.collapse() print( 'p1-,p1) would produce the output: pl-15x4 Implement the collapse method and submit the entire Polynomial class For example Test Result p1 - Polynomial) 4x4 pl.add_term(2, 4) p1.add (pl) p1.collapse() print (pl)

Answer 1

CODE:

# Coefficient and exponent will be maintained as list of tuples [ (coeff,expo)] in terms list
class Polynomial():
    def __init__(self):
        self.terms = [] 
        
    def __str__(self):
        if self.terms == []: # If there are no terms in the list
            return '0'
        else:
            s = ""
            for tup in self.terms: # Traversing over list of coeff and expo and returing polynomial
                c,e = tup
                if c>0:
                    s+="+"+str(c)+"x^"+str(e)
                else:
                    s+=str(c)+"x^"+str(e)
            return s
        
    def add_term(self,c,e): # Adding term to the given polynomial
        self.terms.append((c,e))
    
    def evaluate(self,x):
        ans = 0
        for c,e in self.terms: # Performing evaluation for given value of x
            ans += c*pow(x,e)
        return ans
    
    def collapse(self):
        netc,nete = 0,0
        for c,e in self.terms: 
            netc+=c
            nete+=e
        self.terms = [(netc,nete)]
    
    def scale(self,factor):
        newlist = []
        for c,e in self.terms: 
            netc=c*factor
            newlist.append((netc,e))
        self.terms = newlist[:]
        
    def get_degree(self):
        deg = -100
        for c,e in self.terms:
            if deg < e:
                deg = e
        return deg
    
p1 = Polynomial()
p1.add_term(2,4)
p1.add_term(1,2)
p1.add_term(-7,1)
p1.add_term(13,0)
print("p1 =",p1)
print("Evaluating with value 2 =",p1.evaluate(2))
p1.scale(2)
print("Scaling with value 2 = ",p1)
print("Degree of the polynomial is = ",p1.get_degree())
p1.collapse()
print("Collapsing polynomial ",p1)

OUTPUT:

class Polynomial): def init(self): self.terms[] def _str_(self): if self.terms[] return 'e else for tup in self.terms: c,e-tup if c>e: s+="+"+str(c)+"x"+str(e) else: ststr(c)+ "x"+str(e) return s def add_term(self,c,e): self.terms.append ((c,e)) def evaluate(self,x): ans for c,e in self.terms: c*pow(x,e) return ans def collapse(self): netc,nete-0,e for c,e in self.terms: netc+-c nete+-e self.terms[(netc,nete)] return self.terms def scale (self,factor): ewlist-[] for c,e in self.terms: netc-c*factor newlist.append ((netc,e)) self.terms newlist L:

def get_degree(self) deg = -100 for c,e in self.terms: if deg 〈 e: deg = e return deg p Polynomial() p1.add_term(2,4) p1.add_term(1,2) p1.add_term(-7,1) p1.add_term (13,0) print("p1-",p1) print ("Evaluating with value 2-",p1.evaluate(2)) p1.scale (2) print ("Scaling with value 2-",p1) print ("Degree of the polynomial is- ",p1.get_degree)) Evaluating with value 2 = 35 Scaling with value 2 +4xA4+2x 2-14x 1+26xA0 Degree of the polynomial is 4

NOTE:

Explain the difference between add() and __add__() functions, so that I can also add them.