[SOLVED] CS102- Lab 02

Description

Lab Objectives: Arrays, Classes & Objects, reuse in OOP​

For all labs in CS 102, your solutions must conform to these CS101/102 style guideline​ s.​

Question In​ this lab, you will use the Polynomial​ class​ that you implemented in the first lab assignment.

Implement the following operations for

• add( Polynomial p2 ):​ Sums this polynomial (polynomial for which the method​ is called) and polynomial p2, and returns the result as a new polynomial.

 

• sub( Polynomial p2 ):​ Subtracts polynomial p2 from this polynomial for which​ the method is called on, and returns the result as a new polynomial.

 

• mul( Polynomial p2 ):​ Multiplies this polynomial (polynomial for which the​ method is called), and polynomial p2 and returns the result as a new polynomial.

For polynomials P(x) and Q(x), the results of addition, subtraction and multiplication operations are:

P(x) = 3 + 4x + 5x​^2​ + 2x³​

Q(x) = 2 + 4x + 1x²​

 

P(x) + Q(x) = 5 + 8x + 6x​^2​ + 2x³​

P(x) – Q(x) = 1 + 4x​^2​ + 2x³​

P(x) * Q(x) = 6 + 20x + 29x​^2​ + 28x³​ ^​ + 13x​^4​ + 2x⁵​

 

2. Implement compose and div methods. You can use add, sub, mul methods you already implemented to simplify compose and div methods.

 

• compose( Polynomial p2 ):​ Returns the composition of this polynomial with p2.​

 

 

For polynomials P(x) and Q(x), the result of composition (P(Q(x))) is:

P(x) = 3 + 4x + 1x²​

Q(x) = 2 + 1x

 

P(Q(x)) = 3 + 4 (2 + 1x) + 1 (2 + 1x)²​

P(Q(x)) = 15 + 8x + 1x²​

 

• div( Polynomial p2 ):​ Divides this polynomial with p2 and returns the quotient.​

 

P(x) = 3 + 4x + 1x​^2​ + 3x​^3​ + 2x⁵​

Q(x) = 2 + 1x

 

For polynomials P(x) and Q(x), the result of the division operation, P(x) / Q(x), is found as follows:

 

• Find the leading term (non zero term with highest degree) of the P(x) and Q(x).

 

lead(P(x)) = 2x⁵​ lead(Q(x)) = x

 

• Find polynomial T(x) such that:

 

T(x) = lead(P(x)) / lead(Q(x)) = 2x⁴​

• Subtract T(x) * Q(x) from P(x) and assign the result to P(x).

P(x) – Q(x) * T(x) = 3 + 4x + 1x​^2​ + 3x​^3​ + -x​⁴

• Add T(x) to the result and repeat this process until the degree of P(x) is higher than the degree of Q(x).

 

Dividend (P(x))                                 T(x) = lead(P(x)) / lead(Q(x))

3 + 4x + 1x​^2​ + 3x​^3​ + 2x​⁵                                           2x⁴​

3 + 4x + 1x​^2​ + 3x​^3​ – 4x​⁴                                             -4x³​

3 + 4x + 1x​^2​ + 11x​³                                                         11x²​

3 + 4x – 21x​²                                                                            -21x

3 + 46x                                              46

-89

 

Result of P(x) / Q(x) is 46 – 21x + 11x​^2​ – 4x​^3​ + 2x​^4​. Note that remainder is ignored.

 

3. Modify the PolynomialTester​ class from the first assignment to test your Polynomial​ class for the above operations.