Exercises:

1.

Add a map method to the IntList class that takes an Operation and applies it to each element of this to produce a new IntList with exactly the same number of elements as this.

2.

Assume that a vector

< a₀ , a₁ , a₂, ... , a_n >

is represented by the list

$${\tt\small (} a_0 \; a_1 \; a_2 \; ... \; a_n {\tt\small )}.$$

where the coefficient's a_i are objects of type Double. Add a method

double norm()

to IntList computes the norm by v by squaring the elements, adding the squares together and taking the square-root of the sum. You can compute the vector of squares using map and the define a method double sum() to compute the sum.

3.

Assume that a polynomial

a₀ x + a₁ x + a₂ x² + ... + a_n xⁿ

is represented by the list

$${\tt\small (} a_0 \; a_1 \; a_2 \; ... \; a_n {\tt\small )}0$$

where the coefficient's a_i are objects of type Double. Write a method

double eval(IntList p, Double x)

to evaluate the polynomial at coordinate x. Use Horner' rule asserting that

$$a_0 + a_1 x + a_2 x^2 + ... + a_n x^n = \\ a_0 + x \cdot (a_1 + x \cdot (a_2 + ... x \cdot a_n))$$

Remember to use the structural design pattern for processing lists (and by association polynomials as we have represented them).