Millais / PolynomialArithmetic

Simple polynomial arithmetic implemented using SBCL.

Polynomial Arithmetic using Common Lisp

An assignment to determine a representation for polynomials, and to implement simple polynomial arithmetic using this representation (as part of CM20214: Advanced Programming Principles).

This assignment came with three requirements:

• Implement the three polynomial arithmetic operations: + - and *. These must be named p+, p- and p*.
• Expand and collect together like terms. For example: summing (x+y, x) must return 2x + y, rather than x + y + x.
• p+, p- and p* must be functions that take two polynomial arguments, and return a polynomial in the chosen representation. For example:
  • p1: x + y + 1
  • p2: 2xy + x + z
  • (p+ p1 p2): 2xy + 2x + y + z + 1
  • (p- (p+ p1 p2) p2): x + y + 1

This coursework also required pure functional programming: no side-effects, no assignments, and referential transparency.

Representation

Polynomials are represented by a list of terms adhering to the following specification:

(coefficient xexp yexp zexp ... )

Some examples:

2xy² = (2 1 2)

7xz² = (7 1 0 2)

3xy⁵a² = (3 1 5 0 2)

xyz = (1 1 1 1)

See the pdf for further explanation, examples, and test cases.

Running

Simple Example

(2x + y + z) + (3x + 5y - z)

= (5x + 6y)

(p+’((2 1) (1 0 1) (1 0 0 1)) ‘((3 1) (5 0 1) (-1 0 0 1)))

> ((5 1) (6 0 1))

Complex Example

((3x² + 2yz²) * (20y -x²)) * (3y +4x)

= -12x⁵ +240x³y - 8x³yz² + 160xy²z² - 9x⁴y + 180x²y² - 6x²y²z² + 120y³z²

(p*(p* ‘((3 2) (2 0 1 2)) ‘((20 0 1) (-1 2))) ‘((3 0 1) (4 1)))

> ((-12 5) (240 3 1) (-8 3 1 2) (160 1 2 2) (-9 4 1) (180 2 2) (-6 2 2 2) (120 0 3 2))

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Graded as a strong first.