Knots.Graded

Documentation

data Graded a

Constructors

Graded

Fields

grade :: Int

components :: Map Int a

Instances

Functor Graded

Foldable Graded

Eq a => Eq (Graded a)

Read a => Read (Graded a)

Show a => Show (Graded a)

(Monoid a, AbelianGroup a) => Monoid (Graded a)

Default (Graded a)

AbelianGroup a => AbelianGroup (Graded a)

Ring r => Ring (Graded r)

This is practically multiplication of polynomials in one variable, if we interpret the keys of the components map as exponents. If we write r[X] for the ring of polynomials over r, then the grade can be interpreted as the degree of the variable X. This should justify how the instance is defined.

graded :: Int -> [(Int, a)] -> Graded a