field

Field

Field

Mathematically a Field is a Commutative Ring all whose non-zero elements have multiplicative inverses.

By convention one != zero, otherwise the algebra consists of just one unique element.

Important

Contract: Field initializer parameters must have

• add closed, commutative and associative on reps

• mult closed, commutative and associative on reps

• one an identity on reps, rep*one == rep == one*rep

• zero an identity on reps, rep+zero == rep == zero+rep

• inv is the mult inverse function on all non-zero reps

• negate function to negate all proper rep values

• invert function to invert all proper rep values

• zero != one (by convention)