Module un_algebra::field::field

Algebraic fields.

An algebraic field is a commutative ring (with identity) R, where each invertible field element f has a unique multiplicative inverse f^-1. The inverse operation is called invert.

Axioms

∀g, 1 ∈ R

Inverse: ∃g^-1 ∈ R: g × g^-1 = g^-1 × g = 1.

References

See references for a formal definition of a field.

Traits

Field

An algebraic field.

Functions

add_cancellation	The derived property of additive cancellation.
inverse	The two sided multiplicative inverse axiom.
left_inverse	The left multiplicative inverse axiom.
mul_cancellation	The derived property of multiplicative cancellation.
num_add_cancellation	The derived property of numeric additive cancellation.
num_inverse	The two sided numeric multiplicative inverse axiom.
num_left_inverse	The left numeric multiplicative inverse axiom.
num_mul_cancellation	The derived property of numeric multiplicative cancellation.
num_right_inverse	The right numeric multiplicative inverse axiom.
num_zero_cancellation	The derived property of numeric zero cancellation.
right_inverse	The right multiplicative inverse axiom.
zero_cancellation	The derived property of zero cancellation.