| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Factory.Data.QuotientRing
Contents
Description
AUTHOR- Dr. Alistair Ward
DESCRIPTION
- Describes a Quotient Ring; https://en.wikipedia.org/wiki/Quotient_ring.
- This is a ring composed from a residue-class resulting from modular division.
- class Ring q => QuotientRing q where
- quot' :: QuotientRing q => q -> q -> q
- rem' :: QuotientRing q => q -> q -> q
- areCongruentModulo :: (Eq q, QuotientRing q) => q -> q -> q -> Bool
- isDivisibleBy :: (Eq q, QuotientRing q) => q -> q -> Bool
Type-classes
class Ring q => QuotientRing q where Source #
Defines a sub-class of Ring, in which division is implemented.
Minimal complete definition
Instances
| (Eq c, Fractional c, Num e, Ord e) => QuotientRing (Polynomial c e) Source # | Defines the ability to divide polynomials. |
| (Eq c, Num c, Num e, Ord e, Show c, Show e) => QuotientRing (MonicPolynomial c e) Source # | |
Functions
Arguments
| :: QuotientRing q | |
| => q | Numerator. |
| -> q | Denominator. |
| -> q |
Returns the quotient, after division of the two specified QuotientRings.
Arguments
| :: QuotientRing q | |
| => q | Numerator. |
| -> q | Denominator. |
| -> q |
Returns the remainder, after division of the two specified QuotientRings.
Predicates
Arguments
| :: (Eq q, QuotientRing q) | |
| => q | LHS. |
| -> q | RHS. |
| -> q | Modulus. |
| -> Bool |
Trueif the two specifiedQuotientRings are congruent in modulo-arithmetic, where the modulus is a thirdQuotientRing.- http://www.usna.edu/Users/math/wdj/book/node74.html.
Arguments
| :: (Eq q, QuotientRing q) | |
| => q | Numerator. |
| -> q | Denominator. |
| -> Bool |
True if the second operand divides the first.