AUTHOR
 Dr. Alistair Ward
DESCRIPTION
 Describes a Quotient Ring; http://en.wikipedia.org/wiki/Quotient_ring.
 This is a ring composed from a residueclass resulting from modular division.
 class Ring q => QuotientRing q where
 quotRem' :: q > q > (q, q)
 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
Typeclasses
class Ring q => QuotientRing q whereSource
Defines a subclass of Ring
, in which division is implemented.
:: q  
> q  
> (q, q)  Divides the first operand by the second, to yield a pair composed from the quotient and the remainder. 
(Fractional c, Num e, Ord e) => QuotientRing (Polynomial c e)  Defines the ability to divide polynomials. 
(Num c, Num e, Ord e) => QuotientRing (MonicPolynomial c e) 
Functions
:: QuotientRing q  
=> q  Numerator. 
> q  Denominator. 
> q 
Returns the quotient, after division of the two specified QuotientRing
s.
:: QuotientRing q  
=> q  Numerator. 
> q  Denominator. 
> q 
Returns the remainder, after division of the two specified QuotientRing
s.
Predicates
:: (Eq q, QuotientRing q)  
=> q  LHS. 
> q  RHS. 
> q  Modulus. 
> Bool 

True
if the two specifiedQuotientRing
s are congruent in moduloarithmetic, where the modulus is a thirdQuotientRing
.  http://www.usna.edu/Users/math/wdj/book/node74.html.
:: (Eq q, QuotientRing q)  
=> q  Numerator. 
> q  Denominator. 
> Bool 
True
if the second operand divides the first.