IEuclidean
Defined in: euclidean.ts:24
A Euclidean domain — an integral domain equipped with a degree function that admits division with remainder, which is what makes the Euclidean algorithm (and therefore GCD) applicable.
ℤ and the polynomial ring K[X] over a field K are Euclidean domains.
Extends
Section titled “Extends”IRing<T>
Type Parameters
Section titled “Type Parameters”T extends IEuclidean<T>
The carrier set of the domain.
Methods
Section titled “Methods”add(
other):T
Defined in: additive.ts:11
The additive operation a + b.
Parameters
Section titled “Parameters”T
Returns
Section titled “Returns”T
Inherited from
Section titled “Inherited from”degree()
Section titled “degree()”degree():
number
Defined in: euclidean.ts:26
The Euclidean degree, used as the termination measure of the algorithm.
Returns
Section titled “Returns”number
divmod()
Section titled “divmod()”divmod(
other):QuotientRemainder<T,T>
Defined in: euclidean.ts:35
Quotient and remainder computed in a single pass.
Parameters
Section titled “Parameters”T
Returns
Section titled “Returns”QuotientRemainder<T, T>
divTrunc()
Section titled “divTrunc()”divTrunc(
other):T
Defined in: euclidean.ts:29
Quotient of the Euclidean division a ÷ b.
Parameters
Section titled “Parameters”T
Returns
Section titled “Returns”T
mul(
other):T
Defined in: multiplicative.ts:14
The operation a · b.
Parameters
Section titled “Parameters”T
Returns
Section titled “Returns”T
Inherited from
Section titled “Inherited from”neg():
T
Defined in: additive.ts:25
The additive inverse −a.
Returns
Section titled “Returns”T
Inherited from
Section titled “Inherited from”rem(
other):T
Defined in: euclidean.ts:32
Remainder of the Euclidean division a mod b.
Parameters
Section titled “Parameters”T
Returns
Section titled “Returns”T
sub(
other):T
Defined in: additive.ts:28
Subtraction a − b, equivalent to a.add(b.neg()).
Parameters
Section titled “Parameters”T
Returns
Section titled “Returns”T