laws
laws
spire.laws
ActionLaws
ActionLaws
ActionProperties
AdditiveProperties
MultiplicativeProperties
BaseLaws
BaseLaws
CombinationLaws
CombinationLaws
GroupLaws
GroupLaws
AdditiveProperties
GroupProperties
InvalidTestException
InvalidTestException
InvolutionLaws
InvolutionLaws
LatticeLaws
LatticeLaws
LatticeProperties
LatticePartialOrderLaws
LatticePartialOrderLaws
LatticePartialOrderProperties
LogicLaws
LogicLaws
OrderLaws
OrderLaws
OrderProperties
PartialActionLaws
PartialActionLaws
ActionProperties
PartialGroupLaws
PartialGroupLaws
RingLaws
RingLaws
MultiplicativeProperties
RingProperties
RingProperties
VectorSpaceLaws
VectorSpaceLaws
SpaceProperties
SpaceProperties
arb
gen
spire.laws.shadows
Shadow
Shadow
ShadowAdditiveAbGroup
ShadowAdditiveCMonoid
ShadowAdditiveCSemigroup
ShadowCRig
ShadowCRing
ShadowCRng
ShadowCSemiring
ShadowEq
ShadowEuclideanRing
ShadowGCDRing
ShadowInstances0
ShadowInstances1
ShadowInstances2
ShadowInstances3
ShadowInstances4
ShadowInstances5
ShadowInstances6
ShadowInstances7
ShadowInvolution
ShadowMultiplicativeCMonoid
ShadowMultiplicativeCSemigroup
ShadowOrder
ShadowPartialOrder
ShadowSigned
ShadowTruncatedDivision
Shadowing
Shadowing
laws
/
spire.laws.shadows
/
ShadowEuclideanRing
ShadowEuclideanRing
trait
ShadowEuclideanRing
[
A
,
S
]
extends
EuclideanRing
[
Shadow
[
A
,
S
]]
with
ShadowGCDRing
[
A
,
S
]
Graph
Supertypes
trait
ShadowGCDRing
[
A
,
S
]
trait
ShadowCRing
[
A
,
S
]
trait
ShadowCRng
[
A
,
S
]
trait
ShadowAdditiveAbGroup
[
A
,
S
]
trait
ShadowCRig
[
A
,
S
]
trait
ShadowMultiplicativeCMonoid
[
A
,
S
]
trait
ShadowCSemiring
[
A
,
S
]
trait
ShadowMultiplicativeCSemigroup
[
A
,
S
]
trait
ShadowAdditiveCMonoid
[
A
,
S
]
trait
ShadowAdditiveCSemigroup
[
A
,
S
]
trait
EuclideanRing
[
Shadow
[
A
,
S
]]
trait
GCDRing
[
Shadow
[
A
,
S
]]
trait
CommutativeRing
[
Shadow
[
A
,
S
]]
trait
CommutativeRng
[
Shadow
[
A
,
S
]]
trait
CommutativeRig
[
Shadow
[
A
,
S
]]
trait
MultiplicativeCommutativeMonoid
[
Shadow
[
A
,
S
]]
trait
CommutativeSemiring
[
Shadow
[
A
,
S
]]
trait
MultiplicativeCommutativeSemigroup
[
Shadow
[
A
,
S
]]
trait
Ring
[
Shadow
[
A
,
S
]]
trait
Rng
[
Shadow
[
A
,
S
]]
trait
AdditiveCommutativeGroup
[
Shadow
[
A
,
S
]]
trait
AdditiveGroup
[
Shadow
[
A
,
S
]]
trait
Rig
[
Shadow
[
A
,
S
]]
trait
MultiplicativeMonoid
[
Shadow
[
A
,
S
]]
trait
Semiring
[
Shadow
[
A
,
S
]]
trait
MultiplicativeSemigroup
[
Shadow
[
A
,
S
]]
trait
AdditiveCommutativeMonoid
[
Shadow
[
A
,
S
]]
trait
AdditiveCommutativeSemigroup
[
Shadow
[
A
,
S
]]
trait
AdditiveMonoid
[
Shadow
[
A
,
S
]]
trait
AdditiveSemigroup
[
Shadow
[
A
,
S
]]
trait
Serializable
class
Object
trait
Matchable
class
Any
Value members
Implicits
Value members
Concrete methods
def
emod
(
x:
Shadow
[
A
,
S
],
y:
Shadow
[
A
,
S
]):
Shadow
[
A
,
S
]
def
equot
(
x:
Shadow
[
A
,
S
],
y:
Shadow
[
A
,
S
]):
Shadow
[
A
,
S
]
override
def
equotmod
(
x:
Shadow
[
A
,
S
],
y:
Shadow
[
A
,
S
]): (
Shadow
[
A
,
S
],
Shadow
[
A
,
S
])
Definition Classes
EuclideanRing
def
euclideanFunction
(
x:
Shadow
[
A
,
S
]):
BigInt
Inherited methods
override
def
additive
:
CommutativeGroup
[
Shadow
[
A
,
S
]]
Definition Classes
AdditiveCommutativeGroup
->
AdditiveCommutativeMonoid
->
AdditiveCommutativeSemigroup
->
AdditiveGroup
->
AdditiveMonoid
->
AdditiveSemigroup
Inherited from:
AdditiveCommutativeGroup
override
def
fromBigInt
(
n:
BigInt
):
Shadow
[
A
,
S
]
Definition Classes
ShadowCRing
->
Ring
Inherited from:
ShadowCRing
override
def
fromInt
(
n:
Int
):
Shadow
[
A
,
S
]
Definition Classes
ShadowCRing
->
Ring
Inherited from:
ShadowCRing
override
def
gcd
(
x:
Shadow
[
A
,
S
],
y:
Shadow
[
A
,
S
])(
implicit
ev:
Eq
[
Shadow
[
A
,
S
]]):
Shadow
[
A
,
S
]
Definition Classes
ShadowGCDRing
->
GCDRing
Inherited from:
ShadowGCDRing
override
def
isOne
(
x:
Shadow
[
A
,
S
])(
implicit
ev:
Eq
[
Shadow
[
A
,
S
]]):
Boolean
Definition Classes
ShadowMultiplicativeCMonoid
->
MultiplicativeMonoid
Inherited from:
ShadowMultiplicativeCMonoid
override
def
isZero
(
x:
Shadow
[
A
,
S
])(
implicit
ev:
Eq
[
Shadow
[
A
,
S
]]):
Boolean
Definition Classes
ShadowAdditiveCMonoid
->
AdditiveMonoid
Inherited from:
ShadowAdditiveCMonoid
override
def
lcm
(
x:
Shadow
[
A
,
S
],
y:
Shadow
[
A
,
S
])(
implicit
ev:
Eq
[
Shadow
[
A
,
S
]]):
Shadow
[
A
,
S
]
Definition Classes
ShadowGCDRing
->
GCDRing
Inherited from:
ShadowGCDRing
override
def
minus
(
x:
Shadow
[
A
,
S
],
y:
Shadow
[
A
,
S
]):
Shadow
[
A
,
S
]
Definition Classes
ShadowAdditiveAbGroup
->
AdditiveGroup
Inherited from:
ShadowAdditiveAbGroup
override
def
multiplicative
:
CommutativeMonoid
[
Shadow
[
A
,
S
]]
Definition Classes
MultiplicativeCommutativeMonoid
->
MultiplicativeCommutativeSemigroup
->
MultiplicativeMonoid
->
MultiplicativeSemigroup
Inherited from:
MultiplicativeCommutativeMonoid
def
negate
(
x:
Shadow
[
A
,
S
]):
Shadow
[
A
,
S
]
Inherited from:
ShadowAdditiveAbGroup
def
one
:
Shadow
[
A
,
S
]
Inherited from:
ShadowMultiplicativeCMonoid
def
plus
(
x:
Shadow
[
A
,
S
],
y:
Shadow
[
A
,
S
]):
Shadow
[
A
,
S
]
Inherited from:
ShadowAdditiveCSemigroup
override
def
pow
(
x:
Shadow
[
A
,
S
],
n:
Int
):
Shadow
[
A
,
S
]
Definition Classes
ShadowMultiplicativeCSemigroup
->
MultiplicativeSemigroup
Inherited from:
ShadowMultiplicativeCSemigroup
override
def
product
(
xs:
IterableOnce
[
Shadow
[
A
,
S
]]):
Shadow
[
A
,
S
]
Definition Classes
ShadowMultiplicativeCMonoid
->
MultiplicativeMonoid
Inherited from:
ShadowMultiplicativeCMonoid
override
def
sum
(
xs:
IterableOnce
[
Shadow
[
A
,
S
]]):
Shadow
[
A
,
S
]
Definition Classes
ShadowAdditiveCMonoid
->
AdditiveMonoid
Inherited from:
ShadowAdditiveCMonoid
override
def
sumN
(
x:
Shadow
[
A
,
S
],
n:
Int
):
Shadow
[
A
,
S
]
Definition Classes
ShadowAdditiveCSemigroup
->
AdditiveSemigroup
Inherited from:
ShadowAdditiveCSemigroup
def
times
(
x:
Shadow
[
A
,
S
],
y:
Shadow
[
A
,
S
]):
Shadow
[
A
,
S
]
Inherited from:
ShadowMultiplicativeCSemigroup
override
def
tryProduct
(
xs:
IterableOnce
[
Shadow
[
A
,
S
]]):
Option
[
Shadow
[
A
,
S
]]
Definition Classes
ShadowMultiplicativeCSemigroup
->
MultiplicativeSemigroup
Inherited from:
ShadowMultiplicativeCSemigroup
override
def
trySum
(
xs:
IterableOnce
[
Shadow
[
A
,
S
]]):
Option
[
Shadow
[
A
,
S
]]
Definition Classes
ShadowAdditiveCSemigroup
->
AdditiveSemigroup
Inherited from:
ShadowAdditiveCSemigroup
def
zero
:
Shadow
[
A
,
S
]
Inherited from:
ShadowAdditiveCMonoid
Implicits
Implicits
implicit
def
A
:
EuclideanRing
[
A
]
implicit
def
S
:
EuclideanRing
[
S
]
Inherited implicits
implicit
def
eqA
:
Eq
[
A
]
Inherited from:
ShadowMultiplicativeCMonoid
implicit
def
eqS
:
Eq
[
S
]
Inherited from:
ShadowMultiplicativeCMonoid
implicit
val
shadowing
:
Shadowing
[
A
,
S
]
Inherited from:
ShadowMultiplicativeCSemigroup