com
.
twitter
.
algebird
Ring
object
Ring
extends
GeneratedRingImplicits
with
ProductRings
with
RingImplicits0
with
Serializable
Linear Supertypes
Serializable
,
Serializable
,
RingImplicits0
,
NumericRingProvider
,
ProductRings
,
GeneratedRingImplicits
,
AnyRef
,
Any
Ordering
Alphabetic
By inheritance
Inherited
Ring
Serializable
Serializable
RingImplicits0
NumericRingProvider
ProductRings
GeneratedRingImplicits
AnyRef
Any
Hide All
Show all
Learn more about member selection
Visibility
Public
All
Value Members
final
def
!=
(
arg0:
AnyRef
)
:
Boolean
Definition Classes
AnyRef
final
def
!=
(
arg0:
Any
)
:
Boolean
Definition Classes
Any
final
def
##
()
:
Int
Definition Classes
AnyRef → Any
final
def
==
(
arg0:
AnyRef
)
:
Boolean
Definition Classes
AnyRef
final
def
==
(
arg0:
Any
)
:
Boolean
Definition Classes
Any
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
,
T
,
U
,
V
]
(
applyX: (
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
,
T
,
U
,
V
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
,
T
,
U
,
V
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
,
oring:
Ring
[
O
]
,
pring:
Ring
[
P
]
,
qring:
Ring
[
Q
]
,
rring:
Ring
[
R
]
,
sring:
Ring
[
S
]
,
tring:
Ring
[
T
]
,
uring:
Ring
[
U
]
,
vring:
Ring
[
V
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
,
T
,
U
]
(
applyX: (
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
,
T
,
U
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
,
T
,
U
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
,
oring:
Ring
[
O
]
,
pring:
Ring
[
P
]
,
qring:
Ring
[
Q
]
,
rring:
Ring
[
R
]
,
sring:
Ring
[
S
]
,
tring:
Ring
[
T
]
,
uring:
Ring
[
U
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
,
T
]
(
applyX: (
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
,
T
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
,
T
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
,
oring:
Ring
[
O
]
,
pring:
Ring
[
P
]
,
qring:
Ring
[
Q
]
,
rring:
Ring
[
R
]
,
sring:
Ring
[
S
]
,
tring:
Ring
[
T
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
]
(
applyX: (
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
,
oring:
Ring
[
O
]
,
pring:
Ring
[
P
]
,
qring:
Ring
[
Q
]
,
rring:
Ring
[
R
]
,
sring:
Ring
[
S
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
]
(
applyX: (
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
,
oring:
Ring
[
O
]
,
pring:
Ring
[
P
]
,
qring:
Ring
[
Q
]
,
rring:
Ring
[
R
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
]
(
applyX: (
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
,
oring:
Ring
[
O
]
,
pring:
Ring
[
P
]
,
qring:
Ring
[
Q
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
]
(
applyX: (
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
,
oring:
Ring
[
O
]
,
pring:
Ring
[
P
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
]
(
applyX: (
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
,
oring:
Ring
[
O
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
]
(
applyX: (
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
]
(
applyX: (
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
]
(
applyX: (
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
]
(
applyX: (
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
]
(
applyX: (
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
]
(
applyX: (
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
]
(
applyX: (
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
,
F
,
G
]
(
applyX: (
A
,
B
,
C
,
D
,
E
,
F
,
G
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
,
F
]
(
applyX: (
A
,
B
,
C
,
D
,
E
,
F
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
,
F
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
,
E
]
(
applyX: (
A
,
B
,
C
,
D
,
E
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
,
E
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
,
D
]
(
applyX: (
A
,
B
,
C
,
D
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
,
D
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
,
C
]
(
applyX: (
A
,
B
,
C
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
,
C
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
def
apply
[
X
,
A
,
B
]
(
applyX: (
A
,
B
) ⇒
X
,
unapplyX: (
X
) ⇒
Option
[(
A
,
B
)]
)
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
)
:
Ring
[
X
]
Definition Classes
ProductRings
final
def
asInstanceOf
[
T0
]
:
T0
Definition Classes
Any
def
asTimesMonoid
[
T
]
(
implicit
ring:
Ring
[
T
]
)
:
Monoid
[
T
]
implicit
def
bigIntRing
:
Ring
[
BigInt
]
implicit
def
boolRing
:
Ring
[
Boolean
]
def
clone
()
:
AnyRef
Attributes
protected[
java.lang
]
Definition Classes
AnyRef
Annotations
@throws
(
...
)
implicit
def
doubleRing
:
Ring
[
Double
]
final
def
eq
(
arg0:
AnyRef
)
:
Boolean
Definition Classes
AnyRef
def
equals
(
arg0:
Any
)
:
Boolean
Definition Classes
AnyRef → Any
def
finalize
()
:
Unit
Attributes
protected[
java.lang
]
Definition Classes
AnyRef
Annotations
@throws
(
classOf[java.lang.Throwable]
)
implicit
def
floatRing
:
Ring
[
Float
]
implicit
def
fromAlgebraRing
[
T
]
(
implicit
r:
algebra.ring.Ring
[
T
]
)
:
Ring
[
T
]
Definition Classes
RingImplicits0
final
def
getClass
()
:
Class
[_]
Definition Classes
AnyRef → Any
def
hashCode
()
:
Int
Definition Classes
AnyRef → Any
implicit
def
indexedSeqRing
[
T
]
(
implicit
arg0:
Ring
[
T
]
)
:
Ring
[
IndexedSeq
[
T
]]
implicit
def
intRing
:
Ring
[
Int
]
final
def
isInstanceOf
[
T0
]
:
Boolean
Definition Classes
Any
implicit
def
jboolRing
:
Ring
[
Boolean
]
implicit
def
jdoubleRing
:
Ring
[
Double
]
implicit
def
jfloatRing
:
Ring
[
Float
]
implicit
def
jintRing
:
Ring
[
Integer
]
implicit
def
jlongRing
:
Ring
[
Long
]
implicit
def
jshortRing
:
Ring
[
Short
]
implicit
def
longRing
:
Ring
[
Long
]
implicit
def
mapRing
[
K
,
V
]
(
implicit
ring:
Ring
[
V
]
)
:
Ring
[
Map
[
K
,
V
]]
This is actually a Rng but we leave the unsafe Ring for legacy reasons
final
def
ne
(
arg0:
AnyRef
)
:
Boolean
Definition Classes
AnyRef
final
def
notify
()
:
Unit
Definition Classes
AnyRef
final
def
notifyAll
()
:
Unit
Definition Classes
AnyRef
implicit
def
numericRing
[
T
]
(
implicit
arg0:
Numeric
[
T
]
)
:
Ring
[
T
]
Definition Classes
NumericRingProvider
def
one
[
T
]
(
implicit
rng:
Ring
[
T
]
)
:
T
def
product
[
T
]
(
iter:
TraversableOnce
[
T
]
)
(
implicit
ring:
Ring
[
T
]
)
:
T
def
productOption
[
T
]
(
it:
TraversableOnce
[
T
]
)
(
implicit
rng:
Ring
[
T
]
)
:
Option
[
T
]
implicit
def
ring10
[
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring11
[
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring12
[
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring13
[
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring14
[
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring15
[
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
,
oring:
Ring
[
O
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring16
[
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
,
oring:
Ring
[
O
]
,
pring:
Ring
[
P
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring17
[
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
,
oring:
Ring
[
O
]
,
pring:
Ring
[
P
]
,
qring:
Ring
[
Q
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring18
[
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
,
oring:
Ring
[
O
]
,
pring:
Ring
[
P
]
,
qring:
Ring
[
Q
]
,
rring:
Ring
[
R
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring19
[
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
,
oring:
Ring
[
O
]
,
pring:
Ring
[
P
]
,
qring:
Ring
[
Q
]
,
rring:
Ring
[
R
]
,
sring:
Ring
[
S
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring2
[
A
,
B
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
)
:
Ring
[(
A
,
B
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring20
[
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
,
T
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
,
oring:
Ring
[
O
]
,
pring:
Ring
[
P
]
,
qring:
Ring
[
Q
]
,
rring:
Ring
[
R
]
,
sring:
Ring
[
S
]
,
tring:
Ring
[
T
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
,
T
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring21
[
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
,
T
,
U
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
,
oring:
Ring
[
O
]
,
pring:
Ring
[
P
]
,
qring:
Ring
[
Q
]
,
rring:
Ring
[
R
]
,
sring:
Ring
[
S
]
,
tring:
Ring
[
T
]
,
uring:
Ring
[
U
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
,
T
,
U
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring22
[
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
,
T
,
U
,
V
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
,
jring:
Ring
[
J
]
,
kring:
Ring
[
K
]
,
lring:
Ring
[
L
]
,
mring:
Ring
[
M
]
,
nring:
Ring
[
N
]
,
oring:
Ring
[
O
]
,
pring:
Ring
[
P
]
,
qring:
Ring
[
Q
]
,
rring:
Ring
[
R
]
,
sring:
Ring
[
S
]
,
tring:
Ring
[
T
]
,
uring:
Ring
[
U
]
,
vring:
Ring
[
V
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
,
J
,
K
,
L
,
M
,
N
,
O
,
P
,
Q
,
R
,
S
,
T
,
U
,
V
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring3
[
A
,
B
,
C
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
)
:
Ring
[(
A
,
B
,
C
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring4
[
A
,
B
,
C
,
D
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
)
:
Ring
[(
A
,
B
,
C
,
D
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring5
[
A
,
B
,
C
,
D
,
E
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring6
[
A
,
B
,
C
,
D
,
E
,
F
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
,
F
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring7
[
A
,
B
,
C
,
D
,
E
,
F
,
G
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring8
[
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
)]
Definition Classes
GeneratedRingImplicits
implicit
def
ring9
[
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
]
(
implicit
aring:
Ring
[
A
]
,
bring:
Ring
[
B
]
,
cring:
Ring
[
C
]
,
dring:
Ring
[
D
]
,
ering:
Ring
[
E
]
,
fring:
Ring
[
F
]
,
gring:
Ring
[
G
]
,
hring:
Ring
[
H
]
,
iring:
Ring
[
I
]
)
:
Ring
[(
A
,
B
,
C
,
D
,
E
,
F
,
G
,
H
,
I
)]
Definition Classes
GeneratedRingImplicits
implicit
def
scMapRing
[
K
,
V
]
(
implicit
ring:
Ring
[
V
]
)
:
Ring
[
Map
[
K
,
V
]]
This is actually a Rng but we leave the unsafe Ring for legacy reasons
implicit
def
shortRing
:
Ring
[
Short
]
final
def
synchronized
[
T0
]
(
arg0: ⇒
T0
)
:
T0
Definition Classes
AnyRef
def
times
[
T
]
(
l:
T
,
r:
T
)
(
implicit
rng:
Ring
[
T
]
)
:
T
def
toString
()
:
String
Definition Classes
AnyRef → Any
final
def
wait
()
:
Unit
Definition Classes
AnyRef
Annotations
@throws
(
...
)
final
def
wait
(
arg0:
Long
,
arg1:
Int
)
:
Unit
Definition Classes
AnyRef
Annotations
@throws
(
...
)
final
def
wait
(
arg0:
Long
)
:
Unit
Definition Classes
AnyRef
Annotations
@throws
(
...
)
Inherited from
Serializable
Inherited from
Serializable
Inherited from
RingImplicits0
Inherited from
NumericRingProvider
Inherited from
ProductRings
Inherited from
GeneratedRingImplicits
Inherited from
AnyRef
Inherited from
Any
Ungrouped