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algebird
Ring
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trait Ring
|
package algebird
object
Ring
extends
GeneratedRingImplicits
with
ProductRings
with
Serializable
Source
Ring.scala
Linear Supertypes
Serializable
,
Serializable
,
ProductRings
,
GeneratedRingImplicits
,
AnyRef
,
Any
Ordering
Alphabetic
By Inheritance
Inherited
Ring
Serializable
Serializable
ProductRings
GeneratedRingImplicits
AnyRef
Any
Hide All
Show All
Visibility
Public
All
Value Members
final
def
!=
(
arg0:
Any
)
:
Boolean
Definition Classes
AnyRef → Any
final
def
##
()
:
Int
Definition Classes
AnyRef → Any
final
def
==
(
arg0:
Any
)
:
Boolean
Definition Classes
AnyRef → 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
val
bigDecimalRing
:
Ring
[
BigDecimal
]
implicit
val
bigIntRing
:
Ring
[
BigInt
]
implicit
val
boolRing
:
Ring
[
Boolean
]
def
clone
()
:
AnyRef
Attributes
protected[
java.lang
]
Definition Classes
AnyRef
Annotations
@throws
(
...
)
implicit
val
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
val
floatRing
:
Ring
[
Float
]
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
val
intRing
:
Ring
[
Int
]
final
def
isInstanceOf
[
T0
]
:
Boolean
Definition Classes
Any
implicit
val
jboolRing
:
Ring
[
Boolean
]
implicit
val
jdoubleRing
:
Ring
[
Double
]
implicit
val
jfloatRing
:
Ring
[
Float
]
implicit
val
jintRing
:
Ring
[
Integer
]
implicit
val
jlongRing
:
Ring
[
Long
]
implicit
val
jshortRing
:
Ring
[
Short
]
implicit
val
longRing
:
Ring
[
Long
]
implicit
def
mapRing
[
K
,
V
]
(
implicit
ring:
Ring
[
V
]
)
:
MapRing
[
K
,
V
]
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
]
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
]
)
:
ScMapRing
[
K
,
V
]
implicit
val
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
ProductRings
Inherited from
GeneratedRingImplicits
Inherited from
AnyRef
Inherited from
Any
Ungrouped