trait Torsor[V, R] extends Action[V, R]
A Torsor[V, R] requires an AbGroup[R] and provides Action[V, R],
plus a diff
operator, <->
in additive notation, such that:
1. (g <-> g) === scalar.id
for all g
in G
.
2. (g <-> h) +> h === g
for all g
, h
in G
.
3. (g <-> h) +> i === (i <-> h) +> g
for all g
, h
in G
.
4. (g <-> h) === -(h <-> g)
for all g
, h
in G
.
- Self Type
- Torsor[V, R]
Linear Supertypes
Ordering
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Inherited
- Torsor
- Action
- RightAction
- LeftAction
- Any
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Visibility
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Abstract Value Members
-
abstract
def
actl(g: R, p: V): V
- Definition Classes
- LeftAction
-
abstract
def
actr(p: V, g: R): V
- Definition Classes
- RightAction
- abstract def diff(v: V, w: V): R
-
abstract
def
getClass(): Class[_]
- Definition Classes
- Any
Concrete Value Members
-
final
def
!=(arg0: Any): Boolean
- Definition Classes
- Any
-
final
def
##(): Int
- Definition Classes
- Any
-
final
def
==(arg0: Any): Boolean
- Definition Classes
- Any
-
final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
-
def
equals(arg0: Any): Boolean
- Definition Classes
- Any
- def fixOrigin(id0: V): AbGroup[V]
-
def
hashCode(): Int
- Definition Classes
- Any
-
final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
-
def
toString(): String
- Definition Classes
- Any