Analytic Hyperbolic Geometry: Mathematical Foundations and Applications

| ? | Gyroaddition, Gyrogroup operation. |
| ? | Gyrosubtraction, Inverse gyrogroup operation. |
| ? | Cogyroaddition, Gyrogroup cooperation. |
| ? | Cogyrosubtraction, Inverse gyrogroup cooperation . |
| ? E | Einstein addition (of relativistically admissible coordinate velocities, and generalizations). |
| ? E | Einstein subtraction. |
| ? E | Einstein coaddition. |
| ? E | Einstein cosubtraction. |
| ? M | M bius addition. |
| ? M | M bius subtraction. |
| ? M | M bius coaddition. |
| ? M | M bius cosubtraction. |
| ? U | PV addition (of relativistically admissible proper velocities, and generalizations). |
| ? U | PV subtraction. |
| ? U | PV coaddition. |
| ? U | PV cosubtraction. |
| ? | Scalar multiplication (scalar gyromultiplication) in a gyrovector space. |
| ? E | Einstein scalar multiplication. |
| ? M | M bius scalar multiplication. |
| ? U | PV scalar multiplication. |
| | Gyropolygonal gyroaddition, Definition 2.13. |
| ab | A segment with distinct endpoints a and b of (i) a gyroline (gyrosegment), or (ii) a cogyroline (cogyrosegment). A gyroline (cogyroline) containing the distinct points a and b. |
| ab | Length of (i) a gyrosegment (gyrolength), or (ii) a cogyrosegment (cogyrolength). |
| abc | A gyrotriangle with vertices a, b and c. |
| a | a = ? a ? is the gyrolength of gyrovector a. |
| a s | a s = a/s in a gyrovector space ( |
| Aut | An automorphism group. |
| Aut 0 | A subgroup of an automorphism group. |
| CM | Center of momentum. |
| c | The vacuum speed of light, |
| gyr | Gyrator. gyr[ a, b] the gyration (gyroautomorphism) generated by a and b. |
| s | Gyrovector space analogue of the vacuum speed of light |