# Bijective reflections meeting
> [name=Stéphane Breuils][color=#907bf7]

###### tags `slides` `geometric algebra` `bijective reflections`

## Meeting February 22nd : bijective reflections
### slides and abstract of the meeting
https://gacv.slides.com/sbreuils/meeting2024_02_20_reflections?token=nAhls8bK
#### Overview
- [x] Remember the problem of Bijectivity characterisation in 3D : what I am exploring
- [x] Primitive Pythagorean quadruple
- [x] certification algorithm

#### Next time
For next time (March 13th),
- [x] adapt the matrix A in the certification algorithm for digitized reflection with the reduced set of remainders
- [x] for a few normal vectors inside $\Delta$, try to express samples of the reduced set of remainders in the symetric difference of the two cells $C1$ and $Cm$

### pour réunion avec Yukiko et Tristan (mardi,mercredi)
- [ ] Finir la lecture du papier pour Tristan et Yukiko
- [ ] se souvenir de la décomposition Hermite Normal Form : HNF
- [ ] se souvenir de quel sous-ensemble de réflection bijective, on voulait discuter :
Le sous ensemble des vecteurs normaux $\mathbf{m}$ where $\mathbf{m} = a \mathbf{e}_1 + b \mathbf{e}_2 + c \mathbf{e}_3$ with
$$
a=k ; b= k+q; c= 2k+q, 2 \leq q <k
$$
Décomposition