** suivant:** Find the matrix of
** monter:** Isometries
** précédent:** Isometries
** Table des matières**
** Index**

##

Recognize an isometry : `isom`

`isom` takes as argument the matrix of an linear
application in dimension 2 or 3.

`isom` returns :
- if the linear application is a direct isometry,

the list of the characteristic elements of this isometry and `+1`,
- if the linear application is an indirect isometry,

the list of the characteristic elements of this isometry and `-1`
- if the linear application is not an isometry,

`[0]`.

Input :
`isom([[0,0,1],[0,1,0],[1,0,0]])`

Output :
`[[1,0,-1],-1]`

which means that this isometry is a 3-d symmetry with respect to the plane
*x* - *z* = 0.

Input :
`isom(sqrt(2)/2*[[1,-1],[1,1]])`

Output :
`[pi/4,1]`

Hence, this isometry is a 2-d rotation of angle
.

Input :
`isom([[0,0,1],[0,1,0],[0,0,1]])`

Output :
`[0]`

therefore this transformation is not an isometry.

giac documentation written by Renée De Graeve and Bernard Parisse