# Classify user-given basis functions into irreducible representations
# (polar x, y, z / axial Rx, Ry, Rz / any polynomial combination)

crystod-group --basis x y z --point-group m-3m

* Point group *
m-3m

* Input basis functions *
 x, y, z

* Closed basis-function space *
 dimension: 3
 basis: [x, y, z]

* Reducible characters *
  E: 3
  C3: 0
  C2: -1
  C4: 1
  C4^2: -1
  i: -3
  S4: -1
  S6: 0
  sgh: 1
  sgd: 1

* Decomposition *
 1.0 [T1u]

* Irreducible representations for basis functions *
  T1u: [x, y, z]



# Axial vectors (magnetic moments) transform as T1g, not T1u
crystod-group --basis Rx Ry Rz --point-group m-3m

* Point group *
m-3m

* Input basis functions *
 Rx, Ry, Rz

* Closed basis-function space *
 dimension: 3
 basis: [Rx, Ry, Rz]

* Reducible characters *
  E: 3
  C3: 0
  C2: -1
  C4: 1
  C4^2: -1
  i: 3
  S4: 1
  S6: 0
  sgh: -1
  sgd: -1

* Decomposition *
 1.0 [T1g]

* Irreducible representations for basis functions *
  T1g: [Rx, Ry, Rz]



# Space-group mode: classify at a k point of the little group
crystod-group --basis x y z --space-group Pm-3m --kpoint 0 0 0

* Space group *
Pm-3m (221)

* Little group of k *
Pm-3m (221)

* k-point (primitive) *
 GM [0.0, 0.0, 0.0]

* Input basis functions *
 x, y, z

* Closed basis-function space *
 dimension: 3
 basis: [x, y, z]

* Little-group characters *
 (48 operations, omitted here -- run the command to see them)

* Decomposition *
 1.0 [GM4-(3)]

* Irreducible representations for basis functions *
  GM4-(3): [x, y, z]



# Without --kpoint, all special k points are analyzed in one run
crystod-group --basis Rx Ry Rz --space-group Pm-3m
