# r2_tori_direct.py: the map of Remark 4.12 computed from its definition on the coefficients of the 12-dimensional representation
tori zxz   group Z*Z  : the 144 coefficients of V_1 (x) z (x) V_2 (x) z^-1 (x) V_1 are mapped to elements supported on 1128 group elements of Lambda^3; rank over Q of the 144 images = 142; kernel dimension 2   [0.0s]
      Phi(a z w z^-1 a* - a* z w z^-1 a) = 0;   Phi(g* z w z^-1 g - g z w z^-1 g*) = 0
tori zxzx  group Z*Z  : the 144 coefficients of V_1 (x) z (x) V_2 (x) z^-1 (x) V_1 are mapped to elements supported on 11264 group elements of Lambda^4; rank over Q of the 144 images = 144; kernel dimension 0   [1.4s]
      Phi(a z w z^-1 a* - a* z w z^-1 a) != 0 (320 terms);   Phi(g* z w z^-1 g - g z w z^-1 g*) != 0 (320 terms)
tori xzx   group Z*Z  : the 144 coefficients of V_1 (x) z (x) V_2 (x) z^-1 (x) V_1 are mapped to elements supported on 1128 group elements of Lambda^3; rank over Q of the 144 images = 142; kernel dimension 2   [1.7s]
      Phi(a z w z^-1 a* - a* z w z^-1 a) != 0 (320 terms);   Phi(g* z w z^-1 g - g z w z^-1 g*) != 0 (320 terms)
tori zxz   group Z_2*Z: the 144 coefficients of V_1 (x) t (x) V_2 (x) t^1 (x) V_1 are mapped to elements supported on 1128 group elements of Lambda^3; rank over Q of the 144 images = 142; kernel dimension 2   [0.0s]
      Phi(a t w t^1 a* - a* t w t^1 a) = 0;   Phi(g* t w t^1 g - g t w t^1 g*) = 0
tori zxzx  group Z_2*Z: the 144 coefficients of V_1 (x) t (x) V_2 (x) t^1 (x) V_1 are mapped to elements supported on 11264 group elements of Lambda^4; rank over Q of the 144 images = 144; kernel dimension 0   [1.4s]
      Phi(a t w t^1 a* - a* t w t^1 a) != 0 (320 terms);   Phi(g* t w t^1 g - g t w t^1 g*) != 0 (320 terms)
