$\frac{A}{|A|} \in U(1)$

q_graph -dir vp -out group_u1 -loop 0 -box 1.1 -command "g_u1 1 2 3 4 1000"

$exp(A - A^*)\in SU(2)$

q_graph -dir vp -out group_SU2 -loop 0 -box 1.1 -command 'q_random_n_11 50000 | q_vector | q_exp'

$(\frac{A}{|A|} exp(A - A^*))^* \frac{B}{|B|} exp(B - B^*) \in SU(3)$

q_graph -dir vp -out group_su3 -loop 0 -box 1.1 -command q_group -group U1xSU2xSU3 -n 50000

$\frac{A}{|A|} exp(A - A^*) \in U(1) \times SU(2)$

q_graph -dir vp -out group_u1xsu2 -loop 0 -box 1.1 -command 'q_group -group U1xSU2 -n 20000'

for the circle: $\frac{q}{\sqrt{q q*}} = \frac{(t, \vec{R})}{t^2 + R^2}$
for the hyperbola: $\frac{q}{\sqrt{\pm scalar(q q)}} = \frac{(t, \vec{R})}{t^2 - R^2}$

q_graph -box 3 -dir trig -out circle -command 'g_u1_n 4 1 2 3 1000' -color yello -command 'g_u1h_n 4 1 2 3 4000' -color red [note: the function for generating the hyperbola has not been released, and its name will probably change]

permutations of $(\pm 1, \pm 1, \pm 1, \pm 1)$

q_graph -out 4D_wire_cube -dir vp -loop 0 -box 1.1 -meta_command generate_cube

$(t, \vec{R}) \rightarrow (t', R') = (\frac{t}{\sqrt{1 - \beta^2}} - \frac{\vec{\beta} \cdot \vec{R}}{\sqrt{1 - \beta^2}},\vec{R} \times \frac{\vec{V}}{|V|} + \frac{1}{\sqrt{1 - \beta^2}}(\vec{R} - \vec{R} \times \frac{\vec{V}}{|V|} - \vec{\beta} t))$

q_graph -out boost -dir vp -loop 0 -box 4 -command 'q_add_n -5 -5 -5 -5 0.010 0.010 0.010 0.010 1000' -color yellow -command 'q_add_n -5 -5 -5 -5 0.010 0.010 0.010 0.010 1000 |q_boost -vx .5' -color blue -command 'q_add_n -5 -5 -5 -5 0.010 0.010 0.010 0.010 1000 | q_boost -vx .3 -vy .4' -color red

$( 1 | i | j | k) (t,x,y,z) ( 1 | i | j | k)$

q_graph -out gamma -dir gamma -box 2.5 -loop 0 -command 'q_add_n 2.9 3.1 3.2 2.8 -0.006 -0.0059 -0.0061 -0.0062 1000' -color yellow -command 'q_add_n 2.9 3.1 3.2 2.8 -0.006 -0.0059 -0.0061 -0.0062 1000| gamma -almost' -color blue

$\phi = (cos(\omega t + \delta), sin(\omega t + \delta), k \delta, 0) \, \textrm{with} \, \delta: 0 \to 10 \pi$

q_graph -out amp_shifted -dir int14 -box 1.6 -command 't_function -t_func cos -x_func sin -y_func zero -z_func zero -n_steps 1000 -pi 10 -n_t_cycles 1000 -n_t_step 0.0314 1 1 0 0 | q_add 0 0 -1.5 0 | q_add_n_m 0 0 0.003 0 1000 1000' -color yellow

$\phi = (cos(\omega t), sin(\omega t), 0, 0)$

q_graph -out amp -dir int10 -box 1.6 -command 't_function -t_function cos -x_function sin -y_function zero -z_function zero -n_steps 199 -pi 4 -n_t_cycles 300 -n_t_step 0 1 1 0 0' -color yellow