def in_the_arc(x): """ helper for hadamard decomp. """ return -2 / (jnp.sqrt(3 + jnp.cos(pi * x)))
def in_the_arc(x): return -2 / (jnp.sqrt(3 + jnp.cos(pi * x)))
def top_right_in(x): """ helper for hadamard decomp. """ return ((3 + jnp.cos(pi * x)) * (jnp.sin(pi * x / 2)**2))**(1 / 4)
def top_right_in(x): return ((3 + jnp.cos(pi * x)) * (jnp.sin(pi * x / 2)**2))**(1 / 4)