Class P_to_H_map

An instance of this class encapsulates data about a cromulent isomorphism $PX(a_P)\to HX(a_H)$ for some specific numerical values of $a_H$ and $a_P$

The degree of polynomials used for approximate power series.

This is the number $d$ that enters into the formula for the schwarzian derivative of $p^{-1}$

Table containing the points $\psi^{-1}(v_{Hi})$

Table containing the points $\phi(v_{Pi})$

Table containing the curves $\psi^{-1}(c_{Hi}(t))$

Table containing the curves $\phi(c_{Pi}(t))$

The coefficient of $z$ in $p_1^{-1}(z)$

Set the a_H field and perform associated bookkeeping. Normally one should only use the set_a_P method directly; then other code will calculate an appropriate value for a_H and call the set_a_H method.

Set the a_H field and perform associated bookkeeping.

Create and add a new chart centred at z0

Create and add $2n+1$ new charts. Of these, one is centred at the origin, $n$ are centred at equally spaced points between $0$ and $i$, and $n$ are centred at equally spaed points between $0$ and test_point.

This sets the d field, then sets the M fields of all charts based on that, then calculates c and a_H and p1_inv as described in the text. It returns an error term, which should be zero if we have the correct value of d.

This calls the set_d method repeatedly with different values of d, searching for the value that makes the set_d error term equal to zero. It also sets the fields c, a_H and p1_inv.

This sets the p1 field based on the p1_inv field.

This generates a plot of the logs of the absolute values of the coefficients of the power series for $p_1(z)$

This generates a plot of the logs of the absolute values of the coefficients of the power series for $p^{-1}_1(z)$