ecpp_class_poly_tower, _ecpp_class_poly_tower

A composition series of the class group with prime quotients p_i gives a tower of fields with relative polynomials, whose coefficients are stored in Hecke form (numerators over the derivative of the polynomial of the level below, so that all coefficients are integers) and computed numerically from the j-values ordered by cosets. Modulo n, a root is found level by level in degrees p_i instead of h. For even D, the values of Weber's function \mathfrak f (a class invariant whose class polynomial has height 72/e times smaller than that of j, with the normalisations of Enge's CM library [EngeCM; Schertz2002; YuiZagier1997]) are used instead of j, and j is recovered from the root modulo n by a closed formula. The Lagrange numerators are built by a subproduct tree, so that about 1.5 times the height of the class polynomial suffices as precision. For odd D the caller may pass 4D: the order of conductor 2 has the same class field (for D \equiv 1 \pmod 8; three times the class number for D \equiv 5 \pmod 8) and admits Weber's function, and its curves have the right order when v is even. Levels of prime degree p \ge 5 also carry Kummer data (the p-th power of the Lagrange resolvent and the ratios of the resolvents, as elements of the level below tensored with \mathbb{Q}(\zeta_p)), so that when p \mid n \pm 1 the level is descended with one p-th root instead of a root of a polynomial of degree p.