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AndrewVSutherland
GitHub Repository: AndrewVSutherland/lmfdb
 Path: blob/main/scripts/belyi/format_plane_model.py
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from sage.all import PolynomialRing, NumberField, QQ, gcd, latex, factor

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import re

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RE_EXP = r"\^(\d+)"

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def bracket_me(m):

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    return "^{%s}" % (m.group(0)).split("^")[1]

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def fix_brackets(rec):

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    if rec.get('plane_model_latex'):

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        latex = rec['plane_model_latex']

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        latex = re.sub(RE_EXP, bracket_me,latex)

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        rec['plane_model_latex'] = latex

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    return rec

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def plane_map_constant(rec):

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    R = PolynomialRing(QQ, 'x')

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    K = NumberField(R(rec['base_field']), 'nu')

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    if rec.get('plane_constant'):

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        a = K(rec['plane_constant'])

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        rec['plane_map_constant'] = 1/a

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    return rec

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def plane_map_constant_factored(rec):

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    R = PolynomialRing(QQ, 'x')

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    K = NumberField(R(rec['base_field']), 'nu')

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    if rec.get('plane_constant'):

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        a = K(rec['plane_constant'])

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        a = 1/a

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        if a == 1:

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            rec['plane_map_constant_factored'] = ''

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        else:

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            d = a.denominator()

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            num = a*d

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            num_list = num.list()

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            n = gcd(num_list)

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            num_list = [el/n for el in num_list]

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            poly = K(num_list)

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            # now LaTeX everything

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            s = ''

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            if a in QQ:

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                s = '-' if a.sign()==-1 else '' # if a in QQ, keep track of sign

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                poly_lat = ''

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            else:

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                if ("+" in str(poly)) or ("-" in str(poly)):

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                    poly_lat = "(%s)" % latex(poly)

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                else:

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                    poly_lat = latex(poly)

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            if d == 1:

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                rec['plane_map_constant_factored'] = "%s" % (latex(factor(n))+poly_lat)

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            else:

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                rec['plane_map_constant_factored'] = r"%s\frac{%s}{%s}%s" % (s,latex(factor(n)), latex(factor(d)), poly_lat)

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    return rec

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def pretty_print_factor(f):

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    d = f.denominator()

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    if d == 1:

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        return (f.factor())

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    else:

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        n = f.numerator().factor()

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        return ('({})/({})'.format(n, d.factor()))

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