WebHMF.py

import math
import logging
import re
from lmfdb.utils import pair2complex, splitcoeff

class WebHMF:
    """Class for presenting a Hilbert modular form on a web page

    """

    def __init__(self, dict):
        self.type = dict['type']
        self.coefficient_period = 0
        self.poles = []
        self.residues = []
        self.kappa_fe = []
        self.lambda_fe = []
        self.mu_fe = []
        self.nu_fe = []
        self.langlands = True

        if self.type == 'lcalcurl':
            from six.moves.urllib.request import urlopen
            self.url = dict['url']
            self.contents = urlopen(self.url).read()
            self.parseLcalcfile_ver1()

        elif self.type == 'lcalcfile':
            self.contents = dict['filecontents']
            self.parseLcalcfile_ver1()

        elif self.type == 'modularform':
            self.level = dict['level']
            self.weight = dict['weight']
            logging.info('My level is ' + self.level + ' and my weight is' + self.weight)

        else:
            raise KeyError

        """
        self.coefficient_type: 1 = integer, 2 = double, 3 = complex
        self.ceofficient_period:  0 = non-periodic
        self.sageLfunction = lc.Lfunction_C(self.title, self.coefficient_type, self.dirichlet_coefficients, self.ceofficient_period, self.Q_fe, self.sign , self.kappa_fe, self.lambda_fe ,self.poles, self.residues)
        """

    def parseLcalcfile_ver1(self):
        lines = self.contents.split('\n', 6)
        self.coefficient_type = int(lines[0])
        self.quasidegree = int(lines[4])
        lines = self.contents.split('\n', 8 + 2 * self.quasidegree)
        self.Q_fe = float(lines[5 + 2 * self.quasidegree])
        self.sign = pair2complex(lines[6 + 2 * self.quasidegree])

        for i in range(self.quasidegree):
            localdegree = float(lines[5 + 2 * i])
            self.kappa_fe.append(localdegree)
            locallambda = pair2complex(lines[6 + 2 * i])
            self.lambda_fe.append(locallambda)
            if math.fabs(localdegree - 0.5) < 0.00001:
                self.mu_fe.append(2 * locallambda)
            elif math.fabs(localdegree - 1) < 0.00001:
                self.nu_fe.append(locallambda)
            else:
                self.nu_fe.append(locallambda)
                self.langlands = False

        """ Do poles here later
        """

        self.degree = round(2 * sum(self.kappa_fe))
        self.level = round(math.pi ** self.degree * 4 ** len(self.nu_fe) * self.Q_fe ** 2)

        self.dirichlet_coefficients = splitcoeff(lines[-1])

        originalfile = re.match(".*/([^/]+)$", self.url)
        originalfile = originalfile.group(1)
#        self.title = "An L-function generated by an Lcalc file: "
        self.title = "An L-function generated by an Lcalc file: " + originalfile
        self.credit = "David Farmer, Sally Koutsoliotas and Stefan Lemurell"


## Sep 2018, really no longer used
## July 2015. no longer used.  delete later
##    def lfuncDStex(self, fmt):
##        numperline = 5
##        numcoeffs = 10
##        ans = ""
##        if fmt == "analytic":
##            ans = "\\begin{align}\n"
##            ans = ans + latex(self.dirichlet_coefficients[0]) + "\\mathstrut&"
##            for n in range(1, numcoeffs):
##                ans = ans + seriescoeff(self.dirichlet_coefficients[n], n + 1, "dirichlet", 0.000000001)
##                if(n % numperline == 0):
##                    ans = ans + "\\cr\n"
##                    ans = ans + "&"
##            ans = ans + "\\cdots\n\\end{align}"
##        return(ans)
#
##===========================
#    def lfuncFEtex(self, fmt):
#        ans = ""
#        if fmt == "lang":
#            ans = "\\begin{align}\n\\Lambda(s)=&"
#            ans = ans + latex(self.level) + "^{-\\frac{s}{2}}"
#            for mu in self.mu_fe:
#                ans = ans + "\Gamma_{\mathbb{R}}(s+" + latex(mu) + ")"
#            for nu in self.nu_fe:
#                ans = ans + "\Gamma_{\mathbb{C}}(s+" + latex(nu) + ")"
#            ans = ans + "\\cdot L(s)\\cr\n"
#            ans = ans + "=\\mathstrut & " + latex(self.sign) +\
#                "\\overline{\\Lambda(1-\\overline{s})}\n\\end{align}\n"
#        return(ans)

#===========================
    def lfuncFEtex(self, fmt):
        ans = ""
        if fmt == "lang":
            ans = "\\begin{aligned}\n\\Lambda(s)=&"
            ans = ans + latex(self.level) + "^{-\\frac{s}{2}}"
            for mu in self.mu_fe:
                ans = ans + r"\Gamma_{\mathbb{R}}(s+" + latex(mu) + ")"
            for nu in self.nu_fe:
                ans = ans + r"\Gamma_{\mathbb{C}}(s+" + latex(nu) + ")"
            ans = ans + "\\cdot L(s)\\cr\n"
            ans = ans + "=\\mathstrut & " + latex(self.sign) +\
                "\\overline{\\Lambda(1-\\overline{s})}\n\\end{aligned}\n"
        return(ans)


def latex(thetext):
    return str(thetext)


def seriescoeff(coeff, index, seriestype, truncation):
    rp = real_part(coeff)
    ip = imag_part(coeff)
# below we use float(abs()) instead of abs() to avoid a sage bug
    if (float(abs(rp)) > truncation) & (float(abs(ip)) > truncation):
        return("+(" + latex(coeff) + ")" + seriesvar(index, seriestype))
    elif (float(abs(rp)) < truncation) & (float(abs(ip)) < truncation):
        return("")
# if we get this far, either pure real or pure imaginary
    if rp > truncation:
        if float(abs(rp - 1)) < truncation:
            return("+" + seriesvar(index, seriestype))
        else:
            return("+" + latex(rp) + seriesvar(index, seriestype))
    elif float(abs(rp + 1)) < truncation:
        return("-" + seriesvar(index, seriestype))
    elif ip > truncation:
        if float(abs(ip - 1)) < truncation:
            return("+" + seriesvar(index, seriestype))
        else:
            return("+" + latex(ip) + seriesvar(index, seriestype))
    elif float(abs(ip + 1)) < truncation:
        return("-" + seriesvar(index, seriestype))
    else:
        return(latex(coeff) + seriesvar(index, seriestype))

#---------


def seriesvar(index, seriestype):
    if seriestype == "dirichlet":
        return(" \\ " + str(index) + "^{-s}")
    else:
        return("\\, " + "q^{" + str(index) + "}")


def real_part(pair):
    return pair[0]


def imag_part(pair):
    return pair[1]