#!/usr/bin/python

# elliptic.py
# (c) William Stein, 2000

import cgi  # cgi-bin
import Documents, HTML

import misc 
import constants
# import mfd  # modular forms database
import magma

import os

print "Content-Type: text/html"      # HTML is following
print                                # blank line, end of headers

form = cgi.FieldStorage()

def is_numeric(c):
    return (c >= '0' and c <='9') or c=='-' or c=='+' or c=='/'

def nextnum(s):
    if len(s) == 0:
        return 0, 0, 0
    i=0
    while not is_numeric(s[i]):
        i = i+1
        if i >= len(s):
            return 0, 0, 0
    j=i+1
    while j < len(s) and is_numeric(s[j]):
        j = j+1
    return 1, s[i:j], s[j:]

def parse(form):
    ERROR_MESSAGE = "Please enter either 2, 3 or 5 rational numbers in the a-invariants field.";
    if not form.has_key("ainvariants"):
        print "<h1>Error</h1>"
        print ERROR_MESSAGE
        return 0, 0
    s = form["ainvariants"].value
    e, n1, s = nextnum(s)
    if not e:
        print "<h1>Error</h1>"
        print ERROR_MESSAGE
        return 0,0
    e, n2, s = nextnum(s)
    if not e:
        print "<h1>Error</h1>"
        print ERROR_MESSAGE
        return 0,0
    e, n3, s = nextnum(s)
    if not e:
        return 1, ('0','0','0',n1,n2)
    e, n4, s = nextnum(s)
    if not e:
        return 1, ('0',n1,'0',n2,n3)
    e, n5, s = nextnum(s)
    if not e:
        print "<h1>Error</h1>"
        print ERROR_MESSAGE
        return 0,0

    return 1, (n1,n2,n3,n4,n5)

def html_curvedata(ainvs,hostname):
    doc = Documents.Document()

    doc.append(HTML.TITLE('Modular Forms Database: Curve data'))

    doc.append(HTML.LINK(rel="stylesheet", type="text/css", \
                         HREF="http://%s/mfd/mfd.css"%hostname, TITLE="was"))

    body = HTML.BODY(klass="top")
    doc.append(body)

    body.append(HTML.CENTER(
        HTML.H1("The elliptic curve defined by [%s,%s,%s,%s,%s]. &nbsp&nbsp "%ainvs)))

    body.append(HTML.CENTER(HTML.A("<br>BACK<br><br>", \
                                  href="http://%s/mfd/elliptic/index.html"%hostname)))

    cmd = "function factor(x) return Factorization(Numerator(x)) cat " +\
          "           [<a[1], -a[2]> : a in Factorization(Denominator(x))]; end function;\n "+\
          "ainvs := [%s,%s,%s,%s,%s];  if not IsEllipticCurve(ainvs) then "%ainvs  +\
          "ans := \"The Weierstrass equation is singular.\"; " + \
          " else E:=EllipticCurve(ainvs); G,f:=TorsionSubgroup(E); " + \
          "eig := qEigenform(E,100); periods := Periods(E); "+ \
          "ans:=Sprintf(\"<center><b>The %o.</b></center><br>  <ul>" + \
          "<li>The <b>minimal</b> Weierstrass equation for E has invariants %o<br><br>" + \
          "<li>The curve E has <b>j-invariant</b> %o, which factors as %o.<br><br>"+\
          "<li> It has <b>discriminant</b> %o, which factors as %o.<br><br>" +\
          "<li>It has <b>conductor</b> %o, which factors as %o.<br><br>"+\
          "<li>The <b>torsion</b> subgroup of E has invariants %o and elements %o.<br><br>"+\
          "<li>The <b>newform</b> attached to E has q-expansion <pre>f = %o.</pre><br>"+\
          "<li>The <b>periods</b> of E are <pre>omega1, omega2 = %o.</pre>" +\
          "\",E,aInvariants(MinimalModel(E)),jInvariant(E),jInvariant(E) eq 0 select 0 else factor(jInvariant(E)), Discriminant(E)," +\
          "factor(Discriminant(E)),Conductor(E),Factorization(Conductor(E))," +\
          "Invariants(G),{f(g) : g in G}, eig, periods); end if;";

    ans = magma.magma(cmd, "%s/gomagma_elliptic-curves"%constants.bin)

    body.append(ans)

    print doc

# If the input is valid render the page. 
valid, ainvs = parse(form)
if valid:
    html_curvedata(ainvs,constants.hostname)