#!/usr/bin/python
# -*- coding: utf-8 -*-
#
# File: symmath_check.py
# Date: 02-May-12 (creation)
#
# Symbolic mathematical expression checker for edX. Uses sympy to check for expression equality.
#
# Takes in math expressions given as Presentation MathML (from ASCIIMathML), converts to Content MathML using SnuggleTeX
import os
import sys
import string
import re
import traceback
from formula import *
import logging
log = logging.getLogger(__name__)
#-----------------------------------------------------------------------------
# check function interface
#
# This is one of the main entry points to call.
def symmath_check_simple(expect, ans, adict={}, symtab=None, extra_options=None):
'''
Check a symbolic mathematical expression using sympy.
The input is an ascii string (not MathML) converted to math using sympy.sympify.
'''
options = {'__MATRIX__': False, '__ABC__': False, '__LOWER__': False}
if extra_options: options.update(extra_options)
for op in options: # find options in expect string
if op in expect:
expect = expect.replace(op, '')
options[op] = True
expect = expect.replace('__OR__', '__or__') # backwards compatibility
if options['__LOWER__']:
expect = expect.lower()
ans = ans.lower()
try:
ret = check(expect, ans,
matrix=options['__MATRIX__'],
abcsym=options['__ABC__'],
symtab=symtab,
)
except Exception, err:
return {'ok': False,
'msg': 'Error %s<br/>Failed in evaluating check(%s,%s)' % (err, expect, ans)
}
return ret
#-----------------------------------------------------------------------------
# pretty generic checking function
def check(expect, given, numerical=False, matrix=False, normphase=False, abcsym=False, do_qubit=True, symtab=None, dosimplify=False):
"""
Returns dict with
'ok': True if check is good, False otherwise
'msg': response message (in HTML)
"expect" may have multiple possible acceptable answers, separated by "__OR__"
"""
if "__or__" in expect: # if multiple acceptable answers
eset = expect.split('__or__') # then see if any match
for eone in eset:
ret = check(eone, given, numerical, matrix, normphase, abcsym, do_qubit, symtab, dosimplify)
if ret['ok']:
return ret
return ret
flags = {}
if "__autonorm__" in expect:
flags['autonorm'] = True
expect = expect.replace('__autonorm__', '')
matrix = True
threshold = 1.0e-3
if "__threshold__" in expect:
(expect, st) = expect.split('__threshold__')
threshold = float(st)
numerical = True
if str(given) == '' and not (str(expect) == ''):
return {'ok': False, 'msg': ''}
try:
xgiven = my_sympify(given, normphase, matrix, do_qubit=do_qubit, abcsym=abcsym, symtab=symtab)
except Exception, err:
return {'ok': False, 'msg': 'Error %s<br/> in evaluating your expression "%s"' % (err, given)}
try:
xexpect = my_sympify(expect, normphase, matrix, do_qubit=do_qubit, abcsym=abcsym, symtab=symtab)
except Exception, err:
return {'ok': False, 'msg': 'Error %s<br/> in evaluating OUR expression "%s"' % (err, expect)}
if 'autonorm' in flags: # normalize trace of matrices
try:
xgiven /= xgiven.trace()
except Exception, err:
return {'ok': False, 'msg': 'Error %s<br/> in normalizing trace of your expression %s' % (err, to_latex(xgiven))}
try:
xexpect /= xexpect.trace()
except Exception, err:
return {'ok': False, 'msg': 'Error %s<br/> in normalizing trace of OUR expression %s' % (err, to_latex(xexpect))}
msg = 'Your expression was evaluated as ' + to_latex(xgiven)
# msg += '<br/>Expected ' + to_latex(xexpect)
# msg += "<br/>flags=%s" % flags
if matrix and numerical:
xgiven = my_evalf(xgiven, chop=True)
dm = my_evalf(sympy.Matrix(xexpect) - sympy.Matrix(xgiven), chop=True)
msg += " = " + to_latex(xgiven)
if abs(dm.vec().norm().evalf()) < threshold:
return {'ok': True, 'msg': msg}
else:
pass
#msg += "dm = " + to_latex(dm) + " diff = " + str(abs(dm.vec().norm().evalf()))
#msg += "expect = " + to_latex(xexpect)
elif dosimplify:
if (sympy.simplify(xexpect) == sympy.simplify(xgiven)):
return {'ok': True, 'msg': msg}
elif numerical:
if (abs((xexpect - xgiven).evalf(chop=True)) < threshold):
return {'ok': True, 'msg': msg}
elif (xexpect == xgiven):
return {'ok': True, 'msg': msg}
#msg += "<p/>expect='%s', given='%s'" % (expect,given) # debugging
# msg += "<p/> dot test " + to_latex(dot(sympy.Symbol('x'),sympy.Symbol('y')))
return {'ok': False, 'msg': msg}
#-----------------------------------------------------------------------------
# helper function to convert all <p> to <span class='inline-error'>
def make_error_message(msg):
# msg = msg.replace('<p>','<p><span class="inline-error">').replace('</p>','</span></p>')
msg = '<div class="capa_alert">%s</div>' % msg
return msg
def is_within_tolerance(expected, actual, tolerance):
if expected == 0:
return (abs(actual) < tolerance)
else:
return (abs(abs(actual - expected) / expected) < tolerance)
#-----------------------------------------------------------------------------
# Check function interface, which takes pmathml input
#
# This is one of the main entry points to call.
def symmath_check(expect, ans, dynamath=None, options=None, debug=None, xml=None):
'''
Check a symbolic mathematical expression using sympy.
The input may be presentation MathML. Uses formula.
This is the default Symbolic Response checking function
Desc of args:
expect is a sympy string representing the correct answer. It is interpreted
using my_sympify (from formula.py), which reads strings as sympy input
(e.g. 'integrate(x^2, (x,1,2))' would be valid, and evaluate to give 1.5)
ans is student-typed answer. It is expected to be ascii math, but the code
below would support a sympy string.
dynamath is the PMathML string converted by MathJax. It is used if
evaluation with ans is not sufficient.
options is a string with these possible substrings, set as an xml property
of the problem:
-matrix - make a sympy matrix, rather than a list of lists, if possible
-qubit - passed to my_sympify
-imaginary - used in formla, presumably to signal to use i as sqrt(-1)?
-numerical - force numerical comparison.
'''
msg = ''
# msg += '<p/>abname=%s' % abname
# msg += '<p/>adict=%s' % (repr(adict).replace('<','<'))
threshold = 1.0e-3 # for numerical comparison (also with matrices)
DEBUG = debug
if xml is not None:
DEBUG = xml.get('debug', False) # override debug flag using attribute in symbolicmath xml
if DEBUG in ['0', 'False']:
DEBUG = False
# options
do_matrix = 'matrix' in (options or '')
do_qubit = 'qubit' in (options or '')
do_imaginary = 'imaginary' in (options or '')
do_numerical = 'numerical' in (options or '')
# parse expected answer
try:
fexpect = my_sympify(str(expect), matrix=do_matrix, do_qubit=do_qubit)
except Exception, err:
msg += '<p>Error %s in parsing OUR expected answer "%s"</p>' % (err, expect)
return {'ok': False, 'msg': make_error_message(msg)}
###### Sympy input #######
# if expected answer is a number, try parsing provided answer as a number also
try:
fans = my_sympify(str(ans), matrix=do_matrix, do_qubit=do_qubit)
except Exception, err:
fans = None
# do a numerical comparison if both expected and answer are numbers
if (hasattr(fexpect, 'is_number') and fexpect.is_number
and hasattr(fans, 'is_number') and fans.is_number):
if is_within_tolerance(fexpect, fans, threshold):
return {'ok': True, 'msg': msg}
else:
msg += '<p>You entered: %s</p>' % to_latex(fans)
return {'ok': False, 'msg': msg}
if do_numerical: # numerical answer expected - force numerical comparison
if is_within_tolerance(fexpect, fans, threshold):
return {'ok': True, 'msg': msg}
else:
msg += '<p>You entered: %s (note that a numerical answer is expected)</p>' % to_latex(fans)
return {'ok': False, 'msg': msg}
if fexpect == fans:
msg += '<p>You entered: %s</p>' % to_latex(fans)
return {'ok': True, 'msg': msg}
###### PMathML input ######
# convert mathml answer to formula
try:
mmlans = dynamath[0] if dynamath else None
except Exception, err:
mmlans = None
if not mmlans:
return {'ok': False, 'msg': '[symmath_check] failed to get MathML for input; dynamath=%s' % dynamath}
f = formula(mmlans, options=options)
# get sympy representation of the formula
# if DEBUG: msg += '<p/> mmlans=%s' % repr(mmlans).replace('<','<')
try:
fsym = f.sympy
msg += '<p>You entered: %s</p>' % to_latex(f.sympy)
except Exception, err:
log.exception("Error evaluating expression '%s' as a valid equation" % ans)
msg += "<p>Error in evaluating your expression '%s' as a valid equation</p>" % (ans)
if "Illegal math" in str(err):
msg += "<p>Illegal math expression</p>"
if DEBUG:
msg += 'Error: %s' % str(err).replace('<', '<')
msg += '<hr>'
msg += '<p><font color="blue">DEBUG messages:</p>'
msg += "<p><pre>%s</pre></p>" % traceback.format_exc()
msg += '<p>cmathml=<pre>%s</pre></p>' % f.cmathml.replace('<', '<')
msg += '<p>pmathml=<pre>%s</pre></p>' % mmlans.replace('<', '<')
msg += '<hr>'
return {'ok': False, 'msg': make_error_message(msg)}
# do numerical comparison with expected
if hasattr(fexpect, 'is_number') and fexpect.is_number:
if hasattr(fsym, 'is_number') and fsym.is_number:
if abs(abs(fsym - fexpect) / fexpect) < threshold:
return {'ok': True, 'msg': msg}
return {'ok': False, 'msg': msg}
msg += "<p>Expecting a numerical answer!</p>"
msg += "<p>given = %s</p>" % repr(ans)
msg += "<p>fsym = %s</p>" % repr(fsym)
# msg += "<p>cmathml = <pre>%s</pre></p>" % str(f.cmathml).replace('<','<')
return {'ok': False, 'msg': make_error_message(msg)}
# Here is a good spot for adding calls to X.simplify() or X.expand(),
# allowing equivalence over binomial expansion or trig identities
# exactly the same?
if fexpect == fsym:
return {'ok': True, 'msg': msg}
if type(fexpect) == list:
try:
xgiven = my_evalf(fsym, chop=True)
dm = my_evalf(sympy.Matrix(fexpect) - sympy.Matrix(xgiven), chop=True)
if abs(dm.vec().norm().evalf()) < threshold:
return {'ok': True, 'msg': msg}
except sympy.ShapeError:
msg += "<p>Error - your input vector or matrix has the wrong dimensions"
return {'ok': False, 'msg': make_error_message(msg)}
except Exception, err:
msg += "<p>Error %s in comparing expected (a list) and your answer</p>" % str(err).replace('<', '<')
if DEBUG: msg += "<p/><pre>%s</pre>" % traceback.format_exc()
return {'ok': False, 'msg': make_error_message(msg)}
#diff = (fexpect-fsym).simplify()
#fsym = fsym.simplify()
#fexpect = fexpect.simplify()
try:
diff = (fexpect - fsym)
except Exception, err:
diff = None
if DEBUG:
msg += '<hr>'
msg += '<p><font color="blue">DEBUG messages:</p>'
msg += "<p>Got: %s</p>" % repr(fsym)
# msg += "<p/>Got: %s" % str([type(x) for x in fsym.atoms()]).replace('<','<')
msg += "<p>Expecting: %s</p>" % repr(fexpect).replace('**', '^').replace('hat(I)', 'hat(i)')
# msg += "<p/>Expecting: %s" % str([type(x) for x in fexpect.atoms()]).replace('<','<')
if diff:
msg += "<p>Difference: %s</p>" % to_latex(diff)
msg += '<hr>'
return {'ok': False, 'msg': msg, 'ex': fexpect, 'got': fsym}