symbolic math: add <symbolicresponse> type; improve error handling in

symmath library; add options for matrices, qubit to symmath_check
2012-06-02 17:17:48 -04:00
parent 9dab2ce4e7
commit 2f33bce7ad
4 changed files with 201 additions and 30 deletions
--- a/djangoapps/courseware/capa/capa_problem.py
+++ b/djangoapps/courseware/capa/capa_problem.py
@@ -26,7 +26,7 @@ from mako.template import Template
 from util import contextualize_text
 import inputtypes

-from responsetypes import NumericalResponse, FormulaResponse, CustomResponse, SchematicResponse, MultipleChoiceResponse,  StudentInputError, TrueFalseResponse, ExternalResponse,ImageResponse,OptionResponse
+from responsetypes import NumericalResponse, FormulaResponse, CustomResponse, SchematicResponse, MultipleChoiceResponse,  StudentInputError, TrueFalseResponse, ExternalResponse,ImageResponse,OptionResponse, SymbolicResponse

 import calc
 import eia
@@ -42,6 +42,7 @@ response_types = {'numericalresponse':NumericalResponse,
                  'truefalseresponse':TrueFalseResponse,
                  'imageresponse':ImageResponse,
                  'optionresponse':OptionResponse,
+                  'symbolicresponse':SymbolicResponse,
                  }
 entry_types = ['textline', 'schematic', 'choicegroup','textbox','imageinput','optioninput']
 solution_types = ['solution']	# extra things displayed after "show answers" is pressed
@@ -55,6 +56,7 @@ html_transforms = {'problem': {'tag':'div'},
                   "externalresponse": {'tag':'span'},
                   "schematicresponse": {'tag':'span'}, 
                   "formularesponse": {'tag':'span'}, 
+                   "symbolicresponse": {'tag':'span'}, 
                   "multiplechoiceresponse": {'tag':'span'}, 
                   "text": {'tag':'span'},
                   "math": {'tag':'span'},
@@ -70,7 +72,7 @@ global_context={'random':random,
 # These should be removed from HTML output, including all subelements
 html_problem_semantics = ["responseparam", "answer", "script"]
 # These should be removed from HTML output, but keeping subelements
-html_skip = ["numericalresponse", "customresponse", "schematicresponse", "formularesponse", "text","externalresponse"]
+html_skip = ["numericalresponse", "customresponse", "schematicresponse", "formularesponse", "text","externalresponse",'symbolicresponse']

 # removed in MC
 ## These should be transformed
@@ -218,8 +220,10 @@ class LoncapaProblem(object):

        #for script in tree.xpath('/problem/script'):
        for script in tree.findall('.//script'):
-            if 'javascript' in script.get('type'): continue	# skip javascript
-            if 'perl' in script.get('type'): continue		# skip perl
+            stype = script.get('type')
+            if stype:
+                if 'javascript' in stype: continue	# skip javascript
+                if 'perl' in stype: continue		# skip perl
            # TODO: evaluate only python 
            code = script.text
            XMLESC = {"&apos;": "'", "&quot;": '"'}
--- a/djangoapps/courseware/capa/responsetypes.py
+++ b/djangoapps/courseware/capa/responsetypes.py
@@ -221,7 +221,10 @@ class NumericalResponse(GenericResponse):

 class CustomResponse(GenericResponse):
    '''
-    Custom response.  The python code to be run should be in <answer>...</answer>.  Example:
+    Custom response.  The python code to be run should be in <answer>...</answer>
+    or in a <script>...</script>
+ 
+    Example:

    <customresponse>
    <startouttext/>
@@ -263,6 +266,7 @@ def sympy_check2():
    '''
    def __init__(self, xml, context, system=None):
        self.xml = xml
+        self.system = system
        ## CRITICAL TODO: Should cover all entrytypes
        ## NOTE: xpath will look at root of XML tree, not just 
        ## what's in xml. @id=id keeps us in the right customresponse. 
@@ -271,8 +275,8 @@ def sympy_check2():
        self.answer_ids += [x.get('id') for x in xml.findall('textbox')]	# also allow textbox inputs
        self.context = context

-        # if <customresponse> has an "expect" attribute then save that
-        self.expect = xml.get('expect')
+        # if <customresponse> has an "expect" (or "answer") attribute then save that
+        self.expect = xml.get('expect') or xml.get('answer')
        self.myid = xml.get('id')

        if settings.DEBUG:
@@ -351,9 +355,14 @@ def sympy_check2():
                             'answers':student_answers,		# dict of student's responses, with keys being entry box IDs
                             'correct':correct,			# the list to be filled in by the check function
                             'messages':messages,		# the list of messages to be filled in by the check function
+                             'options':self.xml.get('options'),	# any options to be passed to the cfn
                             'testdat':'hello world',
                             })

+        # pass self.system.debug to cfn 
+        # if hasattr(self.system,'debug'): self.context['debug'] = self.system.debug
+        self.context['debug'] = settings.DEBUG
+
        # exec the check function
        if type(self.code)==str:
            try:
@@ -381,7 +390,7 @@ def sympy_check2():

                if settings.DEBUG:
                    log.debug('[courseware.capa.responsetypes.customresponse] answer_given=%s' % answer_given)
-                    # log.info('nargs=%d, args=%s' % (nargs,args))
+                    log.info('nargs=%d, args=%s, kwargs=%s' % (nargs,args,kwargs))

                ret = fn(*args[:nargs],**kwargs)
            except Exception,err:
@@ -436,6 +445,32 @@ def sympy_check2():

 #-----------------------------------------------------------------------------

+class SymbolicResponse(CustomResponse):
+    """
+    Symbolic math response checking, using symmath library.
+
+    Example:
+
+    <problem>
+      <text>Compute \[ \exp\left(-i \frac{\theta}{2} \left[ \begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix} \right] \right) \]
+      and give the resulting \(2\times 2\) matrix: <br/>
+        <symbolicresponse answer="">
+          <textline size="40" math="1" />
+        </symbolicresponse>
+      <br/>
+      Your input should be typed in as a list of lists, eg <tt>[[1,2],[3,4]]</tt>.
+      </text>
+    </problem>
+    """
+    def __init__(self, xml, context, system=None):
+        xml.set('cfn','symmath_check')
+        code = "from symmath import *"
+        exec code in context,context
+        CustomResponse.__init__(self,xml,context,system)
+        
+
+#-----------------------------------------------------------------------------
+
 class ExternalResponse(GenericResponse):
    """
    Grade the student's input using an external server.
@@ -502,6 +537,30 @@ class StudentInputError(Exception):
 #-----------------------------------------------------------------------------

 class FormulaResponse(GenericResponse):
+    '''
+    Checking of symbolic math response using numerical sampling.
+
+    Example:
+
+    <problem>
+
+    <script type="loncapa/python">
+    I = "m*c^2"
+    </script>
+
+    <text>
+    <br/>
+    Give an equation for the relativistic energy of an object with mass m.
+    </text>
+    <formularesponse type="cs" samples="m,c@1,2:3,4#10" answer="$I">
+      <responseparam description="Numerical Tolerance" type="tolerance"
+                   default="0.00001" name="tol" /> 
+      <textline size="40" math="1" />    
+    </formularesponse>
+
+    </problem>
+
+    '''
    def __init__(self, xml, context, system=None):
        self.xml = xml
        self.correct_answer = contextualize_text(xml.get('answer'), context)
--- a/lib/symmath/formula.py
+++ b/lib/symmath/formula.py
@@ -30,7 +30,7 @@ from lxml import etree
 import requests
 from copy import deepcopy

-print "[lib.sympy_check.formula] Warning: Dark code. Needs review before enabling in prod."
+print "[lib.symmath.formula] Warning: Dark code. Needs review before enabling in prod."

 os.environ['PYTHONIOENCODING'] = 'utf-8'

@@ -143,11 +143,12 @@ class formula(object):
    Representation of a mathematical formula object.  Accepts mathml math expression for constructing,
    and can produce sympy translation.  The formula may or may not include an assignment (=).
    '''
-    def __init__(self,expr,asciimath=''):
+    def __init__(self,expr,asciimath='',options=None):
        self.expr = expr.strip()
        self.asciimath = asciimath
        self.the_cmathml = None
        self.the_sympy = None
+        self.options = options

    def is_presentation_mathml(self):
        return '<mstyle' in self.expr
@@ -249,7 +250,8 @@ class formula(object):

    def make_sympy(self,xml=None):
        '''
-        Return sympy expression for the math formula
+        Return sympy expression for the math formula.
+        The math formula is converted to Content MathML then that is parsed.
        '''

        if self.the_sympy: return self.the_sympy
@@ -258,7 +260,11 @@ class formula(object):
            if not self.is_mathml():
                return my_sympify(self.expr)
            if self.is_presentation_mathml():
-                xml = etree.fromstring(str(self.cmathml))
+                try:
+                    cmml = self.cmathml
+                    xml = etree.fromstring(str(cmml))
+                except Exception,err:
+                    raise Exception,'Err %s while converting cmathml to xml; cmml=%s' % (err,cmml)
                xml = self.fix_greek_in_mathml(xml)
                self.the_sympy = self.make_sympy(xml[0])
            else:
@@ -277,7 +283,7 @@ class formula(object):
            # print "divide: arg0=%s, arg1=%s" % (args[0],args[1])
            return sympy.Mul(args[0],sympy.Pow(args[1],-1))

-        def op_plus(*args): return sum(args)
+        def op_plus(*args): return args[0] if len(args)==1 else op_plus(*args[:-1])+args[-1]
        def op_times(*args): return reduce(operator.mul,args)

        def op_minus(*args):
@@ -317,7 +323,7 @@ class formula(object):
            elif tag=='msup': return '^'.join([parsePresentationMathMLSymbol(y) for y in xml])
            raise Exception,'[parsePresentationMathMLSymbol] unknown tag %s' % tag

-        # parser tree for content MathML
+        # parser tree for Content MathML
        tag = gettag(xml)
        print "tag = ",tag

@@ -328,7 +334,13 @@ class formula(object):
            if opstr in opdict:
                op = opdict[opstr]
                args = [ self.make_sympy(x) for x in xml[1:]]
-                return op(*args)
+                try:
+                    res = op(*args)
+                except Exception,err:
+                    self.args = args
+                    self.op = op
+                    raise Exception,'[formula] error=%s failed to apply %s to args=%s' % (err,opstr,args)
+                return res
            else:
                raise Exception,'[formula]: unknown operator tag %s' % (opstr)

@@ -351,7 +363,7 @@ class formula(object):
            return float(xml.text)

        elif tag=='ci':			# variable (symbol)
-            if len(xml)>0 and (gettag(xml[0])=='msub' or gettag(xml[0])=='msup'):
+            if len(xml)>0 and (gettag(xml[0])=='msub' or gettag(xml[0])=='msup'):	# subscript or superscript
                usym = parsePresentationMathMLSymbol(xml[0])
                sym = sympy.Symbol(str(usym))
            else:
@@ -359,7 +371,11 @@ class formula(object):
                if 'hat' in usym:
                    sym = my_sympify(usym)
                else:
-                    sym = sympy.Symbol(str(usym))
+                    if usym=='i': print "options=",self.options
+                    if usym=='i' and 'imaginary' in self.options:	# i = sqrt(-1)
+                        sym = sympy.I	
+                    else:
+                        sym = sympy.Symbol(str(usym))
            return sym

        else:				# unknown tag
@@ -462,3 +478,78 @@ def test4():
 </math>
 '''
    return formula(xmlstr)
+
+def test5():		# sum of two matrices
+    xmlstr = u'''
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+  <mstyle displaystyle="true">
+    <mrow>
+      <mi>cos</mi>
+      <mrow>
+        <mo>(</mo>
+        <mi>&#x3B8;</mi>
+        <mo>)</mo>
+      </mrow>
+    </mrow>
+    <mo>&#x22C5;</mo>
+    <mrow>
+      <mo>[</mo>
+      <mtable>
+        <mtr>
+          <mtd>
+            <mn>1</mn>
+          </mtd>
+          <mtd>
+            <mn>0</mn>
+          </mtd>
+        </mtr>
+        <mtr>
+          <mtd>
+            <mn>0</mn>
+          </mtd>
+          <mtd>
+            <mn>1</mn>
+          </mtd>
+        </mtr>
+      </mtable>
+      <mo>]</mo>
+    </mrow>
+    <mo>+</mo>
+    <mrow>
+      <mo>[</mo>
+      <mtable>
+        <mtr>
+          <mtd>
+            <mn>0</mn>
+          </mtd>
+          <mtd>
+            <mn>1</mn>
+          </mtd>
+        </mtr>
+        <mtr>
+          <mtd>
+            <mn>1</mn>
+          </mtd>
+          <mtd>
+            <mn>0</mn>
+          </mtd>
+        </mtr>
+      </mtable>
+      <mo>]</mo>
+    </mrow>
+  </mstyle>
+</math>
+'''
+    return formula(xmlstr)
+
+def test6():		# imaginary numbers
+    xmlstr = u'''
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+  <mstyle displaystyle="true">
+    <mn>1</mn>
+    <mo>+</mo>
+    <mi>i</mi>
+  </mstyle>
+</math>
+'''
+    return formula(xmlstr,options='imaginaryi')
--- a/lib/symmath/symmath_check.py
+++ b/lib/symmath/symmath_check.py
@@ -137,7 +137,7 @@ def check(expect,given,numerical=False,matrix=False,normphase=False,abcsym=False
 #
 # This is one of the main entry points to call.

-def symmath_check(expect,ans,adict={},abname=''):
+def symmath_check(expect,ans,dynamath=None,options=None,debug=None):
    '''
    Check a symbolic mathematical expression using sympy.
    The input may be presentation MathML.  Uses formula.
@@ -148,22 +148,27 @@ def symmath_check(expect,ans,adict={},abname=''):
    # msg += '<p/>adict=%s' % (repr(adict).replace('<','&lt;'))

    threshold = 1.0e-3
-    DEBUG = True
+    DEBUG = debug
+
+    # options
+    do_matrix = 'matrix' in (options or '')
+    do_qubit = 'qubit' in (options or '')
+    do_imaginary = 'imaginary' in (options or '')

    # parse expected answer
    try:
-        fexpect = my_sympify(str(expect))
+        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':msg}

    # if expected answer is a number, try parsing provided answer as a number also
    try:
-        fans = my_sympify(str(ans))
+        fans = my_sympify(str(ans),matrix=do_matrix,do_qubit=do_qubit)
    except Exception,err:
        fans = None

-    if fexpect.is_number and fans and fans.is_number:
+    if hasattr(fexpect,'is_number') and fexpect.is_number and fans and hasattr(fans,'is_number') and fans.is_number:
        if abs(abs(fans-fexpect)/fexpect)<threshold:
            return {'ok':True,'msg':msg}
        else:
@@ -175,10 +180,12 @@ def symmath_check(expect,ans,adict={},abname=''):
        return {'ok':True,'msg':msg}

    # convert mathml answer to formula
-    mmlbox = abname+'_fromjs'
-    if mmlbox in adict:
-        mmlans = adict[mmlbox]
-    f = formula(mmlans)
+    try:
+        if dynamath:
+            mmlans = dynamath[0]
+    except Exception,err:
+        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('<','&lt;')
@@ -186,13 +193,20 @@ def symmath_check(expect,ans,adict={},abname=''):
        fsym = f.sympy
        msg += '<p>You entered: %s</p>' % to_latex(f.sympy)
    except Exception,err:
-        msg += "<p>Error %s in converting to sympy</p>" % str(err).replace('<','&lt;')
-        if DEBUG: msg += "<p><pre>%s</pre></p>" % traceback.format_exc()
+        msg += "<p>Error %s in evaluating your expression '%s' as a valid equation</p>" % (str(err).replace('<','&lt;'),
+                                                                                           ans)
+        if DEBUG:
+            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('<','&lt;')
+            msg += '<p>pmathml=<pre>%s</pre></p>' % mmlans.replace('<','&lt;')
+            msg += '<hr>'
        return {'ok':False,'msg':msg}

    # compare with expected
-    if fexpect.is_number:
-        if fsym.is_number:
+    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}
@@ -225,12 +239,15 @@ def symmath_check(expect,ans,adict={},abname=''):
        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('<','&lt;')
        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('<','&lt;')
        if diff:
            msg += "<p>Difference: %s</p>" % to_latex(diff)
+        msg += '<hr>'

    return {'ok':False,'msg':msg,'ex':fexpect,'got':fsym}