diff --git a/common/static/js/capa/symbolic_mathjax_preprocessor.js b/common/static/js/capa/symbolic_mathjax_preprocessor.js new file mode 100644 index 0000000000..766e5efc03 --- /dev/null +++ b/common/static/js/capa/symbolic_mathjax_preprocessor.js @@ -0,0 +1,35 @@ +/* This file defines a processor in between the student's math input + (AsciiMath) and what is read by MathJax. It allows for our own + customizations, such as use of the syntax "a_b__x" in superscripts, or + possibly coloring certain variables, etc&. + + It is used in the definition like the following: + + + + +*/ +window.SymbolicMathjaxPreprocessor = function () { + this.fn = function (eqn) { + // flags and config + var superscriptsOn = true; + + if (superscriptsOn) { + // find instances of "__" and make them superscripts ("^") and tag them + // as such. Specifcally replace instances of "__X" or "__{XYZ}" with + // "^{CHAR$1}", marking superscripts as different from powers + + // a zero width space--this is an invisible character that no one would + // use, that gets passed through MathJax and to the server + var c = "\u200b"; + eqn = eqn.replace(/__(?:([^\{])|\{([^\}]+)\})/g, '^{' + c + '$1$2}'); + + // NOTE: MathJax supports '\class{name}{mathcode}' but not for asciimath + // input, which is too bad. This would be preferable to this char tag + } + + return eqn; + }; +}; diff --git a/doc/public/course_data_formats/symbolic_response.rst b/doc/public/course_data_formats/symbolic_response.rst new file mode 100644 index 0000000000..8463faab3c --- /dev/null +++ b/doc/public/course_data_formats/symbolic_response.rst @@ -0,0 +1,40 @@ +################# +Symbolic Response +################# + +This document plans to document features that the current symbolic response +supports. In general it allows the input and validation of math expressions, +up to commutativity and some identities. + + +******** +Features +******** + +This is a partial list of features, to be revised as we go along: + * sub and superscripts: an expression following the ``^`` character + indicates exponentiation. To use superscripts in variables, the syntax + is ``b_x__d`` for the variable ``b`` with subscript ``x`` and super + ``d``. + + An example of a problem:: + + + + + + It's a bit of a pain to enter that. + + * The script-style math variant. What would be outputted in latex if you + entered ``\mathcal{N}``. This is used in some variables. + + An example:: + + + + + + There is no fancy preprocessing needed, but if you had superscripts or + something, you would need to include that part. diff --git a/lms/lib/symmath/formula.py b/lms/lib/symmath/formula.py index f3f26699f2..604941ffdd 100644 --- a/lms/lib/symmath/formula.py +++ b/lms/lib/symmath/formula.py @@ -74,6 +74,15 @@ def to_latex(x): # LatexPrinter._print_dot = _print_dot xs = latex(x) xs = xs.replace(r'\XI', 'XI') # workaround for strange greek + + # substitute back into latex form for scripts + # literally something of the form + # 'scriptN' becomes '\\mathcal{N}' + # note: can't use something akin to the _print_hat method above because we sometimes get 'script(N)__B' or more complicated terms + xs = re.sub(r'script([a-zA-Z0-9]+)', + '\\mathcal{\\1}', + xs) + #return '%s{}{}' % (xs[1:-1]) if xs[0] == '$': return '[mathjax]%s[/mathjax]
' % (xs[1:-1]) # for sympy v6 @@ -106,6 +115,7 @@ def my_sympify(expr, normphase=False, matrix=False, abcsym=False, do_qubit=False 'i': sympy.I, # lowercase i is also sqrt(-1) 'Q': sympy.Symbol('Q'), # otherwise it is a sympy "ask key" 'I': sympy.Symbol('I'), # otherwise it is sqrt(-1) + 'N': sympy.Symbol('N'), # or it is some kind of sympy function #'X':sympy.sympify('Matrix([[0,1],[1,0]])'), #'Y':sympy.sympify('Matrix([[0,-I],[I,0]])'), #'Z':sympy.sympify('Matrix([[1,0],[0,-1]])'), @@ -247,6 +257,127 @@ class formula(object): fix_hat(k) fix_hat(xml) + def flatten_pmathml(xml): + ''' Give the text version of certain PMathML elements + + Sometimes MathML will be given with each letter separated (it + doesn't know if its implicit multiplication or what). From an xml + node, find the (text only) variable name it represents. So it takes + + m + a + x + + and returns 'max', for easier use later on. + ''' + tag = gettag(xml) + if tag == 'mn': return xml.text + elif tag == 'mi': return xml.text + elif tag == 'mrow': return ''.join([flatten_pmathml(y) for y in xml]) + raise Exception, '[flatten_pmathml] unknown tag %s' % tag + + def fix_mathvariant(parent): + '''Fix certain kinds of math variants + + Literally replace N + with 'scriptN'. There have been problems using script_N or script(N) + ''' + for child in parent: + if (gettag(child) == 'mstyle' and child.get('mathvariant') == 'script'): + newchild = etree.Element('mi') + newchild.text = 'script%s' % flatten_pmathml(child[0]) + parent.replace(child, newchild) + fix_mathvariant(child) + fix_mathvariant(xml) + + + # find "tagged" superscripts + # they have the character \u200b in the superscript + # replace them with a__b so snuggle doesn't get confused + def fix_superscripts(xml): + ''' Look for and replace sup elements with 'X__Y' or 'X_Y__Z' + + In the javascript, variables with '__X' in them had an invisible + character inserted into the sup (to distinguish from powers) + E.g. normal: + + a + b + c + + to be interpreted '(a_b)^c' (nothing done by this method) + + And modified: + + b + x + + ​ + d + + + to be interpreted 'a_b__c' + + also: + + x + + ​ + B + + + to be 'x__B' + ''' + for k in xml: + tag = gettag(k) + + # match things like the last example-- + # the second item in msub is an mrow with the first + # character equal to \u200b + if (tag == 'msup' and + len(k) == 2 and gettag(k[1]) == 'mrow' and + gettag(k[1][0]) == 'mo' and k[1][0].text == u'\u200b'): # whew + + # replace the msup with 'X__Y' + k[1].remove(k[1][0]) + newk = etree.Element('mi') + newk.text = '%s__%s' % (flatten_pmathml(k[0]), flatten_pmathml(k[1])) + xml.replace(k, newk) + + # match things like the middle example- + # the third item in msubsup is an mrow with the first + # character equal to \u200b + if (tag == 'msubsup' and + len(k) == 3 and gettag(k[2]) == 'mrow' and + gettag(k[2][0]) == 'mo' and k[2][0].text == u'\u200b'): # whew + + # replace the msubsup with 'X_Y__Z' + k[2].remove(k[2][0]) + newk = etree.Element('mi') + newk.text = '%s_%s__%s' % (flatten_pmathml(k[0]), flatten_pmathml(k[1]), flatten_pmathml(k[2])) + xml.replace(k, newk) + + fix_superscripts(k) + fix_superscripts(xml) + + # Snuggle returns an error when it sees an + # replace such elements with an , except the first element is of + # the form a_b. I.e. map a_b^c => (a_b)^c + def fix_msubsup(parent): + for child in parent: + # fix msubsup + if (gettag(child) == 'msubsup' and len(child) == 3): + newchild = etree.Element('msup') + newbase = etree.Element('mi') + newbase.text = '%s_%s' % (flatten_pmathml(child[0]), flatten_pmathml(child[1])) + newexp = child[2] + newchild.append(newbase) + newchild.append(newexp) + parent.replace(child, newchild) + + fix_msubsup(child) + fix_msubsup(xml) + self.xml = xml return self.xml @@ -257,6 +388,7 @@ class formula(object): try: xml = self.preprocess_pmathml(self.expr) except Exception, err: + log.warning('Err %s while preprocessing; expr=%s' % (err, self.expr)) return "Error! Cannot process pmathml" pmathml = etree.tostring(xml, pretty_print=True) self.the_pmathml = pmathml diff --git a/lms/lib/symmath/test_formula.py b/lms/lib/symmath/test_formula.py new file mode 100644 index 0000000000..d3f16ed6b3 --- /dev/null +++ b/lms/lib/symmath/test_formula.py @@ -0,0 +1,115 @@ +""" +Tests of symbolic math +""" + + +import unittest +import formula +import re +from lxml import etree + +def stripXML(xml): + xml = xml.replace('\n', '') + xml = re.sub(r'\> +\<', '><', xml) + return xml + +class FormulaTest(unittest.TestCase): + # for readability later + mathml_start = '' + mathml_end = '' + + def setUp(self): + self.formulaInstance = formula.formula('') + + def test_replace_mathvariants(self): + expr = ''' + + N +''' + + expected = 'scriptN' + + # wrap + expr = stripXML(self.mathml_start + expr + self.mathml_end) + expected = stripXML(self.mathml_start + expected + self.mathml_end) + + # process the expression + xml = etree.fromstring(expr) + xml = self.formulaInstance.preprocess_pmathml(xml) + test = etree.tostring(xml) + + # success? + self.assertEqual(test, expected) + + + def test_fix_simple_superscripts(self): + expr = ''' + + a + + ​ + b + +''' + + expected = 'a__b' + + # wrap + expr = stripXML(self.mathml_start + expr + self.mathml_end) + expected = stripXML(self.mathml_start + expected + self.mathml_end) + + # process the expression + xml = etree.fromstring(expr) + xml = self.formulaInstance.preprocess_pmathml(xml) + test = etree.tostring(xml) + + # success? + self.assertEqual(test, expected) + + def test_fix_complex_superscripts(self): + expr = ''' + + a + b + + ​ + c + +''' + + expected = 'a_b__c' + + # wrap + expr = stripXML(self.mathml_start + expr + self.mathml_end) + expected = stripXML(self.mathml_start + expected + self.mathml_end) + + # process the expression + xml = etree.fromstring(expr) + xml = self.formulaInstance.preprocess_pmathml(xml) + test = etree.tostring(xml) + + # success? + self.assertEqual(test, expected) + + + def test_fix_msubsup(self): + expr = ''' + + a + b + c +''' + + expected = 'a_bc' # which is (a_b)^c + + # wrap + expr = stripXML(self.mathml_start + expr + self.mathml_end) + expected = stripXML(self.mathml_start + expected + self.mathml_end) + + # process the expression + xml = etree.fromstring(expr) + xml = self.formulaInstance.preprocess_pmathml(xml) + test = etree.tostring(xml) + + # success? + self.assertEqual(test, expected)