Sympy and MathML... ideas?

[peibol]

Hi all:

Is there no support for importing MathML expressions into Sympy yet?

As the issue is still open, maybe someone knows a workaround for what I'm trying to do. My web application renders some mathematical exercises, so as the students are able to enter a solution and check if it's right or not. I'm using sympy to manipulate expressions and calculate the result (can be algebraic or arithmetic manipulations). My problem now is that if the feature of importing MathML isn't available yet, I don't know how to validate the results. Students enter the results in MathML, but it differs slightly from the one Sympy produces (no mrows for example). Ideally I'd also like to consider semantics, for example, if the soultion is 'x^2+x', x+x^2 is also right.

There is mathdom, but I haven't managed to parse a mathML string yet...

Any ideas?

Thanks

Pablo

[Stefan Krastanov]

This is probably not very helpful, but why require the students to
write their results in MathML? It is not a very natural way to write
expression. On the other hand, if you use valid python expression it
would probably be much easier.

[peibol]

Hehe, they don't write the expression in MathML, I'm not that kind of demon. 

They enter expressions in a textarea by means of http://mathdox.org/formulaeditor/, from which I can get the openmath or the (presentation) mathml .The web app is for K12 students, well 12-16 years old, so I think this way to enter mathematical expressions is one of the easiest...

[Stefan Krastanov]

I am sorry, I do not think there is an out-of-the-box way to do this currently.

What I can suggest is to use the xml2dict python library to parse the
openmath xml and then write your own small routine for traversing the
dictionary and transforming it into a sympy expression.

If you do this I am sure that the sympy team would be very interested
to have your work merged.

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[Ondřej Čertík]

On Tue, Jul 2, 2013 at 10:35 AM, Stefan Krastanov
<krastano...@gmail.com> wrote:
> I am sorry, I do not think there is an out-of-the-box way to do this currently.
>
> What I can suggest is to use the xml2dict python library to parse the
> openmath xml and then write your own small routine for traversing the
> dictionary and transforming it into a sympy expression.
>
> If you do this I am sure that the sympy team would be very interested
> to have your work merged.

Absolutely. Pablo, if you would send us a PR that could do that,
that would be awesome.

Ondrej

[Aaron Meurer]

Just to be clear, is this presentation mathml or content mathml? I
believe the latter would be much easier to parse.

Aaron Meurer

[peibol]

The mathdox box produces Presentation Mathml.

Sympy produces Content Mathml in the printing module, but there is the c2p function in utils module that converts Content Mathml into Presentation Mathml.

So I'm trying the xml2dict parsing with presentation mathml... I think that once I have the dict, at least for easy expressions like fractions, with addings, algebraic... it's nothing more than a -sophisticated- replacement with some parenthesis abuse.

[peibol]

I think xml2dict cannot accomplish it, since I get the same key for multiple values...

For example: mathml_prueba='''<mrow> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>5</mn> </mrow> </mfrac> </mrow> '''

I get the following dict: 

{'mrow': {'mfrac': {'mrow': [{'mn': '3'}, {'mn': '5'}]}}}

Notice the merged 'mrow' key...

Any suggestion for a xml lib to parse the expression?

[Ondřej Čertík]

On Tue, Jul 2, 2013 at 12:32 PM, peibol <pab...@gmail.com> wrote:
> I think xml2dict cannot accomplish it, since I get the same key for multiple
> values...
>
> For example: mathml_prueba='''<mrow> <mfrac> <mrow> <mn>3</mn> </mrow>
> <mrow> <mn>5</mn> </mrow> </mfrac> </mrow> '''
>
> I get the following dict:
> {'mrow': {'mfrac': {'mrow': [{'mn': '3'}, {'mn': '5'}]}}}
> Notice the merged 'mrow' key...
>
> Any suggestion for a xml lib to parse the expression?

lxml seems to be able to parse the expression:

http://nbviewer.ipython.org/5912034

Ondrej

[peibol]

Thanks, I'll try to make my function the more generic I can.

[peibol]

It will be something like that. For the moment, I'm just implemented the basics of presentation mathml. I will add features as I need them.

After running it, sympify should be called. What do you think about it?

def parseMML(mmlinput):

from lxml import etree

from StringIO import *

from lxml import objectify

mmlinput= mmlinput.replace(' xmlns="', ' xmlnamespace="')

parser = etree.XMLParser(ns_clean=True,remove_pis=True,remove_comments=True)

tree   = etree.parse(StringIO(mmlinput), parser)

objectify.deannotate(tree,cleanup_namespaces=True,xsi=True,xsi_nil=True)

mmlinput=etree.tostring(tree.getroot())

exppy="" #this is the python expression

symvars=[]  #these are symbolic variables which can eventually take part in the expression

events = ("start", "end")

level = 0

context = etree.iterparse(StringIO(mmlinput),events=events)

for action, elem in context:

if (action=='start') and (elem.tag=='mfrac'):

level += 1

mmlaux=etree.tostring(elem[0])

(a,b)=parseMML(mmlaux)

symvars.append(b)

exppy+=a

exppy+='/'

mmlaux=etree.tostring(elem[1])

(a,b)=parseMML(mmlaux)

symvars.append(b)

exppy+=a

if (action=='end') and (elem.tag=='mfrac'):

level -= 1

if level:

continue

if (action=='start') and (elem.tag=='mrow'):

exppy+='('

if (action=='end') and (elem.tag=='mrow'):

exppy+=')'

if action=='start' and elem.tag=='mn': #this is a number

exppy+=elem.text

if action=='start' and elem.tag=='mi': #this is a variable

exppy+=elem.text

symvars.append(elem.text) #we'll return the variable, so sympy can sympify it afterwards

if action=='start' and elem.tag=='mo': #this is a operation

exppy+=elem.text

return (exppy, symvars)

With the example: mmlinput='''<?xml version="1.0"?> <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.w3.org/1998/Math/MathML http://www.w3.org/Math/XMLSchema/mathml2/mathml2.xsd"> <mrow> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>57</mn> </mrow> </mfrac> </mrow> </math>'''

We get:

exppy='((3)/(57))'

[Ondřej Čertík]

Pablo,

I think that's a great start. I assume you pass the expression to
sympify() and obtain a SymPy expression as a result.

Aaron, I think we should have this in sympy, what do you think? We can
install lxml in .travis.yml and have this tested. If so, I can help
you Pablo with sending a PR and get it setup.

Ondrej

[Aaron Meurer]

Yes, definitely. Eventually, I would like to have a nice framework to
make parsing things like this easier and have a nicer, more extensible
API, but for now, I think even simple parsers like this are better
than nothing.

Aaron Meurer

[Ondřej Čertík]

Excellent.

Pablo, can you please send a PR with this? We'll then improve it there
and I can help with setting up the tests. Please ask if you get stuck.

Ondrej

[peibol]

Sure. Call me stupid, but what's a PR? I'll need some help with the procedure.

Are you using GIT or what?

[Ondřej Čertík]

Hi Pablo,

sorry for my shortcut. :) PR = pull request, here is how it works:

https://help.github.com/articles/using-pull-requests

yes we use git and github. Start by:

git clone https://github.com/sympy/sympy

and try to follow the help article. Please ask if you get stuck.

Using git and github is a great way to do development, you can use it
for any other project as well, not just sympy.

Ondrej

[peibol]

Ok, I'll try tonight.