MathML

A parser for the MathML XML standard.

Uses Symbolics.jl under the hood for defining equations and uses EzXML.jl for XML parsing.

MathML Specification: https://www.w3.org/TR/MathML3/

using MathML, EzXML, Symbolics, AbstractTrees
xml = xml"""<math xmlns="http://www.w3.org/1998/Math/MathML">
   <apply>
      <times />
      <ci>compartment</ci>
      <ci>k1</ci>
      <ci>S1</ci>
   </apply>
</math>"""

num = parse_node(xml)
# 1-element Vector{Num}:
#  S1*compartment*k1

# to pretty print the tree use `print_tree`
print_tree(xml)
# math
# └─ apply
#    ├─ times
#    ├─ ci
#    ├─ ci
#    └─ ci

# you can also just go directly from EzXML.Document or String
str = "<apply><power/><ci>x</ci><cn>3</cn></apply>"
MathML.parse_str(str)
# x^3

# derivatives also work!
str = """
<apply><diff/>
  <bvar><ci>x</ci><degree><cn>2</cn></degree></bvar>
  <apply><power/><ci>x</ci><cn>4</cn></apply>
</apply>
"""
expand_derivatives(MathML.parse_str(str))
# 12(x^2)

# there is also a macro @MathML_str to directly call `parse_str`
ml = MathML"""
<apply><diff/>
  <bvar><ci>x</ci><degree><cn>2</cn></degree></bvar>
  <apply><power/><ci>x</ci><cn>4</cn></apply>
</apply>
"""
expand_derivatives(ml)
# 12(x^2)

Check the tests in test/parse.jl to see a more exaustive list of what is covered.

• calculus:
  • ivars fix, make ODESystem(parse_node(readxml("lorenz.xml").root)) work
  • partial derivatives partialdiff tags
  • integration int tags - needs JuliaSymbolics/Symbolics.jl#58
    • often a var like dPidt is assigned to Differential(time)(Pi) where dPidt is refered to after this <eq> (I think solution is Symbolics.diff2term)
  • diffs with no independent variable: like <apply><diff/><ci>f</ci></apply>

• nested apply
• fix sep/ tags in cn, take type attribute into account
  • rational, e-notation, complex, complex polar
• basic diff handling
• bound variables like bvar, might be lingering issues though
• eq nodes sometimes needs to be ~ and sometimes needs to be =
• fix sep tags in cis, take type attribute into account
• piecewise tags: make heaviside test work
• fix undefined namespacing issues JuliaIO/EzXML.jl#156
  • parsers like SBML and CellMLToolkit should be handling
• to_mathml: julia expr -> mathml and Symbolics Num -> mathml. round tripping