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February 8, 2018 17:50
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A draft to transform some limited subset of Mathematica's FullForm expression into a SymPy expression.
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| import re | |
| replacements = dict( | |
| Times="Mul", | |
| Plus="Add", | |
| Power="Pow", | |
| ) | |
| def parse_full_form(wmexpr): | |
| out = [] | |
| stack = [out] | |
| generator = re.finditer(r'[\[\],]', wmexpr) | |
| last_pos = 0 | |
| for match in generator: | |
| if match is None: | |
| break | |
| position = match.start() | |
| last_expr = wmexpr[last_pos:position].replace(',', '').replace(']', '').replace('[', '').strip() | |
| if match.group() == ',': | |
| if last_expr != '': | |
| stack[-1].append(last_expr) | |
| elif match.group() == ']': | |
| if last_expr != '': | |
| stack[-1].append(last_expr) | |
| stack.pop() | |
| current_pos = stack[-1] | |
| elif match.group() == '[': | |
| stack[-1].append([last_expr]) | |
| stack.append(stack[-1][-1]) | |
| last_pos = match.end() | |
| return out[0] | |
| def generate_sympy_from_parsed(parsed, depth=0): | |
| out = "" | |
| if not isinstance(parsed, list): | |
| return parsed | |
| if parsed[0] == "If": | |
| out += "\nif ("+generate_sympy_from_parsed(parsed[1])+"):\n" | |
| out += shift4(generate_sympy_from_parsed(parsed[2])) | |
| if len(parsed) > 2: | |
| out += "\nelse:\n" | |
| out += shift4(generate_sympy_from_parsed(parsed[3])) | |
| else: | |
| if parsed[0] in replacements: | |
| out += replacements[parsed[0]] | |
| else: | |
| out += parsed[0] | |
| if len(parsed) == 1: | |
| return out | |
| out += "(" | |
| out += ", ".join([generate_sympy_from_parsed(i) for i in parsed[1:]]) | |
| out += ")" | |
| return out | |
| def shift4(out): | |
| return ' '*4 + re.sub(r'\n', '\n ', out) |
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| A Mathematica expression should be exposed to both __HoldForm__ and __FullForm__, that is | |
| FullForm[HoldForm[ expression ]] | |
| after this, copy the result into a Python string, let's say _expr_, then call: | |
| list_tree = parse_full_form(expr) | |
| generate_sympy_from_parsed(list_tree) |
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Example: given the expression:
FullForm[HoldForm [ ... ]] will reduce it to
The variable
list_treewill beand the (currently wrong) SymPy expression