Solve equation systems including units with pint and sympy

pint-sympy-example.py

"""
Note: the most recent version of pint contains [a bug](https://github.com/hgrecco/pint/pull/1701). 
Install [this version of pint](https://github.com/BenPortner/pint/tree/fix-subtraction-error) to 
run below code.
"""

from pint.facets.plain.registry import build_eval_tree, tokenizer
from pint.util import string_preprocessor
from pint import UnitRegistry
from sympy.parsing.sympy_parser import parse_expr
from sympy import Symbol, solve

# define system of equations (Note: 0 = 1 m - A instead of A = 1 m)
equations = [
    "1 m - A",
    "A + 200 mm - B",
    "B * kg/m - C",
    "A * B * C - D"
]

# define unknowns
unknowns = ["A", "B", "C", "D"]

# parse equations
# note: parsing first with pint to convert 200 mm -> 200 * mm etc.
parsed = [
  parse_expr(build_eval_tree(tokenizer(string_preprocessor(eq))).to_string())
  for eq in equations
]

# solve equation system
solution = solve(parsed, [Symbol(s) for s in unknowns])

# parse units in solution
ureg = UnitRegistry()
solution = [ureg(str(r)).to_base_units() for r in solution[0]]

# for reference
expected = [
    ureg("1 m"),  # A
    ureg("1.2 m"),  # B
    ureg("1.2 kg"),  # C
    ureg("1.44 kg * m^2"),  # D
]