[BUG]: Keep greek letters in extracted model somehow

[pascaleproulx]

Describe the bug
Keep greek letters in extracted model somehow

Screenshots

[YohannParis]

Only the name should be translated to unicode characters.

[liunelson]

So, when one sends Greek letters in the LaTeX to "Create model from equations" operator, the SymPy intermediate code writes them as words, which MIRA then uses to make the AMR with names beta, gamma, ... as opposed to the unicode characters.

A solution would be to pass the model AMR through some regex that will convert any Greek letter words in the state/parameter/observable "name" (not "id" nor anywhere else) to the unicode character, e.g. beta -> β

https://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics,_science,_and_engineering

Caveat:

• there may be epsilon, theta, phi, ... versus varepsilon, vartheta, varphi, ...
• they each map to their own specific unicode characters: https://tex.stackexchange.com/a/304576
  
• https://www.w3.org/2003/entities/2007doc/#epsilon

LaTeX

[
  "\\frac{d S(t)}{d t} = - \\beta * S(t) * I(t) - \\mu",
  "\\frac{d I(t)}{d t} = \\beta * S(t) * I(t) - \\gamma * I(t) - \\mu",
  "\\frac{d R(t)}{d t} = \\gamma * I(t) - \\mu"
]

becomes SymPy:

import sympy

# Define time variable
t = sympy.symbols("t")

# Define variables with time derivative to be time-dependent functions
S, I, R = sympy.symbols("S I R", cls=sympy.Function)

# Define all parameters
beta, mu, gamma = sympy.symbols("beta mu gamma")

# Define the equations without time-derivative on the left hand side
equation_output = [
    sympy.Eq(S(t).diff(t), (-beta * S(t) * I(t) - mu).expand()),
    sympy.Eq(I(t).diff(t), (beta * S(t) * I(t) - gamma * I(t) - mu).expand()),
    sympy.Eq(R(t).diff(t), (gamma * I(t) - mu).expand())
]

and then this AMR

{
  "header": {
    "name": "Model",
    "schema": "https://raw.githubusercontent.com/DARPA-ASKEM/Model-Representations/petrinet_v0.6/petrinet/petrinet_schema.json",
    "schema_name": "petrinet",
    "description": "Model",
    "model_version": "0.1"
  },
  "properties": {},
  "model": {
    "states": [
      {
        "id": "I",
        "name": "I(t)",
        "grounding": {
          "identifiers": {},
          "modifiers": {}
        },
        "units": {
          "expression": "1",
          "expression_mathml": "1"
        }
      },
      {
        "id": "S",
        "name": "S(t)",
        "grounding": {
          "identifiers": {},
          "modifiers": {}
        },
        "units": {
          "expression": "1",
          "expression_mathml": "1"
        }
      },
      {
        "id": "R",
        "name": "R(t)",
        "grounding": {
          "identifiers": {},
          "modifiers": {}
        },
        "units": {
          "expression": "1",
          "expression_mathml": "1"
        }
      }
    ],
    "transitions": [
      {
        "id": "t0:I->",
        "input": [
          "I"
        ],
        "output": [],
        "properties": {
          "name": "t0:I->"
        }
      },
      {
        "id": "t1:S->",
        "input": [
          "S"
        ],
        "output": [],
        "properties": {
          "name": "t1:S->"
        }
      },
      {
        "id": "t2:R->",
        "input": [
          "R"
        ],
        "output": [],
        "properties": {
          "name": "t2:R->"
        }
      },
      {
        "id": "t3:S->I",
        "input": [
          "I",
          "S"
        ],
        "output": [
          "I",
          "I"
        ],
        "properties": {
          "name": "t3:S->I"
        }
      },
      {
        "id": "t4:I->R",
        "input": [
          "I"
        ],
        "output": [
          "R"
        ],
        "properties": {
          "name": "t4:I->R"
        }
      }
    ]
  },
  "semantics": {
    "ode": {
      "rates": [
        {
          "target": "t0:I->",
          "expression": "mu",
          "expression_mathml": "mu"
        },
        {
          "target": "t1:S->",
          "expression": "mu",
          "expression_mathml": "mu"
        },
        {
          "target": "t2:R->",
          "expression": "mu",
          "expression_mathml": "mu"
        },
        {
          "target": "t3:S->I",
          "expression": "I*S*beta",
          "expression_mathml": "ISbeta"
        },
        {
          "target": "t4:I->R",
          "expression": "I*gamma",
          "expression_mathml": "Igamma"
        }
      ],
      "initials": [
        {
          "target": "I",
          "expression": "0.0",
          "expression_mathml": "0.0"
        },
        {
          "target": "S",
          "expression": "0.0",
          "expression_mathml": "0.0"
        },
        {
          "target": "R",
          "expression": "0.0",
          "expression_mathml": "0.0"
        }
      ],
      "parameters": [
        {
          "id": "mu",
          "name": "mu",
          "value": 0,
          "units": {
            "expression": "1",
            "expression_mathml": "1"
          }
        },
        {
          "id": "beta",
          "name": "beta",
          "value": 0,
          "units": {
            "expression": "1",
            "expression_mathml": "1"
          }
        },
        {
          "id": "gamma",
          "name": "gamma",
          "value": 0,
          "units": {
            "expression": "1",
            "expression_mathml": "1"
          }
        }
      ],
      "observables": [],
      "time": {
        "id": "t",
        "units": {
          "expression": "day",
          "expression_mathml": "day"
        }
      }
    }
  },
  "metadata": {
    "annotations": {}
  }
}