[BUG]: Named SymPy functions are not handled on the way into and out of TemplateModel

[liunelson]

There are several places where SymPy functions could be used:

• initial expressions
• observable expressions
• template/transition rate laws

MIRA throws no error when I use for example sympy.sin(t) as an expression string:

t = sympy.Symbol('t')
S, I, R, V = sympy.symbols('S I R V', cls = sympy.Function)
a, b, c, d, g, k = sympy.symbols('a b c d g k')

odes = [
    sympy.Eq(S(t).diff(t), - S(t) * (a * I(t) + b * R(t) + c * R(t) + d * V(t))),
    sympy.Eq(I(t).diff(t), S(t) * (a * I(t) + b * R(t) + c * R(t) + d * V(t)) - g * I(t)),
    sympy.Eq(R(t).diff(t), k * g * I(t)),
    sympy.Eq(V(t).diff(t), (1 - k) * g * I(t))
]

model4 = template_model_from_sympy_odes(odes)

model4.observables = {
    'Dummy': Observable(name = 'Dummy', expression = safe_parse_expr('S + I + R + V + sympy.sin(t)', local_dict = _clash))
}

However, it is interpreted as sympyXX_XXsin(t)

and exported as is in the AMR.

If I were to use a SymPy function as part of the ODE:

odes[3] = sympy.Eq(V(t).diff(t), (1 - k) * g * I(t) - sympy.exp(a) * V(t))

then I get this error