feat: detect non-polynomial dependence on the variables - #80
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Averaging only makes sense for equations that are polynomial in the variables, and nothing here could check for that. `is_harmonic` reasons about time dependence and cannot see `sin(x(t))` at all, because `get_variables(sin(x(t)))` yields `x(t)` and never `t`, so `get_independent` calls the term t-independent. `nonpolynomial_terms` returns every subexpression where a variable sits under something other than `+`, `*` or a non-negative integer power, with `is_polynomial` as the predicate on top and a method for a whole `DifferentialEquation`.
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Averaging only makes sense for equations that are polynomial in the variables. Harmonic balance replaces each variable by a truncated Fourier series, and only sums, products and non-negative integer powers keep that series finite. A term like
sin(x)or1/xproduces an infinite spectrum instead, and the Fourier projection then discards every harmonic of it.Nothing here could spot that.
is_harmonicreasons about time dependence, and it cannot seesin(x(t))at all:get_variables(sin(x(t)))yieldsx(t)and nevert, soget_independentcalls the term t-independent and an equation built from it looks free of time dependence.nonpolynomial_terms(x, vars)walks the expression and returns every subexpression where a variable sits under something other than+,*or a non-negative integer power, recursing through derivatives and flagging state-dependent denominators along with negative, fractional and symbolic exponents.is_polynomialis the predicate on top, and aDifferentialEquationmethod checks a whole system at once.