SymPy has some routines to make formulas more palatable. For instance, it can print sympy.Expr objects (expressions) in LATEX:
The second argument of solve() indicates the set of “output” variables. Indeed, we have three equations for twelve variables. Each equation can be used to express one variable as function of the others. Thus, we can pick three variables and express them as functions of the remaining nine.
in IPython qtconsole (which one could embed inside a custom PyQt/PySide application, and keep track of all the defined symbols
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I know this doesn’t address your problem directly but typical technique is to divide into 2^n samples chunks and process; possibly with overlapping blocks, possibly applying a window function (Google it) depending on desired frequency response. If you are modifying the FFT and applying an inverse you will want overlapping blocks, cross-faded in output, because you will get audible clicks between blocks if the apparent phase (or the 0Hz constant term) changes. BTW, frequency (Hz) is index * sample_rate / block_size