Python:Symbolic Computations
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This is a sandbox for information on symbolic computation with Python. It is about as organized as one might expect...
Contents
Preamble
- This page will be consistent with Python:Nicknames in terms of module imports. Note that there are several ways to get the SymPy package into Python:
- import sympy as sym (what this page does)
- import sympy as sp (this is more consistent with bringing in NumPy, but that's what we will use for SciPy)
- from sympy import * (if you are sure nothing in SymPy will contradict anything in built-in Python)
- from sympy import TUPLE OF THINGS (if you just have a few specific things you want to do with SymPy)
- sym.init_session() will automatically bring in x, y, z, and t as symbols; k, m, n as integers; f, g, h as function names; and sym.init_printing HOWEVER it brings in all of sympy with from sympy import *!
Defining Symbols
- a, b, c = sym.symbols('a b c') or a, b, c = sym.symbols('a, b, c')
- The symbolic representation can be entirely different from the variable with a, b, c = sym.symbols('let\'s go Duke')
- If the symbolic and variable names exactly match more efficient to use sym.var('a b c') or sym.var('a, b, c')
- May want to assign this to a variable or append a ; since this returns a tuple with the variables in it
Substitutions
- use .subs(variable, value) or .subs(iterable) where iterable has a collection of variables and values
Output
- To make output prettier: sym.init_printing()
- Display depends on if LaTeX is installed or not
Solving
- sym.solve() and sym.solveset()
- sym.dsolve()
Interesting Things
- sym.lambdify((variables), expression, "numpy") will return a function that performs the calculation in the expression
- sym.simplify(expression) will work to simplify an expression
- sym.Matrix() can have symbols and will calculate things symbolically
Philosophical Things =
- How to declare things? Knowns versus unknowns? All symbols and then all functions or batches of each?
- Name equations or just number them?
- When to solve after numbers are in versus before?
- How much time to spend figuring out nice subscripts (probably less than already spent)?
References
Future Work
- Subscripts are...strange. Numbers coming at the end of a variable print as subscripts but letters end that behavior. One workaround is to define a variable with the xa = sym.Symbol('x_a') command but that will only take a single character superscript.
