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SymPy

SymPy http://www.sympy.org is a Python library for symbolic math.

In symbolic math, symbols are used to represent mathematical expressions. An example of a symbolic math expression is below.

$x^{2} + y^{2} = z$

The expression contains the symbols $x$ , $y$ , and $z$ .

If we define a second symbolic math expression:

$x = a + b$

then we can substitue in $a + b$ for $x$ .

The result is the expression:

$(a + b)^{2} + y^{2} = z$

$a^{2} + 2ab + b^{2} + y^{2} = z$

Solving for $y$ in terms of $a$ , $b$ and $z$ results in:

$y = \sqrt{z - a^{2} - 2ab - b^{2}}$

In the symbolic math substitution above, symbolic math variables were rearranged, grouped and inserted. None of the variables were equal to a specific number, like 5 or 0.001, but we can still solve for one variable in terms of the other variables when we use symbolic math. If we have numerical values for $z$ , $a$ and $b$ , we can use Python to calculate the value of $y$ .

But if we don't have numerical values for $z$ , $a$ and $b$ , Python and the SymPy package can be used to rearrange terms and solve for one variable in terms of the other.

Working with mathematical symbols in a programmatic way instead of working with numerical values in a programmatic way is called symbolic math.