To define variables with SymPy, first import the symbols() function from the SymPy module:
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from sympy import symbols
Symbolic math symbols are declared using SymPy's symbols() function. Note that in the arguments of the symbols() function, symbol names are separated by a space (no comma) and surrounded by quotes. The output of the symbols() function are SymPy symbol objects. These output objects need to be separated by comas with no quotation marks.
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x, y = symbols('x y')
Now that the symbols x and y are instantiated, a symbolic math expression using x and y can be created.
A symbolic math expression is a combination of symbolic math variables with numbers and mathematical opporators (such as +,-,/ and *. The standard Python rules for calculating numbers apply in SymPy symbolic math expressions.
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expr = 2*x + y
Use the .subs() method to insert a numerical value into a symbolic math expression, . The first argument of the .subs() method is the variable and the second argument is the numerical value. In the expression above:
If we substitute
$$ x = 2 $$The resulting expression should be
$$ 2(2) + y $$$$ 4 +y $$
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expr.subs(x, 2)
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The .subs() method does not replace variables in place, it only completes a one-time substitution. If expr is called after the .subs() method is applied, the originol expr expression is returned.
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expr
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In order to make the substitution permanent, a new expression object needs to be instantiated as the output of the .subs() method.
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expr = 2*x + y
expr2 = expr.subs(x, 2)
expr2
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SymPy variables can also be substituted into SymPy expressions
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x, y, z = symbols('x y z')
expr = 2*x + y
expr2 = expr.subs(x, z)
expr2
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More complex substitutions can also be used. Consider the following:
$$ 2x + y $$substitute in
$$ y = 2x^2 + z^{-3} $$results in
$$ 2x + 2x^2 + z^{-3} $$
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x, y, z = symbols('x y z')
expr = 2*x + y
expr2 = expr.subs(y, 2*x**2 + z**(-3))
expr2
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A more practical example could involve a large equation and several variable substitutions
$$ n_0e^{-Q_v/RT} $$$$ n_0 = 3.48 \times 10^-6 $$$$ Q_v = 12,700 $$$$ R = 8.31 $$$$ T = 1000 + 273 $$
In [9]:
from sympy import symbols, exp
n0, Qv, R, T = symbols('n0 Qv R T')
expr = n0*exp(-Qv/(R*T))
Multiply SymPy subs() methods can be chained together to substitue multiple variables in one line of code
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expr.subs(n0, 3.48e-6).subs(Qv,12700).subs(R, 8031).subs(T, 1000+273)
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To evaluate an expression as a floating point number, use the .evalf() method.
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expr2 = expr.subs(n0, 3.48e-6).subs(Qv,12700).subs(R, 8031).subs(T, 1000+273)
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expr2.evalf()
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