How to define a lot of symbols in SymPy

Question

I am trying to define a lot of variables in "sympy" for symbolic processing.

import sympy as sp

b_0 = sp.symbols('b_0')
b_1 = sp.symbols('b_1')
...
b_X = sp.symbols('b_X')

and so on with the X going from 1 to 1000.

Is there an easy way to do it?

Answer 1

There are a few options:

>>> sp.symbols('b_0:10')
(b_0, b_1, b_2, b_3, b_4, b_5, b_6, b_7, b_8, b_9)

or, using a formatted string,

>>> n = 10
>>> sp.symbols('b_0:{}'.format(n))
(b_0, b_1, b_2, b_3, b_4, b_5, b_6, b_7, b_8, b_9)

These return a tuple of symbols. There are more formatting options: see symbols docs.

There is also a function to generate a NumPy array of symbols:

>>> sp.symarray('b', 10)
array([b_0, b_1, b_2, b_3, b_4, b_5, b_6, b_7, b_8, b_9], dtype=object)

All of these examples are meant to be assigned to something. For example, b = sp.symbols('b_0:10') assigns the tuple of symbols to b, so they can be accessed as b[0], b[1], etc. SymPy symbols are not accessed by the string representing them, such as "b_0" or "b_1".

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Finally, there are Indexed objects in case you need an array of symbols of undetermined size: Indexed objects are created on the fly as you use A[n] notation with A being an IndexedBase.

Answer 2

If you want to still be able to call individuals symbols, like b_0:

Since:

from sympy import symbols

# Number of symbols you need
X = 5

b = symbols(f"b_0:{X}")
>>> b
(b_0, b_1, b_2, b_3, b_4)

>>> b_0
NameError: name 'b_0' is not defined

You could add them to the local variables through a dictionary:

from sympy import symbols

# Number of symbols you need
X = 5

# To still have b[i]
b = symbols(f"b_0:{X}")

b_dict = {f"b_{i}": b[i] for i in range(X)}
locals().update(b_dict)