Difference between Python and SageMath: operator ^ does not work for sets

XOR
sets

asked 2026-07-02 07:09:59 +0200

ortollj
1399 ●32 ●72 ●113

In standard Python, the operator ^ is overloaded for set objects and performs the symmetric difference:

{1, 2, 3} ^ {3, 4, 5} # returns {1, 2, 4, 5} However, in SageMath, the same expression raises an error:

A = {1, 2, 3}
B = {3, 4, 5}

def test():
    print("hello")
    C = A ^ B
    return C

test()

Result:

hello TypeError: unsupported operand type(s) for ** or pow(): 'set' and 'set' This is surprising because:

the traceback shows ** instead of ^, the error message refers to exponentiation (pow), the line number corresponds to the correct location, but the operator displayed is not the one written in the code. This suggests that SageMath does not overload ^ for sets (unlike Python), and internally treats ^ as the exponentiation operator, even when applied to sets. The resulting error message is therefore misleading.

Workaround Use the explicit symmetric difference:

A.symmetric_difference(B)

or implement XOR manually:

def xorF(s0, s1):
    return (s0 - s1) | (s1 - s0)

Question Is this behavior intentional in SageMath? Should SageMath overload ^ for sets as Python does, or at least provide a clearer error message?

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2 Answers

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answered 2026-07-02 18:26:25 +0200

John Palmieri

9006 ●20 ●74 ●195 http://www.math.washin...

updated 2026-07-02 18:27:48 +0200

This is intentional, and it's part of the SageMath preparser, which automatically converts "^" to "**". One way to get around this is to turn it off:

A = {1, 2, 3}
B = {3, 4, 5}
preparser(False) # turn off preparsing when Sage reads the function definition

def test():
    print("hello")
    C = A ^ B
    return C

preparser(True) # safe to turn it back on now
test()

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Comments

Thank for the answer John Palmieri. One small observation: in a Jupyter notebook, the preparser seems to run on the entire cell before execution, so preparser(False) does not prevent the ^ → * conversion inside a function defined in that cell. As a result, A ^ B still becomes A * B in the traceback.

This is not a major issue at all, but I thought it might be useful to mention for notebook users.