sage sum not python sum

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From $SAGE_ROOT/local/sage-exp/src/sage/misc/functional.py :

def symbolic_sum(expression, *args, **kwds):
"...."

    if hasattr(expression, 'sum'):                ## This catches possible specialized methods of some objects
        return expression.sum(*args, **kwds)
    elif len(args) <= 1:                          ## If 0 or 1 argument, call Python's sum
        return sum(expression, *args)
    else:
        from sage.symbolic.ring import SR
        return SR(expression).sum(*args, **kwds)  ## Use SR.sum by default

Then, from $SAGE_ROOT/local/sage-exp/src/sage/misc/all.py :

from .functional import (additive_order,
#...
                        symbolic_sum as sum,
# ...
)

At compilation time, when symbolic_sum is defined, Python's sum is accessible as sum, and used when no or a single argument is passed to symbolic sum.

At run time, the global identifier sum points to Sage's symbolic_sum ; however, thanks to Python's lexical scoping, this function still calls Python's sum if necessary : the definitions in use are those present when symbolic_sum was defined.

HTH,

Sage provides some functions with the same names as some Python built-in functions.

In the case of sum it tries to be unobtrusive, as @Emmanuel Charpentier's answer explains.

To force the use of Python's sum:

sage: from builtins import sum as python_sum
sage: python_sum([3, 4, 5])
12

To check where the currently active sum is from:

sage: import_statements(sum)
from sage.misc.functional import symbolic_sum

To have sum be Python's and symbolic_sum be Sage's:

sage: from builtins import sum
sage: from sage.misc.functional import symbolic_sum

To use symbolic_sum as sage_sum:

sage: from sage.misc.functional import symbolic_sum as sage_sum

The documentation could be improved on this topic. See the dedicated ticket:

• Sage Trac ticket 29516: Cross-link documentation of sum, prod, product