On Wed, Nov 4, 2009 at 8:35 AM, Vincent D <20100.delecr...@gmail.com> wrote:
>
> I understand now (and agree on) the design: sqrt(2) is symbolic and
> any sage expression containing a symbolic expression is also symbolic.
> But, considering the non comparison, it seems to give a set theoritic
> contradiction:
>
> sage: sqrt(2) in RR
> True
You might find the relevant source code that implements Sage's general
"in" of interest:
def __contains__(self, x):
r"""
True if there is an element of self that is equal to x under
==, or if x is already an element of self. Also, True in other
cases involving the Symbolic Ring, which is handled specially.
For many structures we test this by using :meth:`__call__` and
then testing equality between x and the result.
The Symbolic Ring is treated differently because it is
ultra-permissive about letting other rings coerce in, but
ultra-strict about doing comparisons.
EXAMPLES::
sage: 2 in Integers(7)
True
sage: 2 in ZZ
True
sage: Integers(7)(3) in ZZ
True
sage: 3/1 in ZZ
True
sage: 5 in QQ
True
sage: I in RR
False
sage: SR(2) in ZZ
True
sage: RIF(1, 2) in RIF
True
sage: pi in RIF # there is no element of RIF equal to pi
False
sage: sqrt(2) in CC
True
sage: pi in RR
True
sage: pi in CC
True
sage: pi in RDF
True
sage: pi in CDF
True
"""
P = parent_c(x)
if P is self or P == self:
return True
try:
x2 = self(x)
EQ = (x2 == x)
if EQ is True:
return True
elif EQ is False:
return False
elif EQ:
return True
else:
from sage.symbolic.expression import is_Expression
if is_Expression(EQ): # if comparing gives an
Expression, then it must be an equation.
# We return *true* here, even though the equation
# EQ must have evaluated to False for us to get to
# this point. The reason is because... in practice
# SR is ultra-permissive about letting other rings
# coerce in, but ultra-strict about doing
# comparisons.
return True
return False
except (TypeError, ValueError):
return False
>
> And RR is an ordered field.
>
> I think it goes in the same direction as the question asked by Gonzalo
> on SR(1) + SR(2).
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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