On 1 August 2013 11:10, chris wuthrich <[email protected]> wrote:
>
>
>> No - because sqrt is multivalued, the answer can be, and in this case is,
>> multivalued: sometimes true and sometimes false. This isn't desperately
>> helpful, or course, and can be cast in other ways in terms of the defect
>>
> If a boolean is "sometimes true and sometimes false" it is false and that is
> what I want sage to give back. Sage does not have "multi-valued booleans" I
> believe.
I mostly agree, but in the following:
sage: var('a b')
(a, b)
sage: bool(a==a)
True
sage: bool(a==a+1)
False
sage: bool(a==a*a)
False # bad? it is True for a=0,1
sage: bool(b*a==a*b)
True
sage: bool((a+b)^2==a^2+2*a*b+b^2)
True
sage: bool(sqrt(a)^2==a)
True #bad? is is False for all a<0
I don't like seeing True unless the expression is a tautology, i.e. an
identity, and I don't like seeing False unless it is always false (the
negation of a tautology. This is a different questions from the one
about branches of sqrt.
I try to avoid using symbolic expressions at all costs because of
things like this. After setting x = a==a+1 os that x has type
sage.symbolic.expression.Expression we have bool(x) is False, but I
don't know how bool(x) is evaluated. The documentation says that
bool(x) returns False because x is not always True, but
bool(x.negation()) is True even though x.negation() is 'a != a^2'
which is *not* always True. So that is surely a bug, anyway.
John
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