Dear William,
> This is completely orthogonal to the real question, which is about
> design. You've replaced the question of whether or not sqrt(2) > 1
> should be *simplified* automatically, by the question of how to do
> such simplifications. How to do them, is a black box that can change
> over time -- in fact right now it *does* user intervals in some cases
> -- you'll recall that Robert Bradshaw spent significant time writing
> code to do this in order to optimize Sage symbols (using Maxima to do
> such simplifications made things massively too slow).
[...]
> Simplifying "foo > bar" to True or False in cases when we can
> unambiguously do so is a change at least worth discussing. We
> simplify x + x, so why not simplify sqrt(2) > 1?
> Next, let's think about changes. If we change Sage to simplify
> sqrt(2) > 1 by default, we are making a potentially major backwards
> incompatible change. So the argument for this has to be compelling.
[...]
> This reminds me of / being a constructor for elements of QQ, no matter
> what, i.e., a/b for a and b both integers (with b!=0) is a rational,
> no matter what:
>
> sage: type(2/3)
> <type 'sage.rings.rational.Rational'>
> sage: type(2/1)
> <type 'sage.rings.rational.Rational'>
>
> This was an important design decision that David Kohel pushed hard for
> early on. Having sqrt(2) > 1 *not* simplify by default is consistent
> with this design decision in that "foo > bar" for either foo or bar
> symbolic, is a constructor for a symbolic equation.
+1 to no simplification...
Rationale: I think indeed that it is very important that the type of the
result of an operator depends only of the type of the operands and not of
their actual values. If > is a constructor for symbolic equation, it sounds me
perfectly good that sage returns the following:
sage: SR
Symbolic Ring
sage: SR(1) > SR(2)
1 > 2
because it returns:
sage: x > 2
x > 2
if x is symbolic.
Cheers,
Florent
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