[sage-devel] Re: Opinions wanted on simplification method for real expressions

2014-11-05 Thread kcrisman 


 In http://trac.sagemath.org/ticket/14630, I have a patch that adds a 
 simplify_real() method to symbolic expressions. Pretty much the only 
 thing it does is simplify, 

   sqrt(x^2) - abs(x) 

 In the past, you could obtain this with simplify_radical(), even though 
 the variable `x` involved was assumed to be complex. That was busted, so 
 it was removed. But some people need the simplification above (see e.g. 


Just to clarify, current behavior is

sage: a = sqrt(x^2)
sage: a.simplify_radical()
x


 

 #14305), so the patch at least provides a way to get it. 


Still well worth a read, though perhaps too many opinions to come to 
resolution.

Anyway, as to your solution, I think that after this time rws is probably 
right that since no one actually implemented a context manager or domain 
parameter or whatever else then the option on the ticket (which needs to be 
a branch, sigh) is better than nothing.  At least it finally allows 
sqrt(x^2) - abs(x) again.  Though it should be tried with lots of 
irrelevant and perhaps strange assumptions like integer around to make sure 
it really re-assumes all assumptions when needed.

  So you're kind of on your own regarding how many simplifications to try 
and in what order.

Yes, that is currently the case anyway.  

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Re: [sage-devel] Re: Opinions wanted on simplification method for real expressions

2014-11-05 Thread Michael Orlitzky 
On 11/05/2014 08:34 AM, kcrisman wrote:

 
 Just to clarify, current behavior is
 
 sage: a = sqrt(x^2)
 sage: a.simplify_radical()
 x

Yeah, previously, simplify_radical() was silently setting the domain to
'real', calling radcan(), and then setting the domain back to 'complex'.

The round trip through Maxima (with the domain set to 'real') made the
simplification sqrt(x^2) - abs(x), at which point radcan() could do
nothing with it. By fixing one bug, the output actually became worse
because now radcan() sees the full sqrt(x^2) and will choose one root
arbitrarily but consistently.


 Anyway, as to your solution, I think that after this time rws is
 probably right that since no one actually implemented a context manager
 or domain parameter or whatever else then the option on the ticket
 (which needs to be a branch, sigh) is better than nothing.  At least it
 finally allows sqrt(x^2) - abs(x) again.  Though it should be tried
 with lots of irrelevant and perhaps strange assumptions like integer
 around to make sure it really re-assumes all assumptions when needed.

I just posted a branch with an additional test for assumptions(). It
also fixes an earlier bug (that I most likely introduced!) -- a test
earlier in the file that didn't forget() its assumptions.


  So you're kind of on your own regarding how many simplifications to
 try and in what order.
 
 Yes, that is currently the case anyway.  

We could always brute-force them. Tools like pngcrush use this to find
the best compression settings. Expression.simplify_rectform() already
checks to see if the result is simpler (via a highly complicated
algorithm, len(str(x))), so there's no reason we couldn't try 100
simplifications and see which is less complex.

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