square root expression simplification



On 11/2/10 12:41 PM, Leo Butler wrote:
>
> On Mon, 1 Nov 2010, Richard Fateman wrote:
>
> < Here is a suggestion on simplification, in terms of setting policy.
> < 
> < Each person who makes a suggestion must fit it into a table, for
> < simplification
> < of  x^y.   (simpexpt program, or some subroutine of it will implement the
> < policy).
> < 
> < Across the top of the table you list the characteristics of x, and down the
> < side
> < you list the characteristics of y.  The entry in the table says what to
> < return.
> < 
> < the characteristics for x include:
> < 
> < x is an atomic symbolic literal
> < x is an explicit positive integer
> < x is an explicit positive rational number
> < x is an explicit negative rational number
> < x is zero
> < x is a symbolic expression of the form (a^(z))  where gcd(1/z, y)= n >0, and
> < a=polynomial.
> < x is a symbolic expression that, after factoring, is of the form a^z ..
> < x can be deduced by using assumptions to be positive, negative, non-negative,
> < ....
> < 
> <  and many more.
> < 
> < 
> < The characteristics for y include some of the same characteristics for x, but
> < may include more
> < 
> < There may also be a need for additional tables. For example, a whole new table
> < for each combination
> < of global flags that affect the simplification of x^y.   If there are 3 such
> < flags, each true/false, then there
> < may need to be 8 tables.
>
>
>  RJF,
>  Your suggestion is silly, a straw man.
>
>  You apparently are trying to ridicule the notion that one should be
>  explicit about the simplification policies one uses.
>
You may think it's silly, but he makes a good point.  How can we decide
on future policies if we don't even know what the policy is today?  And
how do all the flags affect the outcome?

Granted x^y is particularly nasty, but consider that something simple
like numerical evaluation of things other than x^y is messy.  There are
bug reports on how inconsistent we are with numer and float.  Float
doesn't always convert everything to a float.  Numer sometimes does.

If nothing else, such a table will tell us where we are.

Ray