[Axiom-developer] [#69 sqrt(-1/abs(x))-1/sqrt(-abs(x))]

[kratt6]

Changes http://wiki.axiom-developer.org/69Sqrt1AbsX1SqrtAbsX/diff
--
Just for the archive, here is the patch::

  --- /home/rubey/axiom/mnt/linux/src/algebra/algfunc.spad      2004-05-21 
18:51:30.000000000 +0200
  +++ algfunc.spad      2004-05-25 13:39:19.000000000 +0200
  @@ -431,9 +431,20 @@
         hackroot(x, n) ==
   --        one? n or one? x => x
           (n = 1) or (x = 1) => x
  +
  +--  the following is FALSE! if x can be negative. Example: x=-1/2 would pass 
the
  +--  test and give 1/(-2)^(1/n) ~= (-1/2)^(1/n)
   --        (x ^= -1) and (one?(num := numer x) or (num = -1)) =>
  -        (x ^= -1) and (((num := numer x) = 1) or (num = -1)) =>
  -           inv hackroot((num * denom x)::F, n)
  +--        (x ^= -1) and (((num := numer x) = 1) or (num = -1)) =>
  +--           inv hackroot((num * denom x)::F, n)
  +
  +--  permissible when denom x is a positive number
  +
  +        (((dx := denom x) ^= 1) and
  +      ((rx := retractIfCan(dx)@Union(Integer,"failed")) case Integer) and
  +      positive?(rx))
  +         => hackroot((numer x)::F, n)/hackroot(rx::Integer::F, n)
  +
           (x = -1) and n = 4 =>
             ((-1::F) ** (1::Q / 2::Q) + 1) / ((2::F) ** (1::Q / 2::Q))
           kernel(oproot, [x, n::F])
--
forwarded from http://wiki.axiom-developer.org/address@hidden