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MathGroup Archive 2005

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Strange Min/Max result

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62324] Strange Min/Max result
  • From: neillclift at msn.com
  • Date: Sat, 19 Nov 2005 23:19:24 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

While playing with a equation for addition chains I wanted to
manipulate something like this:

n = 2i + Sum[Min[i - j, 2^(d - r + 1 - j)], {j, 0, r - 3}]

Now Mathematica doesn't seem to be able to do much with equations like
this.
I had no clue but Mathematica knows much more than me. I happened to be
flipping
though The Mathematica Guidebook for Symbolics and saw this being used:

max[x_, y_] := 1/2(x + y + Sqrt[(x - y)^2])

Very smart. So I thought I could do:

min1[x_, y_] := 1/2(x + y - Sqrt[(x - y)^2])

This gives the wrong results though:

n = 2i + Sum[min1[i - j, 2^(d - r + 1 - j)], {j, 0, r - 3}]

n = 2^(2+d-2r)(-4+2^r) + 2i

I can see its wrong with something like this:

n = 2i + Sum[min1[
          i - j, 2^(d - r + 1 - j)], {j,
              0, r - 3}] /. d -> 8 /. r -> 4 /. i -> 16
n = 80

The real answer is
n = 2i + Sum[Min[
          i - j, 2^(d - r + 1 - j)], {j,
              0, r - 3}] /. d -> 8 /. r -> 4 /. i -> 16
n = 63

So whats going on here and is there any way to manipulate equations
with Min and Max in them?
Thanks.
Neill.


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