       Assumptions, Abs, etc.

• To: mathgroup at smc.vnet.net
• Subject: [mg110171] Assumptions, Abs, etc.
• From: "S. B. Gray" <stevebg at ROADRUNNER.COM>
• Date: Sun, 6 Jun 2010 06:41:04 -0400 (EDT)

```Can anyone tell me why the following results appear?

Clear[xc1, xc2]
Simplify[Abs[xc1 - xc2]^2, Assumptions -> {xc1 < 0, xc2 < 0}]
Simplify[Abs[xc1 - xc2]^2, Assumptions -> {xc1 < 0, xc2 > 0}]
Simplify[Abs[xc1 - xc2]^2, Assumptions -> {xc1 > 0, xc2 < 0}]
Simplify[Abs[xc1 - xc2]^2, Assumptions -> {xc1 > 0, xc2 > 0}]
(xc1 - xc2)^2
(xc1 - xc2)^2
(xc1 - xc2)^2
(xc1 - xc2)^2

Simplify[Abs[xc1 - xc2]^2, Assumptions -> xc2 < 0]
Simplify[Abs[xc1 - xc2]^2, Assumptions -> xc2 > 0]
Simplify[Abs[xc1 - xc2]^2, Assumptions -> xc1 > 0]
Simplify[Abs[xc1 - xc2]^2, Assumptions -> xc1 < 0]
Abs[xc1 - xc2]^2
Abs[xc1 - xc2]^2
Abs[xc1 - xc2]^2
Abs[xc1 - xc2]^2
Abs[xc1 - xc2]^2

Simplify[Abs[xc1 - xc2]^2 - (xc1 - xc2)^2, Assumptions -> {xc1 -> 0}]
Simplify[Abs[xc1 - xc2]^2 - (xc1 - xc2)^2, Assumptions -> {xc2 -> 0}]
-xc2^2 + Abs[xc2]^2
-xc2^2 + Abs[xc2]^2

(* the next lines say that xc1, xc2 are Reals **)

Simplify[Abs[xc1 - xc2]^2, Assumptions -> {xc1 \[Element] \!\(\*
ButtonBox["Reals",
ButtonData->"paclet:ref/Reals"]\), xc2 \[Element] \!\(\*
ButtonBox["Reals",
ButtonData->"paclet:ref/Reals"]\)}]
Abs[xc1 - xc2]^2

I would expect all 9 answers to be (xc1 - xc2)^2. Wrong?

Steve Gray

```

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