Curious weakness in Simplify with Assumptions

• To: mathgroup at smc.vnet.net
• Subject: [mg19011] Curious weakness in Simplify with Assumptions
• From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
• Date: Tue, 3 Aug 1999 13:44:47 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Today I noticed a weakness in Simplify with assumptions. I tried

In[1]:=
Simplify[Sqrt[x] \[Element] Reals, x >= 0]
Out[1]=
Sqrt[x] \[Element] Reals

This leads to the following curious situation:

In[2]:=
Simplify[Sqrt[a^2 + b^2] \[Element] Reals,
a \[Element] Reals && b \[Element] Reals]
Out[2]=
2    2
Sqrt[a  + b ] \[Element] Reals

even though:

In[3]:=
Simplify[Sqrt[a^2 + b^2] \[Element] Reals, (a \[Element] Reals) && (b > 0)]
Out[3]=
True

In[4]:=
Simplify[Sqrt[a^2 + b^2] \[Element] Reals, (a \[Element] Reals) && (b < 0)]
Out[4]=
True

and

In[5]:=
Simplify[Sqrt[a^2 + b^2] \[Element] Reals, (a \[Element] Reals) && (b == 0)]
Out[5]=
True

which covers all the possibilities. Surely this is something that ought to
be fixed quite easily?

--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp

```

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