Re: How to use sign[] for symbolic operations?

• To: mathgroup at smc.vnet.net
• Subject: [mg19526] Re: [mg19513] How to use sign[] for symbolic operations?
• From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
• Date: Sun, 29 Aug 1999 17:21:24 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```In mathematica 4.0 you can do this:

In[1]:=
Simplify[Sign[a*b] > 0, a > 0 && b > 0]
Out[1]=
True

Although this is not quite what you are asking for in practice one can
This does not work in mathematica 3.0 there is another approach which I
think does work and which sometimes can be more convenient. Simply tell
Mathematica that a and b are negative:

In[1]:=
a /: Sign[a] = -1; b /: Sign[b] = -1;

Now you can do things like:
In[2]:=
Sign[Pi*a^3*b^2-1]
Out[2]=
-1
In[3]:=
Sign[Pi*a^4*b^2 + 1]
Out[3]=
1

(I am doing all this using Mathematica 4.0 but I expect it to work in the
same way in v. 3. If it doesn't it is easy to write one's own function sign
which does).
--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp

----------
>From: LD <doellinger at t-online.de>
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net
>Subject: [mg19526] [mg19513] How to use sign[] for symbolic operations?
>Date: Sat, Aug 28, 1999, 8:53 PM
>

> I use Mathematica 3.0. My question is how to solve the following
> problem:
> I define a < 0 and b < 0 (to intend that the sign is negative in both
> cases). Now I like to
> know the sign of the produkt of a*b, it should be positive by the hand.
> But how can I express it
> within mathematica 3.0? In general: how can I get the sign of an
> expression in symbolic form?
> In  1: Sign[a*b] ?
> Out 1: > 0 or positive.
>
> Many thanks for your help.
>
> Lothar Dillinger
>
> EMail: doellinger at t-online.de
>
>

```

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