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Re: Reduce and Indeterminate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg87800] Re: Reduce and Indeterminate
  • From: dh <dh at metrohm.ch>
  • Date: Thu, 17 Apr 2008 06:57:48 -0400 (EDT)
  • References: <fu6mb9$nl0$1@smc.vnet.net>


Hi Szabolcs,

it would certainly be nice and consistent if a message about a invalid 

comparison is produced. But we must ask if real harm can be produced 

from this result and I think this is possible. Although all arthmetic 

operations on Indeterminate give Indeterminate, it is not hard to come 

up with a simple example where things go wrong:

f[x_]:=If[Reduce[x>0],"pos","neg","ind"];

Therefore, I think a warning is a must.

Daniel



Szabolcs Horvát wrote:

> If a complex number appears in an inequality, Reduce issues a warning:

> 

> Reduce[I > 0]

> 

> This is useful (to avoid mistakes).  But if Indeterminate appears in an 

> inequality, Reduce will immediately say False:

> 

> Reduce[Indeterminate > 0]

> 

> While it is debatable what is the correct thing to do mathematically, I 

> naively believe that it would be useful if Reduce at least gave a 

> warning.  It is true that it is not a good idea to manipulate 

> expressions completely blindly (without paying attention to what they 

> contain), but some functions may return very large expressions ... and 

> the main advantage of using computers is that they can do large and 

> tedious calculations quickly.

> 

> What do MathGroup readers think about this?

> 

> Here's a somewhat artificial example:

> 

> In[1]:= Integrate[1/x, {x, a, b}]

> 

> Out[1]= If[(-Im[b] Re[a] + Im[a] Re[b])/(Im[a] - Im[b]) >=

>     0 && ((Re[a/(-a + b)] >= 0 && a/(-a + b) != 0) ||

>      Re[a/(a - b)] >= 1 || Im[a/(-a + b)] != 0), -Log[a] + Log[b],

>   Integrate[1/x, {x, a, b},

>    Assumptions -> ! ((-Im[b] Re[a] + Im[a] Re[b])/(Im[a] - Im[b]) >=

>         0 && ((Re[a/(-a + b)] >= 0 && a/(-a + b) != 0) ||

>          Re[a/(a - b)] >= 1 || Im[a/(-a + b)] != 0))]]

> 

> In[2]:= First[%]

> 

> Out[2]= (-Im[b] Re[a] + Im[a] Re[b])/(Im[a] - Im[b]) >=

>    0 && ((Re[a/(-a + b)] >= 0 && a/(-a + b) != 0) ||

>     Re[a/(a - b)] >= 1 || Im[a/(-a + b)] != 0)

> 

> In[3]:= Reduce[% && (a | b) \[Element] Reals]

> 

> Out[3]= False

> 

> Note that unlike Reduce, FullSimplify gives a warning:

> 

> In[4]:= FullSimplify[%%, (a | b) \[Element] Reals]

> 

> During evaluation of In[4]:= FullSimplify::infd: Expression (-Im[b] \

> Re[a]+Im[a] Re[b])/(Im[a]-Im[b]) simplified to Indeterminate. >>

> 

> Out[4]= Indeterminate >=

>    0 && (Im[a/(-a + b)] != 0 ||

>     Re[a/(a - b)] >= 1 || (a/(a - b) != 0 && Re[a/(-a + b)] >= 0))

> 

> In[5]:= Reduce[Rest[%] && (a | b) \[Element] Reals, {a, b}]

> 

> Out[5]= (a < 0 && (b < a || a < b <= 0)) || (a >

>      0 && (0 <= b < a || b > a))

> 

> 




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