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Re: Unconventional Max[] behavior

• To: mathgroup at smc.vnet.net
• Subject: [mg28095] Re: [mg28048] Unconventional Max[] behavior
• From: Ralph Benzinger <mma-l at endlos.net>
• Date: Fri, 30 Mar 2001 04:12:50 -0500 (EST)
• References: <200103290824.DAA03053@smc.vnet.net> <B6E8F603.BC12%andrzej@platon.c.u-tokyo.ac.jp>
• Sender: owner-wri-mathgroup at wolfram.com

On March 29, you wrote:
> Note that it is quite easy to modify Simplify in such a way that
> it will work with Max and symbolic expressions, e.g.:
> 
> In[1]:=
> Unprotect[Simplify];
> Simplify[Max[a___,x_,b___,y_,c___],assum_:{}]/;Simplify[x>y,assum]:=Simplify
> [Max[a,x,b,c],assum];
> Simplify[Max[a___,x_,b___,y_,c___],assum_:{}]/;Simplify[x<y,assum]:=Simplify
> [Max[a,b,y,c],assum];
> Protect[Simplify];
> {Simplify};

Thanks, Andrzej, for this suggestion; I like it a lot.  It never
occurred to me to use Simplify in a Condition, but then -- viewing
Mathematica as a programming language -- I'm not quite used to the
distinction between evaluation and simplification anyway.  Note, by
the way, that

In[1]:=
	Simplify[Max[a+3,a^2+a+3,a],a>0]
Out[1]=
	3 + a + a^2

even without your additional rules.  Simplify is quite smart after
all!

> The answer to the second question is similar, that is, you have
> ot modify Simplify in the above manner or define your own
> version.

Yes, but since my main research involves theorem provers, I
traditionally shy away from Unprotecting things. :-)  I thought
of writing a wrapper function, but the one I'd propose for above
example, i.e.

	maxSimplify[Max[a___, x_, b___, y_, c___], assum_:{}] /; 
		maxSimplify[x > y, assum] :=
		maxSimplify[Max[a, x, b, c], assum];
	maxSimplify[x_,assum_:{}] :=
		Simplify[x,assum]

probably breaks down for cases where Simplification yields a Max
term that only maxSimplify can handle (I cannot come up with such
an example right now but I'm rather sure that one must exist).  Is
there a more proper way to write a wrapper function for Simplify --
or am I just too paranoid?

Ralph

-- 
Ralph Benzinger          "This is my theory, it is mine, I own it,
Cornell University        and what it is, too." -- Ann Elk (Mrs.)

• References:
  • Unconventional Max[] behavior
    • From: Ralph Benzinger <mma-l@endlos.net>