Path: utzoo!attcan!uunet!cs.utexas.edu!yale!cmcl2!acf4!csd2!mitsolid
From: mitsolid@csd2.NYU.EDU (Thanasis Mitsolides)
Newsgroups: comp.binaries.ibm.pc.d
Subject: Re: man(1) for MSDOS?
Message-ID: <24460002@csd2.NYU.EDU>
Date: 7 Feb 90 19:29:00 GMT
References: <1990Feb1.175125.922@usenet.ins.cwru.edu>
Organization: New York University
Lines: 82

/* csd2:comp.binaries.ibm.pc.d / marshall@alpha.ces.cwru.edu ( ) /  9:51 am  Feb  5, 1990 */
>
>	Amazing how easy it is to produce so much confusion.

You ain't seen nothin' yet!

Thanasis


Relay-Version: version nyu B notes v1.6 9/18/89; site acf4.NYU.EDU
From: mainieri@acf2.NYU.EDU (Ronnie Mainieri)
Date: 7 Feb 90 11:09 EST
Date-Received: 7 Feb 90 11:09 EST
Subject: Re: MACSYMA flunks high school math (and REDUCE too)
Message-ID: <12040002@acf2.NYU.EDU>
Path: acf4!acf2!mainieri
Newsgroups: sci.math.symbolic
Posting-Version: version nyu B notes v1.6 9/18/89; site acf2.NYU.EDU
Organization: New York University
References: <167@sc2a.unige.ch>

/* acf2:sci.math.symbolic / pfennige@sc2a.unige.ch /  6:04 am  Feb  6, 1990 */
In article <2754@umbc3.UMBC.EDU>, rouben@math9.math.umbc.edu (Rouben Rostamian) writes:
> There is a quite a serious bug in MACSYMA  [UNIX MACSYMA Release 309.2.]  
[...]
> Problem:  Integrate the function
>                                    1
>               f(x) =  sqrt ( x +  --- - 2 )
>                                    x
> over the interval (0,1).
> 
> Note that f(x) is a well-defined, real-valued, non-negative function on the
> half-axis x>0.  The integral is easy to compute (by high school methods) and
> the correct answer is 4/3.   MACSYMA gives the erroneous answer -4/3:  A
> negative integral for a positive integrand!
> 
> Does anyone else get this too?
> 

Yes, REDUCE 3.3 (Vax/VMS) finds the same negative answer as your version of
MACSYMA.  In REDUCE the problem comes from a bug with the square root, indeed 
implicitely SQRT(x^2) simplifies into x.  There is a flag ('PRECISE') 
supposed to prevent such a simplification, i.e. SQRT(x^2) -> ABS(x), but 
it fails when x is a polynomial.  Below is a sample session of REDUCE:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

REDUCE 3.3, 15-Jul-87 ...

1: on precise;		% The flag is set on

2: sqrt(x^2);

ABS(X)			% The answer is correct for real numbers

3: sqrt((1-x)^2);

X - 1			% Here is the bug

4: load "algint";	% Module for integrants containing square roots

5: f:=sqrt(x+1/x-2);	% The function to integrate

       X - 1
F := ---------		% It simplifies badly
      SQRT(X)

6: int(f,x);

 2*SQRT(X)*(X - 3)
-------------------	% The answer is negative for x<3
         3

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

I would be curious to know how many current algebra systems simplifies
correctly radicals of expressions belonging to real numbers.  
At least I could experiment that mu-Math on an Apple II did not simplify such
things as ((x-1)^2)^(1/2) when the appropriate flag is set. 

	Daniel Pfenniger, Geneva Observatory
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