From: fateman@gmail.com   
      
   On Sunday, November 5, 2023 at 7:19:47 PM UTC-8, Richard Fateman wrote:   
   > On Monday, October 16, 2023 at 4:04:35 AM UTC-7, Peter Luschny wrote:    
   > > What are the prime factors of 0, really?    
   > >   
   > >    
   >    
   > In Maxima, you get this:    
   > (%i1) ifactors(0);    
   >    
   > ifactors: argument must be a positive integer; found: 0    
   >    
   > -- an error. To debug this try: debugmode(true);   
      
   In the context of symbolic mathematical computer systems it is useful to   
   consider "factors" in a polynomial domain (say, over the integers), in which   
   an expression factors into "content" and "primitive part".Thus 2*x+4 has   
   content 2, and pp x+2.What are    
   the factors of   x+3? content 1, pp x+3.  This doesn't address "prime   
   factors", but it does say that 1 is a factor in this context.   
   What about 0?   uh, this actually comes up when one asks what is the gcd(0,   
   x+3)?    answer: x+3.   Acknowledging that x+3 is a factor of 0. what   
   about gcd(0,0)?   answer 0.  why?  It is convenient so that programs don't   
   break. If you insist    
   on something else for gcd, then you would need to check for 0 before calling   
   gcd, virtually every place.  So why not just agree about default for gcd   
   inside gcd?   
      
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