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sci / sci.math.symbolic / Re: What are the prime factors of 0, really?

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* Re: What are the prime factors of 0, really?Richard Fateman
`- Re: What are the prime factors of 0, really?Richard Fateman

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Subject: Re: What are the prime factors of 0, really?
From: Richard Fateman
Newsgroups: sci.math.symbolic
Date: Mon, 6 Nov 2023 03:19 UTC
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Subject: Re: What are the prime factors of 0, really?
From: fateman@gmail.com (Richard Fateman)
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On Monday, October 16, 2023 at 4:04:35 AM UTC-7, Peter Luschny wrote:
> What are the prime factors of 0, really?
>
><snip>

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);

Subject: Re: What are the prime factors of 0, really?
From: Richard Fateman
Newsgroups: sci.math.symbolic
Date: Fri, 10 Nov 2023 15:53 UTC
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Subject: Re: What are the prime factors of 0, really?
From: fateman@gmail.com (Richard Fateman)
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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?
> >
> ><snip>
>
> 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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