Re: Should facts() show duplicate facts?

I appreciate your CAD input (probably too big of a project for a
non-mathematician like myself, even with AI superpowers), but I'd also
appreciate some opinions on whether facts() should show the duplicated
facts :-)

TLDR: The same fact can exist multiple times in the database, but facts()
hides it from the user by deduplicating the output. The consequence is that
forgetting a fact seems successful (forget returns [fact]), but afterwards
it's still listed by facts(). And forget(facts()) doesn't work reliably, as
one might reasonably expect. Important: The duplicate facts themselves are
not a bug, but a necessity. They act as a kind of reference count.

I propose that facts() should "stop lying to the user".

Am Fr., 28. Aug. 2026 um 13:24 Uhr schrieb Barton Willis via Maxima-discuss
<[email protected]>:

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> ------------------------------
> *From:* Stavros Macrakis <[email protected]>
> *Sent:* Thursday, August 27, 2026 3:49 PM
> *To:* Richard J. FATEMAN <[email protected]>
> *Cc:* <[email protected]> <
> [email protected]>
> *Subject:* Re: [Maxima-discuss] Should facts() show duplicate facts?
>
> Caution: Non-NU Email
>
> Yes, CAD implementation would be nice. But ...
>
>    - The best is the enemy of the good.
>    - Who will bell the cat?
>
> Fixing the many bugs in the existing system is a Good Thing, and I'm very
> thankful that David Scherfgen has undertaken the task (with AI help).
>
> What's more, many of the bugs he's addressing are orthogonal to the
> qualities of CAD. They're about maintaining the database of facts, not
> about making inferences based on those facts.
>
> On Thu, Aug 27, 2026 at 4:39 PM Richard J. FATEMAN via Maxima-discuss <
> [email protected]> wrote:
>
> I think that addressing the creation and querying of a 'database of
> algebraic inequalities'
> may require an implementation of a system we have avoided for decades, but
> has been the topic of discussion in some other systems. Cylindrical
> algebraic decomposition would allow a program to determine, given a set of
> (algebraic) equations defining a region, whether a point is inside that
> region.  This doesn't address log, exp, etc functions.
> The 'assume' database works for very simple cases, but I think 'debugging'
> it is not going to address serious shortcomings.
> see https://en.wikipedia.org/wiki/Cylindrical_algebraic_decomposition
> <https://urldefense.com/v3/__https://en.wikipedia.org/wiki/Cylindrical_algebraic_decomposition__;!!PvXuogZ4sRB2p-tU!FDGytD_qHH2qVA2FPfYwl4fXT7UnedatI1upOf8zpCP-Ecj9hf-JFrSAgaSCBsXYUgZV6pO4GnGMiZE$>
> You might read that CAD
>  is Fundamental to CAS,  which of course makes one wonder how we've done
> without it.
> Read the wikipedia article and some references.
>   One issue is that -- whatever it is you want to do with CAD, it comes
> with a cost, namely the algorithms are generally doubly-exponential in the
> number of variables.  The interest in it (by G.E.Collins) was sparked by
> finding an alternative for Tarski's decision procedure.
> RJF
>
> On Thu, Aug 27, 2026 at 6:56 AM David Scherfgen via Maxima-discuss <
> [email protected]> wrote:
>
> I found this while working on bug #5120, and it surprised me, so I suspect
> it will surprise others too: The fact database can hold the same fact more
> than once, and facts() does not tell you.
>
> assume(notequal(a, 0))$
> assume(notequal(a*b, 0))$
> facts();
>   [notequal(a, 0), notequal(b, 0)]
>
> forget(notequal(a, 0))$
> facts();
>   [notequal(a, 0), notequal(b, 0)]
>
> The fact notequal(a, 0) existed twice, but facts() shows it only once. One
> must call forget() twice for the fact to actually disappear.
>
> The reason is that some assumptions are filed as several facts.
> notequal(a*b, 0) is stored as notequal(a, 0) together with notequal(b, 0),
> because that is the form the database can actually answer questions from.
> These internal facts are stored even if the database already contained
> them. On the other hand, trying to establish the same fact twice using the
> user-level function assume() will answer [redundant] from the second time
> on.
>
> That second copy of the fact is not a bug, and I want to be clear about
> that, because my first instinct was to call it a bug. It works as a "count
> of reasons", and it is what makes this case come out right:
>
> assume(notequal(a*b, 0))$
> assume(notequal(a*c, 0))$
> forget(notequal(a*b, 0))$
> facts();
>   [notequal(a, 0), notequal(c, 0)]
>
> notequal(a, 0) correctly survives, because notequal(a*c, 0) still says so.
> If the two assumptions shared a single entry, that forget would have taken
> it away.
>
> The one thing that does seem wrong is facts() not showing the duplicate
> facts, and because it is the only window users have, the whole thing looks
> inconsistent: forget() says it removed something, but then facts() says it
> is still there. And forget(facts()) doesn't work as one might reasonably
> expect.
>
> My proposal is simply that facts() should stop suppressing duplicates.
> forget(facts()) then becomes exact, and facts() agrees with what forget was
> already reporting.
>
> Duplicates appear only where there genuinely are two independent reasons
> for the same statement, which is exactly the situation a user needs to know
> about.
>
> This doesn't cause any test failures. But it is a user-visible change, so
> it would want a line in the manual saying a statement can appear more than
> once when more than one assumption supports it. It changes nothing about
> what assume means or what the database stores, only about what you are
> allowed to see.
>
> Is anyone opposed, or relying on facts() returning each fact at most once?
>
> There is a larger question behind this about whether the database should
> record what the user said or what Maxima knows, and the counting above is
> an approximation of the former. I would rather leave that for another
> thread and just stop hiding the count.
>
> Best regards
> David Scherfgen
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