It is very much hallucinating. Worse, it seems that it does not know the
sage codebase very well, since sage has actually some dedicated tools
helping with the question - in the case at hand, oeis, findstat and
Bijectionist come to mind. Is there a fundamental reason it does not know
them? The rest of this post is a quote.
How can sage help with finding a bijection?
Great question! SageMath, or simply Sage, is a robust open-source
mathematical software system that can be used to study a wide range of
mathematical structures.
Finding a bijection, or a one-to-one correspondence between two sets, falls
within the domain of combinatorics or graph theory subsets of mathematics,
both of which Sage is well-equipped to help with.
Here's a sample of how you might use Sage to find a bijection between two
sets:
# Define two sets A = Set([1, 2, 3, 4, 5]) B = Set(['a', 'b', 'c', 'd', 'e'])
# Define a bijection from A to B f = A.bijection(B, lambda x: chr(96 + x))
In the above snippets, we create a bijection from the set {1, 2, 3, 4, 5}
to the set {'a', 'b', 'c', 'd', 'e'} using the bijection() method in Sage's
Set class. This bijection is defined by the lambda function lambda x:
chr(96 + x), which translates each integer x in A to a corresponding letter
in B (using ASCII values).
In addition, SageMath contains numerous packages (sage-data-elliptic_curves,
sage-data-polytopes_db, sage-data-conway_polynomials, etc.) related to
different mathematical fields that may be used based on your specific
requirements.
Remember, each problem may require a different approach, and this is just a
basic example. You will need to tailor the approach depending on the
complexity of the sets and the bijection you are attempting to establish.
On Saturday, 1 July 2023 at 20:25:27 UTC+2 Robert Bruner wrote:
For example, I asked how to compute a resolution of a module over the
Steenrod algebra. The answer is basically right, but contains the
misleading phrase
"To prove that the output is a resolution, we can check that the
composition of consecutive maps results in the zero map by using the helper
function is_complex() as displayed in the provided files."
Of course anyone who is likely to ask such a question will know that not
all complexes are exact, so this isn't all that dangerous, but it is wrong.
Bob Bruner
________________________________________
From: sage-...@googlegroups.com <sage-...@googlegroups.com> on behalf of
William Stein <wst...@gmail.com>
Sent: Saturday, July 1, 2023 11:31 AM
To: sage-...@googlegroups.com
Subject: Re: [sage-devel] Re: Ask about the SageMath codebase using ChatGPT
[EXTERNAL]
On Sat, Jul 1, 2023 at 2:56 AM Nils Bruin <nbr...@sfu.ca> wrote:
>
> On Friday, 30 June 2023 at 20:41:51 UTC+2 William Stein wrote:
>
> The point is that instead of using GPT's vague memory of what it might
> have seen, this instead uses the actual Sage source code, and mainly
> uses GPT to make sense of it.
>
>
> Given that only some select code fragments are included in the prompts,
wouldn't you still end up relying on GPT's vague, hallucination-prone
general memory to come up with a broader interpretation of the context
provided? It runs a real risk of just generating harder-to-spot errors.
>
This video is a good place to start: https://youtu.be/ZNW1XhT7qC4
--
William (http://wstein.org)
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