How to construct GuessFinite?

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Neven Sajko

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Oct 7, 2021, 4:30:51 PM10/7/21
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I'm playing around with the Guess packages, but when I wanted to try
out GuessFinite I got errors like this:
GuessFinite(InnerFiniteField(2,1)) is not a valid type.
or
GuessFinite(FiniteField(2,1)) is not a valid type.
when I give a command such as this to the fricas prompt:
GuessFinite(InnerFiniteField(2, 1))

The situation is the same with both 1.3.7 and the latest Git commit
(30fb98da5db8ea3cd66).

Regards,
Neven

Ralf Hemmecke

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Oct 7, 2021, 4:39:01 PM10/7/21
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Hi Neven,
When I look at

https://fricas.github.io/api/GuessFinite.html?highlight=guessfinite

I see

F: Join(FiniteFieldCategory, ConvertibleTo Integer)

But neither InnerFiniteField(2, 1) nor FiniteField(2, 1) match the
category ConvertibleTo(Integer). However, PrimeField(2) does.

Maybe it's enough for you.

Ralf

Neven Sajko

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Oct 7, 2021, 4:43:19 PM10/7/21
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Thank you. I should have checked if the domain is convertible to
Integer before sending the mail.

This raises the question, why is FiniteField(p,n) not convertible to
Integer? I mean is it just an omission?

Regards,
Neven

Ralf Hemmecke

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Oct 7, 2021, 4:53:44 PM10/7/21
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> This raises the question, why is FiniteField(p,n) not convertible to
> Integer? I mean is it just an omission?

I would like to say, I leave this to you as an exercise. ;-)
Of course, conversion can "somehow" be done.
For PrimeField the conversion is quite natural, but how would you
convert between the integers 0,1,2,3 and the elements of FiniteField(2,2)?


(339) -> FF ==> FiniteField(2,2)
(340) -> a1 := 1$FF
(340) 1

(341) -> a2 := a1+a1
(341) 0

(342) -> a3 := a1+a1+a1
(342) 1

Hmmmm... isn't that strange? ;-)

Ralf

Neven Sajko

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Oct 7, 2021, 5:06:59 PM10/7/21
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Hah, turns out that finite fields are something quite different from
what I assumed them to be. Thank you.

Neven
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