<lus|wazze>
hm I'm not sure how you would define multiplication for that
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<Vincenz>
per-element
<lus|wazze>
but basically yes, that could be a method
<lus|wazze>
no per-element doesn't work
<Vincenz>
why not?
<Vincenz>
it's an operatio
<Vincenz>
operation
<lus|wazze>
in a field you can't have a*b=0 when a and b are both not 0
<lus|wazze>
(0,1)*(1,0) = (0,0)
<Vincenz>
hmm, oh yeah
<lus|wazze>
but neither (0,1) nor (1,0) are zero
<lus|wazze>
anyway, I already gave an example above
<Vincenz>
I haven't touched heavy field mathematics, just the definition in 2nd year college, and a refresh of primefields in my crypto course
<lus|wazze>
simply take those 2x2 matrixes with entries from the field with 3 elements
<Vincenz>
but basically
<Vincenz>
any two fields of the same amount of elements are isomorphic
<lus|wazze>
of the above-mentioned form
<Vincenz>
yup yup
<lus|wazze>
thats not true either , only for finite fields :)
<Vincenz>
well, you're working with a prime
<Vincenz>
so your field is finit
<Vincenz>
e
<lus|wazze>
for example,. |Q (the rational numbers) and |Q(sqrt(2)) (the rational numbers including all powers and products of powers of the square root of 2)
<lus|wazze>
are equally large, but not isomorphic
<lus|wazze>
yes
<lus|wazze>
but what I want to do is prove this special case of that theorem
<lus|wazze>
that any two finite fields of same order are isomorphic
<Vincenz>
hmm
<lus|wazze>
only just for fields of order p^2
<Vincenz>
I'm afraid I have not had enough mathematics for that
<Vincenz>
I studied EE, not math
<lus|wazze>
I already DO know that fields of order p are isomorphic, and that a field of order p^n is a vector space of dimension n over that field
<lus|wazze>
:)
<lus|wazze>
well I do ;)
<Vincenz>
you study math?
<Vincenz>
pure math?
<Vincenz>
neat
<lus|wazze>
yup^^
<lus|wazze>
anyway we got a little carried away
<Vincenz>
yup
<lus|wazze>
I was looking for yoru example
<Vincenz>
lol
<lus|wazze>
I just thought asking couldn't hurt ;)
<lus|wazze>
(Where entrypoint is the name of another entry point in the same lexer definition.) Recursively call the lexer on the given entry point. Useful for lexing nested comments, for example.
<lus|wazze>
i.e. you can define several rules, and again call a lexer on the current state
<lus|wazze>
for example you could do it something like
<lus|wazze>
rule foobar = COMMENT-OPENER -> { baz state } | ... and baz COMMENT-OPENER -> { baz state } | COMMENT-CLOSER -> { done } | ANYTHING ELSE -> { ignore it }
<Vincenz>
no I know
<Vincenz>
I call the comment closer function
<Vincenz>
if that one finds an open comment
<Vincenz>
I call it again before letting it get out
<Vincenz>
:)
<lus|wazze>
exactly :)
<lus|wazze>
simple recursion^^
<Vincenz>
yup
<lus|wazze>
damn now I have to get back to my algebra homework
* Vincenz
pats lus|wazze on the back
<lus|wazze>
and Ive already done all the other problems
<lus|wazze>
but this one seems exceedingly difficult to me
<Vincenz>
what was another problem?
* Vincenz
wants to have a go
<lus|wazze>
what I posted above as an example - constructing explicit, finite fields of orders p^2 and p^p
<Vincenz>
ah
<Vincenz>
p^p
<Vincenz>
?
<lus|wazze>
p to the p'th power
<Vincenz>
is that a special case?
<Vincenz>
what makes p^p more special than....p^143
<Vincenz>
taht's just a pth dimension vector that you make a pth dimension matrix of (or a p*p matrix?)
<lus|wazze>
you can construct such fields relatively easily if you know that X^p = X in the field with p elements
<Vincenz>
ah true
<lus|wazze>
well, the way you do that is you prove that the polynomial X^p - X + 1 is irreducible in the field |F_p , that is, the field {0,1,..,p-10
<lus|wazze>
well, the way you do that is you prove that the polynomial X^p - X + 1 is irreducible in the field |F_p , that is, the field {0,1,..,p-1}
<lus|wazze>
when you knw that, and also know that an irreducible polynomial produces a maximal ideal in that ring, and that a commutative ring modulo a maximal ideal produces a field, you have what you were looking for
<Vincenz>
ugh, I wish you used dutch terms
<Vincenz>
I might be able to follow more
<lus|wazze>
I don't know dutch unfortunately :)
<lus|wazze>
hm and the german terms are almost in all cases the same as the english ones
<lus|wazze>
except field = körper they are pretty much alike
<lus|wazze>
an ideal in ring-theory is pretty similar to a normal subgroup in group theory if that helps
<Vincenz>
ah
<Vincenz>
you speaking of ring because each element gets generated from a single element a that is a prime w.r.t p?
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<lus|wazze>
ring is the name of a certain algebraic structure
<lus|wazze>
the set of whole numbers is a ring, for example
<Vincenz>
so ring <> group because?
<lus|wazze>
a ring is a special case of an abelian group
<Vincenz>
ugh
<Vincenz>
I should buy a book on math
<Vincenz>
brush up
<lus|wazze>
ah dont worry
<Vincenz>
problem is I saw most of this stuff like a year ago
<Vincenz>
you finish college
<Vincenz>
you forget it all
<lus|wazze>
those are already pretty specific areas
<Vincenz>
we had most of it
<lus|wazze>
these things dont have much use outside of, say, number theory :)
<Vincenz>
for algebra and crypo
<Vincenz>
crypto
<lus|wazze>
group theory is the most important part of algebra for CS type people
<Vincenz>
generative polynomials
<Vincenz>
fields
<lus|wazze>
you don't really need much field and basically next to no ring theory
<Vincenz>
groups
<Vincenz>
rings
<lus|wazze>
hm
<Vincenz>
I did, ee, not cs
* Vincenz
slaps lus|wazze around with a recursive trout
<Vincenz>
feel that tail
<lus|wazze>
well the ring of polynomials is a, now THE really important kind of rings
<lus|wazze>
apart from that
<lus|wazze>
lol :)
<lus|wazze>
polynomials over a field or another commutative ring is really the only really important special case of a ring apart from fields
<lus|wazze>
well that, and rings of matrixes
<lus|wazze>
bt what would that leave to us math-types if all of the EE and CS people already knew everything about rings and fields and groups ;)
<Vincenz>
hehe
<Vincenz>
true
<Vincenz>
now all you need to do is find a loop in the primitive world
<Vincenz>
like, factoring
<Vincenz>
find some math trick that will solve it
<Vincenz>
and goodbye crypto
<Vincenz>
or find the log of a number in a primitive field
<lus|wazze>
eek a tick :(
<lus|wazze>
i didnt even notice what that was tzhat i was just scratching off D:
<lus|wazze>
until i held it in my fingers and looked at it :0
<Vincenz>
ugh
<Vincenz>
disgusting
<Vincenz>
finally someone who talks on ocaml
<Vincenz>
usually it's quieter than a tomb here
<Vincenz>
that's why I hang out on haskell, although I am trying to learn ocaml
<lus|wazze>
=)
<lus|wazze>
i dont really like haskell
<Vincenz>
too pure to be pragmatic
<lus|wazze>
it has a kinda-sorta fanatical "we will allow NO side-effects in our language, even for expressing side-effects!!!!" feel to it imho
<Vincenz>
hehe
<Vincenz>
monads
<Vincenz>
no clue what they are, just their name
<lus|wazze>
exactly
<lus|wazze>
hm
<lus|wazze>
maybe i should pick that tick out of the garbage again, see if its still alive and if so, torture it a bit ... that should learn em nasty little critters >8[
<Vincenz>
plus the fact that you don't have sideeffects means you have to pass the entire environment along in each function
<Vincenz>
wow
<Vincenz>
nasty smiley
<Vincenz>
I'd go for a lighter
<Vincenz>
pin him on a very fine pin
<Vincenz>
and fry him
<Vincenz>
SLOWLY
<lus|wazze>
sadly i think it didnt survive my scratching action
<Vincenz>
damn
<lus|wazze>
luckily i got vaccinated just about a week ago now
<Vincenz>
where do you livE?
<lus|wazze>
so I think I'm safe
<lus|wazze>
southern germany
<Vincenz>
ah
<lus|wazze>
swabia , near the french border
<Vincenz>
not so far
<Vincenz>
I thought us or something
<lus|wazze>
nah
<Vincenz>
cause you speak quite fluently in english
<lus|wazze>
actually Im not really satisfied with my level of mastery of the english language
<lus|wazze>
i want to try to become as close to a native speaker as i can
<lus|wazze>
sadly its pretty hard to really get further with that, especially living in a non-english speaking environment
<lus|wazze>
my father is originally from the us
<lus|wazze>
so i consider it something of a pity that i only know english like a second language, not on the level of a native-speaker like i think i should
<Vincenz>
on the other hand you know other languages cause you live in europe
<lus|wazze>
the only languages i currently know to any reasonable level are german and english
<lus|wazze>
i mean i took some french in school but i dont have anything to show for it
<lus|wazze>
what it mainly taught me is that while french people write like this: "je ne sais pas" and would like their language to be represented as sounding something like this: "jay nay say pah" they really speak something like this: "janspa"
<lus|wazze>
(no offense to any french people here, this only supposed to show my level of ignorance about the language after learning it in school for about ... oh ... 5 years)
<lus|wazze>
:|
<Vincenz>
hmm
<lus|wazze>
hm?
<stefp>
lus|wazze: je ne sais pas de quoi tu parles :)
<lus|wazze>
:p
<stefp>
you are right about the real pronounciation
<stefp>
real languages are very different from what your leanr in school.
<stefp>
and IRC can be even weirder.
<lus|wazze>
well it seemed to me that especially the way french was taught in school was really pretty far off from what the language really is like
<stefp>
but usually in programmatic channels, people try to talks correctly
<lus|wazze>
but I don't really know much anymore either way
<stefp>
BTW if you are interested in Perl. We organize YAPC::EU 2003 in Paris. http://yapc.mongueurs.net
<lus|wazze>
hm i dont really like perl i have to admit
<stefp>
I wanted to invite the OCAML guy to talk about their VM, to compare with the Parrot VM. but there was no interest
<stefp>
I though perler more curious
<stefp>
I am interested in OCAML because I don't know much about type inference
<lus|wazze>
?
<lus|wazze>
yeah type inference is interesting
<stefp>
s/perler/programmer who do perl/
<lus|wazze>
ic
<lus|wazze>
but type inferencing is something quite neat i think
<lus|wazze>
but its really not that difficult
<stefp>
I am a total beginner though. even if the mathematical concepts are not new to me.
<stefp>
I read a little about category theory
<lus|wazze>
once you get how the algorithm works, its really strikingly simple and elegant
<lus|wazze>
heh i don't know any category theory to be honest :)
<lus|wazze>
but I've once seen a very terse SML implementation of a unification function
<stefp>
SML?
<lus|wazze>
before that i never understood the algorithm
<lus|wazze>
but that function was just so ... i dont know ... clear it all was clear to me right away
<lus|wazze>
sml is another dialect of ml
<lus|wazze>
the family of languages, of which ocaml is án example
<stefp>
I have bought "modern compiler implementation in ML"
<stefp>
so I will have to get familiar with that too.
<lus|wazze>
=)
<stefp>
I bought "types an proramming language too".