Thank you Elijah. There is a lot for me to unpack in your approach. I need a cup of coffee and chew on it deeply in the morning.
Thanks again Raul. I looked at the p. verb before - this verb feels kind of strange. For this specific case (x^6+1=0) and the example in NuVoc, they work nicely! I tried something even simpler when I first saw it: x^2 - 1 = 0. The answer looks very strange. p. -1 0 1 +--+--------+ |_1|0j1 0j_1| +--+--------+ So, I have always thought the p. verb is designed for a special kind of polynomial which I don't currently understand, and opted to use the Euler formula based approach instead. Or am I using the p. wrong? Maurice On Sat, Oct 23, 2021 at 9:00 PM Elijah Stone <[email protected]> wrote: > Here is a fun party trick: > > rt=. (] %: -@[) * [: ^ [: j. ] %~ 1p1 + 2p1 * i.@] > pw=. ^ :. rt > f=. 1 + ] pw 6: > (f^:_1) 0 > 0.866025j0.5 6.12323e_17j1 _0.866025j0.5 _0.866025j_0.5 _1.83697e_16j_1 > 0.866025j_0.5 > f (f^:_1) 0 > _2.22045e_16j6.10623e_16 0j3.67394e_16 _2.22045e_16j_6.10623e_16 > _2.22045e_16j2.05391e_15 0j1.10218e_15 0j3.10862e_15 > > (Sadly, the inverter is not smart enough to invert e.g. 1 + pw&3 + pw&6, > so p. is probably the more practical solution.) > > -E > > On Sat, 23 Oct 2021, More Rice wrote: > > > Thank you for the notes - I'll keep it in my bookmark as reference! > > > > I started out this morning with my pre-calculus book trying to practice J > > sentences with. I wanted the numeric answers for complex roots. Like: > > > > // matlab version > > syms x > > eqn = x^6+1 == 0 > > solve(eqn, x) > > > > But, it seems J only gives the principal root (?), not all 6 of them; so, > > another opportunity for practise. But, I ended up writing like ... > > "matlab": > > > > ^ 0j1 * (1p1 + 2p1 * i.6) % 6 NB. 1st version > > > > That was why I was browsing NuVoc, looking for examples/ideas, hoping to > > see something to make my J sentence looks more ... "J-idiomatic" (while > > learning something out of the process). > > > > This is all I can I come up with today: > > > > ^ 0j1 * 6 %~ 1p1 + 2p1 * i.6 NB. 2nd version > > > > How would the same answer look like in the eyes of J Masters? > > > > > > thanks for your thoughts. > > > > On Sat, Oct 23, 2021 at 4:18 PM 'Pascal Jasmin' via Programming < > > [email protected]> wrote: > > > >> a more hollistic explanation, > >> > >> Most conjunctions, and including the & and @ famillies, produce verb > >> phrases when bound. A verb or verb phrase can/has to produce different > >> results/computations depending on monadic or dyadic cases. In u@v, u > is > >> always monadic, and v is ambivalent. in u&v, v is always monadic, and > u is > >> the valence of the verb phrase. > >> > >> A missing "composing conjunction" in J is ([ u v) where u is always > >> dyadic and v is ambivalent. But the fact that it is easy to write as a > >> fork suggests a dedicated conjunction is not needed. > >> > >> > >> On Saturday, October 23, 2021, 03:30:09 p.m. EDT, Raul Miller < > >> [email protected]> wrote: > >> > >> > >> > >> > >> > >> https://www.jsoftware.com/help/dictionary/d631.htm > >> > >> x u&.v y ↔ vi (v x) u (v y) > >> > >> Here: > >> u is + > >> v is *: > >> vi is %: (or *:inv) > >> x is 3 > >> y is 4 > >> > >> So these are equivalent > >> 3 +&.*: 4 > >> %: (*:3) + (*: 4) > >> *:inv (*:3) + (*: 4) > >> > >> I hope this makes sense. > >> > >> -- > >> Raul > >> > >> On Sat, Oct 23, 2021 at 3:03 PM More Rice <[email protected]> wrote: > >> > > >> > Hello, > >> > > >> > (Sorry for the previous empty email - web page problem) > >> > > >> > please excuse another newbie question ... > >> > > >> > Ref: https://code.jsoftware.com/wiki/Vocabulary/starco > >> > > >> > pythag =: +&.*: > >> > 3 pythag 4 > >> > 5 > >> > > >> > + operated dyadically and acted on both x and y - ok. > >> > > >> > but how does *: know to act on x as well? Isn't pythag using the > monadic > >> > definition of *: to square y only? > >> > > >> > so magical ... > >> > > >> > thank you for the pointer and have a great weekend. > >> > > >> > > >> > Maurice > >> > ---------------------------------------------------------------------- > >> > For information about J forums see > http://www.jsoftware.com/forums.htm > >> > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > >> > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
