thank you for another phrase. Will take a close look at it as well. Elijah, you're absolutely right - it was my typo. I'm shocked, considering I didn't detect this in my studies over the last few weekends. Need to re-check my study notes - I may be able to use more verbs now. Thanks for pointing it out.
have a good day! Maurice On Sun, Oct 24, 2021 at 2:19 AM ethiejiesa via Programming < [email protected]> wrote: > FWIW, this alternate phrasing of the rt verb is also possible. > > rt=: (%: -)~ * ^@(%~ 0j1p1+0j2p1*i.)@] > > Elijah Stone <[email protected]> wrote: > > - is always a verb, which negates its right argument. -1 0 1 is - (1 0 > > 1), or _1 0 _1; so p. solves -x^2 - 1 = 0. I expect you want _1 0 1. > > > > -E > > > > On Sun, 24 Oct 2021, More Rice wrote: > > > > > 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 > > ---------------------------------------------------------------------- > > 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
