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Don Coyote

by Don Coyote (Friar)
on Jul 01, 2010 at 17:29 UTC ( #847566=user: print w/replies, xml ) Need Help??

Algebraic Calculus One(May 2020):free trial, see the trailer at youtube search 'Insights into Mathematics', or 'Prof Wildberger'. A novel approach to the calculus.

Hello, I am a perl fanatic from the UK. In my personal projects I strive to find any excuse, no matter how obscure or insignificantly related to the problem to use Perl.

In the monastic tradition I test my faith with inherently fundamental untruths such as other computing languages exist. These journeys only serve to strengthen my belief in the one true source.

Aside from my main allocation of time to Perl in the realm of Computer Science, I also follow geometric and algebraic paths of enlightenment in the Mathematical arena. This has developed over the last twelve or so years. Probably longer if I actually retrieve my age scalar.

Prior to this my interests were fame-laced and language-borne. While more recently I have noticed a general interest in the language pervading the material namespace. I would suggest there is most likely a correlation between these interests and the increasing impact of artificially idiotelligent systems being created by well, pretty much anyone nowadays.

My hopes and aspirations are to combine these disciplines into a purpose of some des‎crip‎tion. And I often find myself looking at online streaming platforms and wondering where on the planet is the Perl version of this stuff.

Around 2012 I discovered a 2nd Edition Camel in a local computer retailer outlet. The flawless condition the flattened scroll once possessed has sadly degraded over time.

Note: You cannot optimize code you have not yet written!

Moving from s‎crip‎ting to programming handy thread for directions

Due to the recent advent of the Rational Trigonometry, originating from the general location of the antipodean pole, here is an interesting observation I have made. Also I am still trying to understand.

It should be mentioned that presentation of this field of Mathematics has been done so under terms of a copyright. Any commercial use of this technology should likely be authorised. I am unsure of the licensing, but am assuming this falls either under a fair-use policy or something similar to the licensing terms Perl itself falls under.

Sequence Lemma: A precursive sequence to the general pythagorean quadrance generation sequence.

Usually the reduced Pythagorean Triples are the subject of the sequence. And it is such that this is essentially the square1 of a precursive sequence to the general pythagorean triples generator.

Why not just work with the reduced triples?
The pythagorean relation is in the quadratic. Further, that relation itself is a special case. The reduced triples are Corollories, after the fact, Lemmas prior.2

Do sequences require proofs like Theorems do?
Not sure

Are you pretending a sequence is a Theorem?
That is probably what I am doing here, yes.

[ n, nat 2>=n; ip, [ i, int[ m, nat 0>=m ] ] ; pOseq, {ip1,ip2,ip3} : pOseq(n) => L(Q), [ Q1, Q3, Q2 ] ] v0.01
What this is attempting to state:
Where, n is a natural number equal or greater than two.
ip an ordered pair of multiset of integers, indexed by l a nat equal or greater than 0, representing the power to which the nat n is exponentiated in that position.
pOseq(ip3) is an Oset(Ordered_Set) consisting of three sequences of three Integral_Polynumbers.
A List L of three quadrances q, L(Q), satisfying the Pythagorean identity can be generated, by evaluating each of the ip in the oset P by the natural number n.

this is going to take some time.

# [ pOnseq(2) > = 9, 25, 16 #{ _ _ , _ _ , _ _ } @2 = [ , , ] # 1\ 1\ 0\ # 4 4 0 # 4 8 4 # 8 8 # 4 4 #
1. Assuming the sequence can be squared. Currently I understand that it is allowable/doable.
2. ... ?

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