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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??

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

Moving from s‎crip‎ting to programming handy thread for directions

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
#
[download]```
1. Assuming the sequence can be squared. Currently I understand that it is allowable/doable.
2. ... ?
9.

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