User:Miui/Drafts/ΙΧΘΥΣ PRIME

ΙΧΘΥΣ PRIME is a joke esoteric language with only two operations: Evaluation of membership in a set derived from ΙΧΘΥΣ and evaluation of that element as a prime number.

A-field

There exists a non divergent K set in the scator three dimensional space with a highly complex boundary J = ∂K ^[1] called the Ix set. A field of K-group with 0 elements in a set is a fractal seed corresponding to the complex boundary of the Ix set. The transformation rule to K-group K₀ -> K₁ is defined: SATOR -> ΙΧΘΥΣ

Ix set

coptic -> LATIN -> GREEK	LATIN -> GREEK	Operation
ςατωρ -> OPERA -> ΙΧΘΥΣ	SATOR -> ΙΧΘΥΣ	icthus
OPERA -> PRIME	PRIME -> PRIME	prime

The words are concrete weights in a field with elements 0, 1 and 2 whos connectives are free variables in the Heaviside step function where A = 1 and E = 2. This is a group of k elements in 1+2 dimensions in dynamic space.

• ΙΧΘΥΣ is the icthus operation (checks membership in Ix set)
• PRIME is a prime-checker and operates on the B-field

B-field

The B-field satisfies the field axioms of a, b, c ∈ F in the B-field Fp where p is the Oxfoi prime, i.e., 2⁶⁴-2³²+1. This means the parameters correspond to prime numbers of memory elements, and the transition function gives rise to low-degree polynomials from the ring of multivariate polynomials over Fp^[2]. This transition function describes K₁ -> K₂ as Mastuomoto's theorem^[3].

X-field

The X-field is the quotient ring of remainders of polynomials after division by the Shah polynomial, X³−X+1. An X-field element is defined ΙΧΘΥΣ PRIME where an element is both icthus (an Ix set element) and prime.

Execution

ΙΧΘΥΣ PRIME compiles Crazy J to the Ix set and outputs assembly code. X field elements are mutable so primes in all bases can be covered. This means if a number is not known to be prime ΙΧΘΥΣ PRIME is unable to calculate it. Prime elements are taken under the limit of omega prime which is resolved at the least-upper-bound of the B-field.

Combinator reduction via Iota

I+I'=I->0

to ΙΧΘΥΣ PRIME

OPERA 1X;ΙΧΘΥΣ;So;0;ON;;;;N;;;;

This operation is an accumulator that performs minkowski addition using a fish that has negative third dimensions and adds a sum with a quotient field on a fractal ring.

How accumulator works

the fish looks like this

See: https://en.wikipedia.org/wiki/Minkowski_addition