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. The X-field takes input as an integer e.g. ςατωρ 17 which at 17 will set ♍ icthus, at which point ♍' is a cyclic function based on the set of icthus primes in the field.

X-field commands

X-field	B-field	A-field
♍	ΙΧΘΥΣ	[150, 180]
♍'	OPERA	PRIME

The interval [150, 180] is just a noteworthy feature of ΙΧΘΥΣ PRIME and represents Virgo's zodiacal degree. This language exists mostly to highlight other fish languages such as deadfish which are interpreted and more programmable.

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

Relationship to Narcissistic numbers

If we define an icthus number as 153 (a narcissistic) then we know the p element of I in Ix is 1³+5³+3³ is 17 which is prime. This coincidentally is the number of fish Jesus helped his disciples catch at the end of the gospel of John

So Simon Peter went aboard and dragged the net to the shore. There were 153 large fish, and yet the net hadn’t torn. - John 21:11

User:Miui found the coincidence worth noting.

See also

Arepo Opera backwards!