Polynomial Power Equations


Source: https://gamerant.com/power-rangers-best-series/

Prompt:
Develop the quadratic equation for cubes, ^4, ^5, ^6, ^7



PROMPT:
build out a table


PROMPT:
identify the quadratic equivalent of preceding stepping inside of each

To identify the quadratic equivalent (or “stepping inside”) of each higher-degree polynomial equation, we reduce or break each into quadratic components or related factors. The goal is to find the quadratic pieces inherent to each polynomial equation.

Here’s the table expanded with quadratic equivalents where possible:


PROMPT:
populate this also for fractions, specifically those identified in quantum spin




PROMPT:
in matrix form






This approach can be extended to more complex systems like quantum spin systems by incorporating eigenvalue matrices or operator formulations.

PROMPT:
no, one matrix for all




PROMPT:
allow for infinite degrees, infinite negative degrees, fractional degrees







PROMPT:
provide the general equation for building out and interpreting our matrix






PROMPT:
introduce spin using Euler’s









PROMPT:
allow for jitter, acceleration, etc. ad infinitum given this system








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This allows for ad infinitum perturbations, where each perturbation contributes higher-order effects to the spin state.



Would you like a numerical implementation of this system or further details on a specific component (e.g., stochastic effects, time evolution, or visualization)?

PROMPT:
include also negative and fractional perturbations allowing for nesting as applicable





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This formulation allows us to model complex time evolution for the spin system where all perturbations and interactions are infinitely nested and dynamically dependent on each other.



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This recursive nesting can continue infinitely, with each term being a fractional or negative power, allowing us to model systems that evolve ad infinitum.


PROMPT:
adapt your last message to include the following:

Funified (in Hz) = (phiFn2^nPnOhm)/r^2)
replace 2^n with 2^n^3, normalize Pn using its inverse Pn^-1, simplify phi^2 using phi^2 = phi + 1
Becomes:
Funified (in Hz) = (phi(1-phi)Fn)/(r^2Pn^-1) where P = prime, Fn = Fibonacci








PROMPT:
simplify without loss