User:Inthar/Endoparticular extensions: Difference between revisions
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== Special case 1 == | == Special case 1 == | ||
Suppose the base temp tempers out (Sk)^m S(k+1)^n for nonzero integers m and n. An extension by one basis element is ''natural'' if it tempers out Sk and S(k+1). | Suppose the base temp tempers out (Sk)^m S(k+1)^n for nonzero integers m and n. An extension by one basis element is ''natural'' if it tempers out Sk and S(k+1). | ||
=== Examples === | |||
==== Porcupine ==== | |||
2.3.5 Porc -> 2.3.5.11 Porc is natural: | |||
250/243 | |||
= (10/9)^3/(4/3) | |||
= (10/9)^2(11/10)S(10)/(4/3) | |||
= (10/9)(11/10)(12/11)/(4/3)*S(10)^2*S(11) | |||
= S(10)^2*S(11) | |||
And 2.3.5.11 Porc indeed tempers out S10 and S11. | |||
==== Kleismic ==== | |||
2.3.5 Kleismic -> 2.3.5.13 Kleismic is natural because 15625/15552 = S(25)^2*S(26). | |||
Revision as of 13:59, 4 February 2026
This is a problematic page or section. It lacks sufficient justification, content, or organization, and is subject to future overhaul or deletion.
Goal: Formalize Leri's notion of temp extension naturalness or a some notion that is stronger than Leri!naturalness.
Special case 1
Suppose the base temp tempers out (Sk)^m S(k+1)^n for nonzero integers m and n. An extension by one basis element is natural if it tempers out Sk and S(k+1).
Examples
Porcupine
2.3.5 Porc -> 2.3.5.11 Porc is natural:
250/243 = (10/9)^3/(4/3) = (10/9)^2(11/10)S(10)/(4/3) = (10/9)(11/10)(12/11)/(4/3)*S(10)^2*S(11) = S(10)^2*S(11)
And 2.3.5.11 Porc indeed tempers out S10 and S11.
Kleismic
2.3.5 Kleismic -> 2.3.5.13 Kleismic is natural because 15625/15552 = S(25)^2*S(26).
