Fundamental cycle

Japanese: 基本周期 - きほんしゅうき

...Any periodic function of a real variable has a minimum positive period. This is called the fundamental period. For example, the fundamental period of sin x and cos x is 2π, and the fundamental period of sin2 x and tan x is π. ...

From [Elliptic Functions]

...Another name for a doubly periodic function that is rational in the complex plane C. In other words, if ω ₁ and ω ₂ are complex numbers other than 0 that satisfy Im(ω ₁ /ω ₂ )＞0, then a function f that is rational in C and satisfies f ( z ＋2 m ω ₁ ＋2 n ω ₂ )＝ f ( z ) for any z ∈ C and any integers m and n is called an elliptic function with fundamental periods 2ω ₁ and 2ω ₂ (the use of 2ω ₁ and 2ω ₂ instead of ω ₁ and ω ₂ has various advantages and is common). A parallelogram with four vertices 0, 2ω ₁ , 2ω ₂ , and 2ω ₁ + 2ω ₂ is called a parallelogram with fundamental period. ...

*Some of the terminology explanations that mention the "fundamental cycle" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

Japanese:

…実変数の周期関数には，正の周期の最小のものがある。それを基本周期という。例えばsinx,cosxの基本周期は2πであり，sin2x,tanxの基本周期はπである。…

【楕円関数】より

…複素平面Cで有理型な二重周期関数の別名である。すなわち，ω₁とω₂を，0と異なる複素数でIm(ω₁/ω₂)＞0を満たすものとしたとき，Cで有理型な関数fで，任意のz∈Cと，任意の整数m,nに対して，　f(z＋2mω₁＋2nω₂)＝f(z)を満たすものを，2ω₁と2ω₂を基本周期とする楕円関数という(ω₁,ω₂を採らず2ω₁,2ω₂を用いるのは，種々の利点があり，慣用となっている)。4点0,2ω₁,2ω₂,2ω₁＋2ω₂を頂点とする平行四辺形を基本周期平行四辺形という。…