1 2# Library 3 4These scripts develop basic theories to support various libraries. 5 6## Enhancement 7* __helperNum__, more theorems on parity, divisibility, inequalities, `MAX` and `MIN`. 8* __helperSet__, more theormes on function images, `SUM_SET` and `PROD_SET`. 9* __helperList__, enhance listTheory with `SUM`, `PROD`, `MAX_LIST`, `MIN_LIST`, `rotate`, and `turn`. 10* __helperFunction__, collect theorems for integer functions: `SQRT`, `ROOT`, `FACT`, `GCD`, and `LCM`. 11 12## Number Theory 13* __Euler__, number-theoretic sets, and Euler's �� function. 14* __Gauss__, coprimes, properties of ��; function, and Gauss' Little Theorem. 15* __Mobius__, work on M��bius inversion. 16 17## Number Patterns 18* __binomial__, properties of binomial coefficients in Pascal's Triangle. 19* __triangle__, properties of Leibniz's Denominator Triangle, relating to consecutive LCM. 20* __primes__, properties of two-factors, and a primality test. 21* __primePower__, properties of prime powers and divisors, an investigation on consecutive LCM. 22* __logPower__, properties of perfect power, power free, and upper logarithm. 23 24## Applications 25* __sublist__, order-preserving sublist and properties.