binomial: Pascal's Arithmetic Triangle

In rogopag/r-binomial: Pascal's Arithmetic Triangle

Description

Every instance of the class represents a single Triangle as a low triangular matrix.We didn't follow Blaise Pascal construction rules (Triangulus Arithmeticus, I-Definitiones in Blaise Pascal, Opere Complete, 2020 Giunti Milano),instead we followed the algorythm presented in Gilbert Strang, Introduction To Linear Algebra, 2.4 A p. 72, as Lij + Lij-1 = Li+1j, which derivesdireclty from Consect. 8 in Pascal treatise: "Summa cellularum basis (i) cujuslibet unitate minuta (i-1) aequatur summae cellularum basium onnium praecedentiumHoc enim est proprium progressionis duplae quae ab unitate incipit, ut quilibet ejus numerus, unitate minutus, aequatur omnium praecedentium.", in equation form(Lij) - 1 = sum(L[i], i==1, i-1).From the 2 preceding equations it is easy to derive the following: Lij = Li-1j + Li-1j-1 which is the usual simplified form we used in our main method pascalBinomial().

Usage

binomial$new(k = 6) -> bb
bb$pascalBinomial()

Examples

binomial$new(k = 6) -> bb
bb$plotPascalBinomial(bb$a2)

rogopag/r-binomial documentation built on Dec. 22, 2021, 5:16 p.m.