rogopag/r-binomial: Pascal's Arithmetic Triangle

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 derives direclty from Consect. 8 in Pascal treatise: "Summa cellularum basis (i) cujuslibet unitate minuta (i-1) aequatur summae cellularum basium onnium praecedentium. Hoc 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().

install.packages("remotes")
remotes::install_github("rogopag/r-binomial")