README.md
In rogopag/r-binomial: Pascal's Arithmetic Triangle
r-binomial
Simple R (RC) Class to collect Pascal's Arithmetic Triangle "consequences".
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:
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().
rogopag/r-binomial documentation built on Dec. 22, 2021, 5:16 p.m.
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r-binomial
Simple R (RC) Class to collect Pascal's Arithmetic Triangle "consequences".
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:
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().
R Package Documentation
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We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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