Below there is a function which generates Pascal triangle by iteratively filling rows of a matrix using recurence formula. Spad array indexing is one based, so we cheat and add 1 to indices.
(1) -> <spad>
)abbrev package PASCAL Pascal Pascal : with ( make_pascal : Integer -> Matrix(Integer) ) == add make_pascal(N : Integer) : Matrix(Integer) == -- coerce here to NonNegativeInteger because this is what -- 'zero' requires nn := N::NonNegativeInteger tab := zero(nn,nn)$Matrix(Integer) n : Integer tab(1, 1) := 1 for n in 2..nn repeat -- Fill row numer n k : Integer tab(n, 1) := 1 tab(n, n) := 1 for k in 2..(n - 1) repeat tab(n, k) := tab(n-1, k) + tab(n-1, k-1) tab</spad>
Compiling FriCAS source code from file /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1379180095272779836-25px001.spad using old system compiler. PASCAL abbreviates package Pascal ------------------------------------------------------------------------ initializing NRLIB PASCAL for Pascal compiling into NRLIB PASCAL compiling exported make_pascal : Integer -> Matrix Integer Time: 0.02 SEC.
(time taken in buildFunctor: 0)
;;; *** |Pascal| REDEFINED
;;; *** |Pascal| REDEFINED Time: 0 SEC.
Cumulative Statistics for Constructor Pascal Time: 0.03 seconds
finalizing NRLIB PASCAL Processing Pascal for Browser database: --->-->Pascal(constructor): Not documented!!!! --->-->Pascal((make_pascal ((Matrix (Integer)) (Integer)))): Not documented!!!! --->-->Pascal(): Missing Description ; compiling file "/var/aw/var/LatexWiki/PASCAL.NRLIB/PASCAL.lsp" (written 21 APR 2025 09:44:11 PM):
; wrote /var/aw/var/LatexWiki/PASCAL.NRLIB/PASCAL.fasl ; compilation finished in 0:00:00.016 ------------------------------------------------------------------------ Pascal is now explicitly exposed in frame initial Pascal will be automatically loaded when needed from /var/aw/var/LatexWiki/PASCAL.NRLIB/PASCAL
Try it out:
make_pascal(5)
See also PascalTriangleNopile.