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PascalTriangleNopile

Edit detail for PascalTriangleNopile revision 1 of 1

	1
Editor: test1 Time: 2014/02/19 18:44:42 GMT+0
Note:

changed:
-
\begin{spad}
)nopile
)abbrev package PASCALN PascalNopile
PascalNopile : with {
    make_pascal : Integer -> Matrix(Integer)
} == add {
make_pascal(N : Integer) : Matrix(Integer) == {
    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
}
}
\end{spad}

Try it:
\begin{axiom}
make_pascal(5)
\end{axiom}

fricas

(1) -> <spad>

fricas

)nopile

fricas

)abbrev package PASCALN PascalNopile
PascalNopile : with {
    make_pascal : Integer -> Matrix(Integer)
} == add {
make_pascal(N : Integer) : Matrix(Integer) == {
    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>

fricas

Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/3692351107100135223-25px001.spad
      using old system compiler.
   PASCALN abbreviates package PascalNopile 
------------------------------------------------------------------------
   initializing NRLIB PASCALN for PascalNopile 
   compiling into NRLIB PASCALN 
   compiling exported make_pascal : Integer -> Matrix Integer
Time: 0.07 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |PascalNopile| REDEFINED

;;;     ***       |PascalNopile| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor PascalNopile
      Time: 0.07 seconds

   finalizing NRLIB PASCALN 
   Processing PascalNopile for Browser database:
--->-->PascalNopile(constructor): Not documented!!!!
--->-->PascalNopile((make_pascal ((Matrix (Integer)) (Integer)))): Not documented!!!!
--->-->PascalNopile(): Missing Description
; compiling file "/var/aw/var/LatexWiki/PASCALN.NRLIB/PASCALN.lsp" (written 21 FEB 2023 12:45:48 PM):

; /var/aw/var/LatexWiki/PASCALN.NRLIB/PASCALN.fasl written
; compilation finished in 0:00:00.029
------------------------------------------------------------------------
   PascalNopile is now explicitly exposed in frame initial 
   PascalNopile will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/PASCALN.NRLIB/PASCALN

Try it:

fricas

make_pascal(5)

$\label{eq1}\left[ \begin{array}{ccccc} 1 & 0 & 0 & 0 & 0 \ 1 & 1 & 0 & 0 & 0 \ 1 & 2 & 1 & 0 & 0 \ 1 & 3 & 3 & 1 & 0 \ 1 & 4 & 6 & 4 & 1$

(1)

Type: Matrix(Integer)