diff options
Diffstat (limited to 'src/algebra/combinat.spad.pamphlet')
| -rw-r--r-- | src/algebra/combinat.spad.pamphlet | 20 |
1 files changed, 13 insertions, 7 deletions
diff --git a/src/algebra/combinat.spad.pamphlet b/src/algebra/combinat.spad.pamphlet index f597f98f..23b4a1eb 100644 --- a/src/algebra/combinat.spad.pamphlet +++ b/src/algebra/combinat.spad.pamphlet @@ -72,8 +72,8 @@ IntegerCombinatoricFunctions(I:IntegerNumberSystem): with n < m::I => P(convert(n)@Z) concat!(P, new((convert(n+1)@Z - m)::N,0)$IndexedFlexibleArray(I,0)) for i in m..convert(n)@Z repeat - s:I := 1 - t:I := 0 + s: I := 1 + t: I := 0 for k in 1.. repeat l := (3*k*k-k) quo 2 l > i => leave @@ -96,18 +96,23 @@ IntegerCombinatoricFunctions(I:IntegerNumberSystem): with F.Fv := f binomial(n, m) == - s,b:I negative? n or negative? m or m > n => 0 m = 0 => 1 n < 2*m => binomial(n, n-m) - (s,b) := (0,1) + s: I := 0 + b: I := 1 if B.Bn = n then B.Bm = m+1 => b := (B.Bv * (m+1)) quo (n-m) B.Bn := n B.Bm := m return(B.Bv := b) - if m >= B.Bm then (s := B.Bm; b := B.Bv) else (s,b) := (0,1) + if m >= B.Bm then + s := B.Bm + b := B.Bv + else + s := 0 + b := 1 for k in convert(s+1)@Z .. convert(m)@Z repeat b := (b*(n-k::I+1)) quo k::I B.Bn := n @@ -122,12 +127,13 @@ IntegerCombinatoricFunctions(I:IntegerNumberSystem): with factorial n quo s permutation(n, m) == - t:I negative? m or n < m => 0 m := n-m p:I := 1 for k in convert(m+1)@Z .. convert(n)@Z by 2 repeat - if k::I = n then t := n else t := (k*(k+1))::I + t: I := + k::I = n => n + (k*(k+1))::I p := p * t p |