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| author | dos-reis <gdr@axiomatics.org> | 2011-10-25 03:47:29 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2011-10-25 03:47:29 +0000 |
| commit | 2092a554d70524bc90440d96367e32c9ede28ee8 (patch) | |
| tree | f60d455b9d03bfe6454bb2ae33b82114aeb3f91b /src/algebra/combinat.spad.pamphlet | |
| parent | 99aeb02edd1614d30e308a9267325f138617d58f (diff) | |
| download | open-axiom-2092a554d70524bc90440d96367e32c9ede28ee8.tar.gz | |
* algebra/perman.spad.pamphlet (Permanent): Specify type of local
variable j.
* algebra/patmatch1.spad.pamphlet (PatternMatchTools): Tidy.
* algebra/padic.spad.pamphlet: Restrict type of literal constants.
* algebra/sttf.spad.pamphlet: Likewise.
* algebra/puiseux.spad.pamphlet: Likewise.
* algebra/odealg.spad.pamphlet (SystemODESolver) [applyLodo0]:
Specify type of local variable ans.
* algebra/numtheor.spad.pamphlet (IntegerNumberTheoryFunctions): Tidy.
* algebra/naalgc.spad.pamphlet (MonadWithUnit) [rightPower]:
Specify type of local variable res.
[leftPower]: Likewise.
* algebra/lodop.spad.pamphlet (NonCommutativeOperatorDivision)
[leftLcm]: Specify type of local variable v.
* algebra/intfact.spad.pamphlet (IntegerRoots) [approxSqrt]:
Specify type of local variables old and new.
* algebra/elfuts.spad.pamphlet
(EllipticFunctionsUnivariateTaylorSeries): Restrict types of
literal constants.
* algebra/ffnb.spad.pamphlet
(FiniteFieldNormalBasisExtensionByPolynomial): Likewise.
* algebra/fnla.spad.pamphlet (FreeNilpotentLie): Likewise.
* algebra/intaux.spad.pamphlet (IntegrationResult): Likewise.
* algebra/defintef.spad.pamphlet
(ElementaryFunctionDefiniteIntegration) [checkSMP]: Specify type
in the definition of local variable n.
* algebra/combinat.spad.pamphlet (IntegerCombinatoricFunctions):
Tidy definition of local variables.
* algebra/clifford.spad.pamphlet (CliffordAlgebra): Specify type in
the definition of local variables k, exchanges, bz.
* algebra/catdef.spad.pamphlet (CartesianTensor): Specify type in the
definition of local varibles rx and offz.
Remove useless variables zol, xol, oly, and zoly.
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 |