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| author | dos-reis <gdr@axiomatics.org> | 2010-04-25 22:10:18 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2010-04-25 22:10:18 +0000 |
| commit | c79e40703ada1ff91b7e057b25d4ae1c4199770a (patch) | |
| tree | e5fd98849be6f127a2c0cd267fdd498ec53c3f90 /src/algebra/cycles.spad.pamphlet | |
| parent | 2e76a77847facaa29b9c0f7c26ea2ba511dc285e (diff) | |
| download | open-axiom-c79e40703ada1ff91b7e057b25d4ae1c4199770a.tar.gz | |
* algebra/partperm.spad.pamphlet (PartitionsAndPermutations): Move
partitions to domain Partitions.
* algebra/cycles.spad.pamphlet (CycleIndicators): User partitions
from Partition. Tidy.
Diffstat (limited to 'src/algebra/cycles.spad.pamphlet')
| -rw-r--r-- | src/algebra/cycles.spad.pamphlet | 22 |
1 files changed, 11 insertions, 11 deletions
diff --git a/src/algebra/cycles.spad.pamphlet b/src/algebra/cycles.spad.pamphlet index c2941dd3..b8dea37f 100644 --- a/src/algebra/cycles.spad.pamphlet +++ b/src/algebra/cycles.spad.pamphlet @@ -94,29 +94,29 @@ CycleIndicators: Exports == Implementation where ++ expressed in terms of power sum symmetric functions. Implementation ==> add - import PartitionsAndPermutations import IntegerNumberTheoryFunctions + import Partition trm: PTN -> SPOL RN trm pt == monomial(inv(pdct(pt) :: RN),pt) - list: Stream L PI -> L L PI + list: Stream PTN -> L PTN list st == entries complete st complete i == i=0 => 1 - +/[trm partition pt for pt in list partitions i] + +/[trm pt for pt in list partitions i] - even?: L PI -> B - even? li == even?( #([i for i in li | even? i])) + even?: PTN -> B + even? p == even?( #([i for i in parts p | even? i])) alternating i == - 2 * _+/[trm partition li for li in list partitions i | even? li] + 2 * _+/[trm p for p in list partitions i | even? p] elementary i == i=0 => 1 - +/[(spol := trm partition pt; even? pt => spol; -spol) + +/[(spol := trm pt; even? pt => spol; -spol) for pt in list partitions i] divisors: I -> L I @@ -142,10 +142,10 @@ CycleIndicators: Exports == Implementation where odd? n => (1/2) * cyclic n + (1/2) * ss(2,k) * powerSum 1 (1/2) * cyclic n + (1/4) * ss(2,k) + (1/4) * ss(2,k-1) * ss(1,2) - trm2: L PI -> SPOL RN + trm2: PTN -> SPOL RN trm2 li == - lli := powers(partition li)$PTN - xx := 1/(pdct partition li) + lli := powers( li)$PTN + xx := 1/(pdct li) prod : SPOL RN := 1 for ll in lli repeat ll0 := first ll; ll1 := second ll @@ -161,7 +161,7 @@ CycleIndicators: Exports == Implementation where prod := c * prod2 * prod xx * prod - graphs n == +/[trm2 li for li in list(partitions n)] + graphs n == +/[trm2 p for p in list(partitions n)] cupp: (PTN,SPOL RN) -> SPOL RN cupp(pt,spol) == |