diff options
Diffstat (limited to 'src/algebra')
| -rw-r--r-- | src/algebra/prtition.spad.pamphlet | 36 |
1 files changed, 20 insertions, 16 deletions
diff --git a/src/algebra/prtition.spad.pamphlet b/src/algebra/prtition.spad.pamphlet index 4f19e1f8..1ebd739c 100644 --- a/src/algebra/prtition.spad.pamphlet +++ b/src/algebra/prtition.spad.pamphlet @@ -32,6 +32,7 @@ import List Partition(): Exports == Implementation where macro L == List macro I == Integer + macro P == PositiveInteger macro OUT == OutputForm macro NNI == NonNegativeInteger macro UN == Union(%,"failed") @@ -40,8 +41,8 @@ Partition(): Exports == Implementation where ConvertibleTo List Integer,CoercibleTo List Integer) with partition: L I -> % ++ partition(li) converts a list of integers li to a partition - powers: L I -> List Pair(I,PositiveInteger) - ++ powers(li) returns a list of pairs. The second component of + powers: % -> List Pair(I,PositiveInteger) + ++ powers(x) returns a list of pairs. The second component of ++ each pair is the multiplicity with which the first component ++ occurs in li. pdct: % -> I @@ -79,17 +80,20 @@ Partition(): Exports == Implementation where (aa := remv(first rep y,x)) case "failed" => "failed" subtractIfCan((aa :: %), per rest rep y) - bite(i: I,li: L I): L I == - empty? li => [0] - first li = i => - li1 := bite(i,rest li) - cons(first(li1) + 1,rest li1) - cons(0,li) - - powers l == - empty? l => nil - li := bite(first l,rest l) - cons(pair(first l,first(li)::PositiveInteger + 1),powers(rest li)) + powers x == + l := rep x + r: List Pair(I,P) := nil + while not empty? l repeat + i := first l + -- Now, count how many times the item `i' appears in `l'. + -- Since parts of partitions are stored in decreasing + -- order, we only need to scan the rest of the list until + -- we hit a different number. + n: P := 1 + while not empty?(l := rest l) and i = first l repeat + n := n + 1 + r := cons(pair(i,n), r) + reverse! r conjugate x == per conjugate(rep x)$PartitionsAndPermutations @@ -106,11 +110,11 @@ Partition(): Exports == Implementation where coerce(x:%):OUT == empty? rep x => rep(x)::OUT - paren(reduce("*",mkexp1(powers rep x))) + paren(reduce("*",mkexp1(powers x))) pdct x == - */[factorial(second a) * (first(a) ** (second(a) pretend NNI)) - for a in powers rep x] + */[factorial(second a) * (first(a) ** second(a)) + for a in powers x] @ \section{domain SYMPOLY SymmetricPolynomial} |