diff options
Diffstat (limited to 'src/algebra/prtition.spad.pamphlet')
| -rw-r--r-- | src/algebra/prtition.spad.pamphlet | 26 |
1 files changed, 12 insertions, 14 deletions
diff --git a/src/algebra/prtition.spad.pamphlet b/src/algebra/prtition.spad.pamphlet index 1ebd739c..062b1753 100644 --- a/src/algebra/prtition.spad.pamphlet +++ b/src/algebra/prtition.spad.pamphlet @@ -32,20 +32,19 @@ import List Partition(): Exports == Implementation where macro L == List macro I == Integer - macro P == PositiveInteger + macro PI == PositiveInteger macro OUT == OutputForm macro NNI == NonNegativeInteger macro UN == Union(%,"failed") - Exports == Join(OrderedCancellationAbelianMonoid, - ConvertibleTo List Integer,CoercibleTo List Integer) with - partition: L I -> % + Exports == Join(OrderedCancellationAbelianMonoid, CoercibleTo L PI) with + partition: L PI -> % ++ partition(li) converts a list of integers li to a partition - powers: % -> List Pair(I,PositiveInteger) + powers: % -> List Pair(PI,PI) ++ 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 + pdct: % -> PI ++ \spad{pdct(a1**n1 a2**n2 ...)} returns ++ \spad{n1! * a1**n1 * n2! * a2**n2 * ...}. ++ This function is used in the package \spadtype{CycleIndicators}. @@ -53,11 +52,10 @@ Partition(): Exports == Implementation where ++ conjugate(p) returns the conjugate partition of a partition p Implementation == add - Rep == List Integer + Rep == L PI 0 == per nil - coerce(s: %): List Integer == rep s - convert x == copy rep x + coerce(s: %): L PI == rep s partition list == per sort(#2 < #1,list) zero? x == empty? rep x x < y == rep x < rep y @@ -68,7 +66,7 @@ Partition(): Exports == Implementation where zero? n => 0 x + (subtractIfCan(n,1) :: NNI) * x - remv(i: I,x: %): UN == + remv(i: PI,x: %): UN == member?(i,rep x) => per remove(i, rep x)$Rep "failed" @@ -82,14 +80,14 @@ Partition(): Exports == Implementation where powers x == l := rep x - r: List Pair(I,P) := nil + r: List Pair(PI,PI) := 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 + n: PI := 1 while not empty?(l := rest l) and i = first l repeat n := n + 1 r := cons(pair(i,n), r) @@ -101,7 +99,7 @@ Partition(): Exports == Implementation where i2 = 1 => (i1 :: OUT) ** (" " :: OUT) (i1 :: OUT) ** (i2 :: OUT) - mkexp1(lli: L Pair(I,PositiveInteger)): L OUT == + mkexp1(lli: L Pair(PI,PI)): L OUT == empty? lli => nil li := first lli empty?(rest lli) and second(li) = 1 => @@ -114,7 +112,7 @@ Partition(): Exports == Implementation where pdct x == */[factorial(second a) * (first(a) ** second(a)) - for a in powers x] + for a in powers x] :: PI @ \section{domain SYMPOLY SymmetricPolynomial} |