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| author | dos-reis <gdr@axiomatics.org> | 2010-04-22 01:40:53 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2010-04-22 01:40:53 +0000 |
| commit | 9fac9abefef7f727a59b7861317d148352a43d88 (patch) | |
| tree | 6cf281301d4609d71aae0540b6cd098abd41de2b /src/algebra/partperm.spad.pamphlet | |
| parent | dca6da4bba9a14e544345d4b54f623450d47f283 (diff) | |
| download | open-axiom-9fac9abefef7f727a59b7861317d148352a43d88.tar.gz | |
* algebra/irsn.spad.pamphlet (IrrRepSymNatPackage): Tidy.
* algebra/partperm.spad.pamphlet (PartitionsAndPermutations): Likewise.
* algebra/cycles.spad.pamphlet (complete$CycleIndicators): Now
take only positive integers.
(powerSum$CycleIndicators): Likewise.
(elementary$CycleIndicators): Likewise.
(alternating$CycleIndicators): Likewise.
(cyclic$CycleIndicators): Likewise.
(dihedral$CycleIndicators): Likewise.
(graphs$CycleIndicators): Likewise.
Diffstat (limited to 'src/algebra/partperm.spad.pamphlet')
| -rw-r--r-- | src/algebra/partperm.spad.pamphlet | 29 |
1 files changed, 16 insertions, 13 deletions
diff --git a/src/algebra/partperm.spad.pamphlet b/src/algebra/partperm.spad.pamphlet index b657fa3a..d4b23b3a 100644 --- a/src/algebra/partperm.spad.pamphlet +++ b/src/algebra/partperm.spad.pamphlet @@ -32,22 +32,24 @@ PartitionsAndPermutations: Exports == Implementation where ST1 ==> StreamFunctions1 ST2 ==> StreamFunctions2 ST3 ==> StreamFunctions3 + macro NNI == NonNegativeInteger + macro PI == PositiveInteger Exports ==> with - partitions: (I,I,I) -> ST L I + partitions: (NNI,NNI,NNI) -> ST L PI ++\spad{partitions(p,l,n)} is the stream of partitions ++ of n whose number of parts is no greater than p ++ and whose largest part is no greater than l. - partitions: I -> ST L I + partitions: NNI -> ST L PI ++\spad{partitions(n)} is the stream of all partitions of n. - partitions: (I,I) -> ST L I + partitions: (NNI,NNI) -> ST L PI ++\spad{partitions(p,l)} is the stream of all ++ partitions whose number of ++ parts and largest part are no greater than p and l. - conjugate: L I -> L I + conjugate: L PI -> L PI ++\spad{conjugate(pt)} is the conjugate of the partition pt. - conjugates: ST L I -> ST L I + conjugates: ST L PI -> ST L PI ++\spad{conjugates(lp)} is the stream of conjugates of a stream ++ of partitions lp. shuffle: (L I,L I) -> ST L I @@ -74,25 +76,26 @@ PartitionsAndPermutations: Exports == Implementation where Implementation ==> add partitions(M,N,n) == - zero? n => concat(empty()$L(I),empty()$(ST L I)) - zero? M or zero? N or n < 0 => empty() - c := map(concat(N,#1),partitions(M - 1,N,n - N)) - concat(c,partitions(M,N - 1,n)) + zero? n => concat(empty()$L(PI),empty()$(ST L PI)) + zero? M or zero? N or n < N => empty() + s := partitions(subtractIfCan(M,1)::NNI,N,subtractIfCan(n,N)::NNI) + c := map(concat(N::PI,#1),s) + concat(c,partitions(M,subtractIfCan(N,1)::NNI,n)) partitions n == partitions(n,n,n) partitions(M,N)== - aaa : L ST L I := [partitions(M,N,i) for i in 0..M*N] - concat(aaa :: ST ST L I)$ST1(L I) + aaa : L ST L PI := [partitions(M,N,i) for i in 0..M*N] + concat(aaa :: ST ST L PI)$ST1(L PI) -- nogreq(n,l) is the number of elements of l that are greater or -- equal to n - nogreq: (I,L I) -> I + nogreq: (I,L PI) -> I nogreq(n,x) == +/[1 for i in x | i >= n] conjugate x == empty? x => empty() - [nogreq(i,x) for i in 1..first x] + [nogreq(i,x)::PI for i in 1..first x] conjugates z == map(conjugate,z) |