diff options
Diffstat (limited to 'src/algebra/cycles.spad.pamphlet')
| -rw-r--r-- | src/algebra/cycles.spad.pamphlet | 26 |
1 files changed, 11 insertions, 15 deletions
diff --git a/src/algebra/cycles.spad.pamphlet b/src/algebra/cycles.spad.pamphlet index 7b1b7c0d..0a92b83a 100644 --- a/src/algebra/cycles.spad.pamphlet +++ b/src/algebra/cycles.spad.pamphlet @@ -54,15 +54,15 @@ CycleIndicators: Exports == Implementation where ++\spad{alternating n} is the cycle index of the ++ alternating group of degree n. - cyclic: PI -> SPOL RN --cyclic group + cyclic: NNI -> SPOL RN --cyclic group ++\spad{cyclic n} is the cycle index of the ++ cyclic group of degree n. - dihedral: PI -> SPOL RN --dihedral group + dihedral: NNI -> SPOL RN --dihedral group ++\spad{dihedral n} is the cycle index of the ++ dihedral group of degree n. - graphs: PI -> SPOL RN + graphs: NNI -> SPOL RN ++\spad{graphs n} is the cycle index of the group induced on ++ the edges of a graph by applying the symmetric function to the ++ n nodes. @@ -100,24 +100,20 @@ CycleIndicators: Exports == Implementation where trm: PTN -> SPOL RN trm pt == monomial(inv(pdct(pt) :: RN),pt) - list: Stream PTN -> L PTN - list st == entries complete st - complete i == i=0 => 1 - +/[trm pt for pt in list partitions i] - - - even?: PTN -> B - even? p == even?( #([i for i in parts p | even? i])) + +/[trm pt for pt in entries partitions i] + + even?: L I -> B + even? li == even?( #([i for i in li | even? i])) alternating i == - 2 * _+/[trm p for p in list partitions i | even? p] + 2 * _+/[trm p for p in entries partitions i | even? p] elementary i == i=0 => 1 - +/[(spol := trm pt; even? pt => spol; -spol) - for pt in list partitions i] + +/[(spol := trm partition pt; even? pt => spol; -spol) + for pt in entries partitions i] divisors: I -> L I divisors n == @@ -161,7 +157,7 @@ CycleIndicators: Exports == Implementation where prod := c * prod2 * prod xx * prod - graphs n == +/[trm2 p for p in list(partitions n)] + graphs n == +/[trm2 p for p in entries partitions n] cupp: (PTN,SPOL RN) -> SPOL RN cupp(pt,spol) == |