diff options
Diffstat (limited to 'src/algebra/permgrps.spad.pamphlet')
| -rw-r--r-- | src/algebra/permgrps.spad.pamphlet | 28 |
1 files changed, 14 insertions, 14 deletions
diff --git a/src/algebra/permgrps.spad.pamphlet b/src/algebra/permgrps.spad.pamphlet index 5d69a574..98e2ab75 100644 --- a/src/algebra/permgrps.spad.pamphlet +++ b/src/algebra/permgrps.spad.pamphlet @@ -116,8 +116,8 @@ PermutationGroup(S:SetCategory): public == private where ++ wordInGenerators(p,gp) returns the word for the permutation p ++ in the original generators of the group {\em gp}, ++ represented by the indices of the list, given by {\em generators}. - movedPoints : % -> FSET S - ++ movedPoints(gp) returns the points moved by the group {\em gp}. + support : % -> FSET S + ++ support(gp) returns the points moved by the group {\em gp}. < : (%,%) -> B ++ gp1 < gp2 returns true if and only if {\em gp1} ++ is a proper subgroup of {\em gp2}. @@ -261,7 +261,7 @@ PermutationGroup(S:SetCategory): public == private where newList := nil()$(L S) workList := orbitList.pos for j in #workList..1 by -1 repeat - newList := cons ( eval ( gen , workList.j ) , newList ) + newList := cons (gen(workList.j) , newList ) if not member?( newList , orbitList ) then orbitList := cons ( newList , orbitList ) pos := pos + 1 @@ -298,10 +298,10 @@ PermutationGroup(S:SetCategory): public == private where true pointList(group : %) : L S == - support : FSET S := brace() -- empty set !! + s : FSET S := brace() -- empty set !! for perm in group.gens repeat - support := union(support, movedPoints perm) - parts support + s := union(s, support perm) + parts s orbitWithSvc ( group : L V NNI , point : NNI ) : REC == -- compute orbit with Schreier vector, "-2" means not in the orbit, @@ -469,7 +469,7 @@ PermutationGroup(S:SetCategory): public == private where for ggg in 1..#gp repeat q := new(degree,0)$(V NNI) for i in 1..degree repeat - newEl := eval ( gp.ggg , supp.i ) + newEl := elt(gp.ggg,supp.i) pos2 := position ( newEl , supp ) q.i := pos2 pretend NNI newGroup := cons ( q , newGroup ) @@ -597,7 +597,7 @@ PermutationGroup(S:SetCategory): public == private where -- internal membership testing supp := pointList gp outlist := nil()$(L NNI) - mP : L S := parts movedPoints p + mP : L S := parts support p for x in mP repeat not member? (x, supp) => return [ false , nil()$(L NNI) ] if flag then @@ -617,7 +617,7 @@ PermutationGroup(S:SetCategory): public == private where degree := # supp pp := new(degree,0)$(V NNI) for i in 1..degree repeat - el := eval ( p , supp.i ) + el := p(supp.i) pos := position ( el , supp ) pp.i := pos::NNI words := nil()$(L L NNI) @@ -649,7 +649,7 @@ PermutationGroup(S:SetCategory): public == private where elt ( gp , i ) == (gp.gens).i - movedPoints ( gp ) == brace pointList gp + support ( gp ) == brace pointList gp random ( group , maximalNumberOfFactors ) == maximalNumberOfFactors < 1 => 1$(PERM S) @@ -707,7 +707,7 @@ PermutationGroup(S:SetCategory): public == private where outSet orbits ( gp ) == - spp := movedPoints gp + spp := support gp orbits := nil()$(L FSET S) while cardinality spp > 0 repeat el := extract! spp @@ -734,17 +734,17 @@ PermutationGroup(S:SetCategory): public == private where shortenWord ( outlist , gp ) gp1 < gp2 == - not empty? difference ( movedPoints gp1 , movedPoints gp2 ) => false + not empty? difference ( support gp1 , support gp2 ) => false not subgroup ( gp1 , gp2 ) => false order gp1 = order gp2 => false true gp1 <= gp2 == - not empty? difference ( movedPoints gp1 , movedPoints gp2 ) => false + not empty? difference ( support gp1 , support gp2 ) => false subgroup ( gp1 , gp2 ) gp1 = gp2 == - movedPoints gp1 ~= movedPoints gp2 => false + support gp1 ~= support gp2 => false if #(gp1.gens) <= #(gp2.gens) then not subgroup ( gp1 , gp2 ) => return false else |