diff --git a/books/bookvol10.3.pamphlet b/books/bookvol10.3.pamphlet
index 27d1d8a..3d9290d 100644
--- a/books/bookvol10.3.pamphlet
+++ b/books/bookvol10.3.pamphlet
@@ -99529,8 +99529,104 @@ Permutation(S:SetCategory): public == private where
)set message auto off
)clear all
---S 1 of 1
-)show PermutationGroup
+--S 1 of 68
+x : PERM INT := [[1,3,5],[7,11,9]]
+--R
+--R
+--R (1) (1 3 5)(7 11 9)
+--R Type: Permutation(Integer)
+--E 1
+
+--S 2 of 68
+y : PERM INT := [[3,5,7,9]]
+--R
+--R
+--R (2) (3 5 7 9)
+--R Type: Permutation(Integer)
+--E 2
+
+--S 3 of 68
+z : PERM INT := [1,3,11]
+--R
+--R
+--R (3) (1 3 11)
+--R Type: Permutation(Integer)
+--E 3
+
+--S 4 of 68
+g1 : PERMGRP INT := [ x , y ]
+--R
+--R
+--R (4) <(1 3 5)(7 11 9),(3 5 7 9)>
+--R Type: PermutationGroup(Integer)
+--E 4
+
+--S 5 of 68
+g2 : PERMGRP INT := [ x , z ]
+--R
+--R
+--R (5) <(1 3 5)(7 11 9),(1 3 11)>
+--R Type: PermutationGroup(Integer)
+--E 5
+
+--S 6 of 68
+g3 : PERMGRP INT := [ y , z ]
+--R
+--R
+--R (6) <(3 5 7 9),(1 3 11)>
+--R Type: PermutationGroup(Integer)
+--E 6
+
+--S 7 of 68
+order g1
+--R
+--R
+--R (7) 720
+--R Type: PositiveInteger
+--E 7
+
+--S 8 of 68
+degree g3
+--R
+--R
+--R (8) 6
+--R Type: PositiveInteger
+--E 8
+
+--S 9 of 68
+movedPoints g2
+--R
+--R
+--R (9) {1,3,5,7,9,11}
+--R Type: Set(Integer)
+--E 9
+
+--S 10 of 68
+orbit (g1, 3)
+--R
+--R
+--R (10) {1,3,5,7,9,11}
+--R Type: Set(Integer)
+--E 10
+
+--S 11 of 68
+orbits g3
+--R
+--R
+--R (11) {{1,3,5,7,9,11}}
+--R Type: Set(Set(Integer))
+--E 11
+
+--S 12 of 68
+member? ( y , g2 )
+--R
+--R
+--R (12) false
+--R Type: Boolean
+--E 12
+
+--S 13 of 68
+)sh PERMGRP
--R
--R PermutationGroup(S: SetCategory) is a domain constructor
--R Abbreviation for PermutationGroup is PERMGRP
@@ -99561,27 +99657,1031 @@ Permutation(S:SetCategory): public == private where
--R wordInStrongGenerators : (Permutation(S),%) -> List(NonNegativeInteger)
--R wordsForStrongGenerators : % -> List(List(NonNegativeInteger))
--R
---E 1
+--E 13
+
+)spool
+)lisp (bye)
+\end{chunk}
+\begin{chunk}{PermutationGroup.help}
+====================================================================
+PermutationGroup examples
+====================================================================
+
+PermutationGroup implements permutation groups acting on a set S,
+i.e. all subgroups of the symmetric group of S, represented as a list
+of permutations (generators). Note that therefore the objects are not
+members of the Axiom category Group.
+
+Using the idea of base and strong generators by Sims, basic routines
+and algorithms are implemented so that the word problem for permutation
+groups can be solved.
+
+ x : PERM INT := [[1,3,5],[7,11,9]]
+
+ (1 3 5)(7 11 9)
+
+ y : PERM INT := [[3,5,7,9]]
+
+ (3 5 7 9)
+
+ z : PERM INT := [1,3,11]
+
+ (1 3 11)
+
+ g1 : PERMGRP INT := [ x , y ]
+
+ <(1 3 5)(7 11 9),(3 5 7 9)>
+
+ g2 : PERMGRP INT := [ x , z ]
+
+ <(1 3 5)(7 11 9),(1 3 11)>
+
+ g3 : PERMGRP INT := [ y , z ]
+
+ <(3 5 7 9),(1 3 11)>
+
+ order g1
+
+ 720
+
+ degree g3
+
+ 6
+
+ movedPoints g2
+
+ {1,3,5,7,9,11}
+
+ orbit (g1, 3)
+
+ {1,3,5,7,9,11}
+
+ orbits g3
+
+ {{1,3,5,7,9,11}}
+
+ member? ( y , g2 )
+
+ false
+
+See Also:
+o )show PermutationGroup
+o )help coerce
+o )help generators
+o )help elt
+o )help random
+o )help order
+o )help degree
+o )help base
+o )help wordsForStrongGenerators
+o )help permutationGroup
+o )help orbit
+o )help orbits
+o )help member?
+o )help wordInStrongGenerators
+o )help wordInGenerators
+o )help movedPoints
+o )help initializeGroupForWordProblem
+
+\end{chunk}
+
+\begin{chunk}{coerce.help}
+====================================================================
+coerce from PermutationGroup (PERMGRP)
+====================================================================
+
+NAME
+====
+
+ coerce
+
+DOMAIN
+======
+
+ PermutationGroup (PERMGRP)
+
+SYNOPSYS
+========
+
+ coerce : % -> List Permutation SetCategory
+ coerce : List Permutation SetCategory -> %
+
+DESCRIPTION
+===========
+
+ coerce : % -> List Permutation SetCategory
+
+ coerce(gp) returns the generators of the group gp.
+
+ coerce : List Permutation SetCategory -> %
+
+ coerce(ls) coerces a list of permutations ls to the group
+ generated by this list.
+
+ARGUMENTS
+=========
+
+RETURN VALUE
+============
+
+EXAMPLES
+========
+
+ x : PERM INT := [[1,3,5],[7,11,9]]
+
+ (1 3 5)(7 11 9)
+
+ y : PERM INT := [[3,5,7,9]]
+
+ (3 5 7 9)
+
+ z : PERM INT := [1,3,11]
+
+ (1 3 11)
+
+ g1 : PERMGRP INT := [ x , y ]
+
+ <(1 3 5)(7 11 9),(3 5 7 9)>
+
+ g2 : PERMGRP INT := [ x , z ]
+
+ <(1 3 5)(7 11 9),(1 3 11)>
+
+ g3 : PERMGRP INT := [ y , z ]
+
+ <(3 5 7 9),(1 3 11)>
+
+NOTES
+=====
+
+REFERENCES
+==========
+
+SEE ALSO
+========
+
+o )show PermutationGroup
+o )d op coerce
+
+\end{chunk}
+
+\begin{chunk}{generators.help}
+====================================================================
+generators from PermutationGroup (PERMGRP)
+====================================================================
+
+NAME
+====
+
+ generators
+
+DOMAIN
+======
+
+ PermutationGroup (PERMGRP)
+
+SYNOPSYS
+========
+
+ generators : % -> List Permuation SetCategory
+
+ generators(gp) returns the generators of the group gp.
+
+DESCRIPTION
+===========
+
+ARGUMENTS
+=========
+
+RETURN VALUE
+============
+
+EXAMPLES
+========
+
+NOTES
+=====
+
+REFERENCES
+==========
+
+SEE ALSO
+========
+
+o )show PermutationGroup
+o )d op generators
+
+\end{chunk}
+
+\begin{chunk}{elt.help}
+====================================================================
+elt from PermutationGroup (PERMGRP)
+====================================================================
+
+NAME
+====
+
+ elt
+
+DOMAIN
+======
+
+ PermutationGroup (PERMGRP)
+
+SYNOPSYS
+========
+
+ elt : (%,NonNegativeInteger) -> Permutation SetCategory
+
+ elt(gp,i) returns the i-th generator of the group gp.
+
+DESCRIPTION
+===========
+
+ARGUMENTS
+=========
+
+RETURN VALUE
+============
+
+EXAMPLES
+========
+
+NOTES
+=====
+
+REFERENCES
+==========
+
+SEE ALSO
+========
+
+o )show PermutationGroup
+o )d op elt
+
+\end{chunk}
+
+\begin{chunk}{random.help}
+====================================================================
+random from PermutationGroup (PERMGRP)
+====================================================================
+
+NAME
+====
+
+ random
+
+DOMAIN
+======
+
+ PermutationGroup (PERMGRP)
+
+SYNOPSYS
+========
+
+ random : (%,Integer) -> Permutation SetCategory
+
+ random(gp,i) returns a random product of maximal i generators
+ of the group gp.
+
+ random : % -> Permutation SetCategory
+
+ random(gp) returns a random product of maximal 20 generators
+ of the group gp.
+ Note: random(gp)=random(gp,20).
+
+DESCRIPTION
+===========
+
+ARGUMENTS
+=========
+
+RETURN VALUE
+============
+
+EXAMPLES
+========
+
+NOTES
+=====
+
+REFERENCES
+==========
+
+SEE ALSO
+========
+
+o )show PermutationGroup
+o )d op random
+
+\end{chunk}
+
+\begin{chunk}{order.help}
+====================================================================
+order from PermutationGroup (PERMGRP)
+====================================================================
+
+NAME
+====
+
+ order
+
+DOMAIN
+======
+
+ PermutationGroup (PERMGRP)
+
+SYNOPSYS
+========
+
+ order : % -> NonNegativeInteger
+
+ order(gp) returns the order of the group gp.
+
+DESCRIPTION
+===========
+
+ARGUMENTS
+=========
+
+RETURN VALUE
+============
+
+EXAMPLES
+========
+
+ x : PERM INT := [[1,3,5],[7,11,9]]
+
+ (1 3 5)(7 11 9)
+
+ y : PERM INT := [[3,5,7,9]]
+
+ (3 5 7 9)
+
+ g : PERMGRP INT := [ x , y ]
+
+ <(1 3 5)(7 11 9),(3 5 7 9)>
+
+ order g
+
+ 720
+
+NOTES
+=====
+
+REFERENCES
+==========
+
+SEE ALSO
+========
+
+o )show PermutationGroup
+o )d op order
+
+\end{chunk}
+
+\begin{chunk}{degree.help}
+====================================================================
+degree from PermutationGroup (PERMGRP)
+====================================================================
+
+NAME
+====
+
+ degree
+
+DOMAIN
+======
+
+ PermutationGroup (PERMGRP)
+
+SYNOPSYS
+========
+
+ degree : % -> NonNegativeInteger
+
+ degree(gp) returns the number of points moved by all permutations
+ of the group gp.
+
+DESCRIPTION
+===========
+
+ARGUMENTS
+=========
+
+RETURN VALUE
+============
+
+EXAMPLES
+========
+
+ y : PERM INT := [[3,5,7,9]]
+
+ (3 5 7 9)
+
+ z : PERM INT := [1,3,11]
+
+ (1 3 11)
+
+ g : PERMGRP INT := [ y , z ]
+
+ <(3 5 7 9),(1 3 11)>
+
+ degree g
+
+ 6
+
+NOTES
+=====
+
+REFERENCES
+==========
+
+SEE ALSO
+========
+
+o )show PermutationGroup
+o )d op degree
+
+\end{chunk}
+
+\begin{chunk}{base.help}
+====================================================================
+base from PermutationGroup (PERMGRP)
+====================================================================
+
+NAME
+====
+
+ base
+
+DOMAIN
+======
+
+ PermutationGroup (PERMGRP)
+
+SYNOPSYS
+========
+
+ base : % -> List SetCategory
+
+ base(gp) returns a base for the group gp.
+
+DESCRIPTION
+===========
+
+ARGUMENTS
+=========
+
+RETURN VALUE
+============
+
+EXAMPLES
+========
+
+NOTES
+=====
+
+REFERENCES
+==========
+
+SEE ALSO
+========
+
+o )show PermutationGroup
+o )d op base
+
+\end{chunk}
+
+\begin{chunk}{wordsForStrongGenerators.help}
+====================================================================
+wordsForStrongGenerators from PermutationGroup (PERMGRP)
+====================================================================
+
+NAME
+====
+
+ wordsForStrongGenerators
+
+DOMAIN
+======
+
+ PermutationGroup (PERMGRP)
+
+SYNOPSYS
+========
+
+ wordsForStrongGenerators : % -> List List NonNegativeInteger
+
+ wordsForStrongGenerators(gp) returns the words for the strong
+ generators of the group gp in the original generators of
+ gp, represented by their indices in the list, given by
+ generators.
+
+DESCRIPTION
+===========
+
+ARGUMENTS
+=========
+
+RETURN VALUE
+============
+
+EXAMPLES
+========
+
+NOTES
+=====
+
+REFERENCES
+==========
+
+SEE ALSO
+========
+
+o )show PermutationGroup
+o )d op wordsForStrongGenerators
+
+\end{chunk}
+
+\begin{chunk}{permutationGroup.help}
+====================================================================
+permutationGroup from PermutationGroup (PERMGRP)
+====================================================================
+
+NAME
+====
+
+ permutationGroup
+
+DOMAIN
+======
+
+ PermutationGroup (PERMGRP)
+
+SYNOPSYS
+========
+
+ permutationGroup : List Permutation SetCategory -> %
+
+ permutationGroup(ls) coerces a list of permutations ls to
+ the group generated by this list.
+
+DESCRIPTION
+===========
+
+ARGUMENTS
+=========
+
+RETURN VALUE
+============
+
+EXAMPLES
+========
+
+NOTES
+=====
+
+REFERENCES
+==========
+
+SEE ALSO
+========
+
+o )show PermutationGroup
+o )d op permutationGroup
+
+\end{chunk}
+
+\begin{chunk}{orbit.help}
+====================================================================
+orbit from PermutationGroup (PERMGRP)
+====================================================================
+
+NAME
+====
+
+ orbit
+
+DOMAIN
+======
+
+ PermutationGroup (PERMGRP)
+
+SYNOPSYS
+========
+
+ orbit : (%,SetCategory) -> Set SetCategory
+
+ orbit(gp,el) returns the orbit of the element el under the
+ group gp, i.e. the set of all points gained by applying
+ each group element to el.
+
+ orbit : (%,Set SetCategory)-> Set Set SetCategory
+
+ orbit(gp,els) returns the orbit of the unordered
+ set els under the group gp.
+
+ orbit : (%,List SetCategory) -> Set List SetCategory
+
+ orbit(gp,ls) returns the orbit of the ordered
+ list ls under the group gp.
+
+DESCRIPTION
+===========
+
+ARGUMENTS
+=========
+
+RETURN VALUE
+============
+
+EXAMPLES
+========
+
+ x : PERM INT := [[1,3,5],[7,11,9]]
+
+ (1 3 5)(7 11 9)
+
+ y : PERM INT := [[3,5,7,9]]
+
+ (3 5 7 9)
+
+ g : PERMGRP INT := [ x , y ]
+
+ <(1 3 5)(7 11 9),(3 5 7 9)>
+
+ orbit(g, 3)
+
+ {1,3,5,7,9,11}
+
+NOTES
+=====
+
+REFERENCES
+==========
+
+SEE ALSO
+========
+
+o )show PermutationGroup
+o )d op orbit
+
+\end{chunk}
+
+\begin{chunk}{orbits.help}
+====================================================================
+orbits from PermutationGroup (PERMGRP)
+====================================================================
+
+NAME
+====
+
+ orbits
+
+DOMAIN
+======
+
+ PermutationGroup (PERMGRP)
+
+SYNOPSYS
+========
+
+ orbits : % -> Set Set SetCategory
+
+ orbits(gp) returns the orbits of the group gp, i.e.
+ it partitions the (finite) of all moved points.
+
+DESCRIPTION
+===========
+
+ARGUMENTS
+=========
+
+RETURN VALUE
+============
+
+EXAMPLES
+========
+
+ y : PERM INT := [[3,5,7,9]]
+
+ (3 5 7 9)
+
+ z : PERM INT := [1,3,11]
+
+ (1 3 11)
+
+ g : PERMGRP INT := [ y , z ]
+
+ <(3 5 7 9),(1 3 11)>
+
+ orbits g
+
+ {{1,3,5,7,9,11}}
+
+NOTES
+=====
+
+REFERENCES
+==========
+
+SEE ALSO
+========
+
+o )show PermutationGroup
+o )d op orbits
+
+\end{chunk}
+
+\begin{chunk}{member?.help}
+====================================================================
+member? from PermutationGroup (PERMGRP)
+====================================================================
+
+NAME
+====
+
+ member?
+
+DOMAIN
+======
+
+ PermutationGroup (PERMGRP)
+
+SYNOPSYS
+========
+
+ member? : (Permutation Set, %)-> Boolean
+
+ member?(pp,gp) answers the question, whether the
+ permutation pp is in the group gp or not.
+
+DESCRIPTION
+===========
+
+ARGUMENTS
+=========
+
+RETURN VALUE
+============
+
+EXAMPLES
+========
+
+ x : PERM INT := [[1,3,5],[7,11,9]]
+
+ (1 3 5)(7 11 9)
+
+ y : PERM INT := [[3,5,7,9]]
+
+ (3 5 7 9)
+
+ z : PERM INT := [1,3,11]
+
+ (1 3 11)
+
+ g : PERMGRP INT := [ x , z ]
+
+ <(1 3 5)(7 11 9),(1 3 11)>
+
+ member? ( y , g )
+
+ false
+
+NOTES
+=====
+
+REFERENCES
+==========
+
+SEE ALSO
+========
+
+o )show PermutationGroup
+o )d op member
-)spool
-)lisp (bye)
\end{chunk}
-\begin{chunk}{PermutationGroup.help}
+
+\begin{chunk}{wordInStrongGenerators.help}
====================================================================
-PermutationGroup examples
+wordInStrongGenerators from PermutationGroup (PERMGRP)
====================================================================
-PermutationGroup implements permutation groups acting on a set S,
-i.e. all subgroups of the symmetric group of S, represented as a list
-of permutations (generators). Note that therefore the objects are not
-members of the Axiom category Group.
+NAME
+====
-Using the idea of base and strong generators by Sims, basic routines
-and algorithms are implemented so that the word problem for permutation
-groups can be solved.
+ wordInStrongGenerators
+
+DOMAIN
+======
+
+ PermutationGroup (PERMGRP)
+
+SYNOPSYS
+========
+
+ wordInStrongGenerators : (Permatation Set, %)-> List NonNegativeInteger
+
+ wordInStrongGenerators(p,gp) returns the word for the
+ permutation p in the strong generators of the group gp,
+ represented by the indices of the list, given by strongGenerators.
+
+DESCRIPTION
+===========
+
+ARGUMENTS
+=========
+
+RETURN VALUE
+============
+
+EXAMPLES
+========
+
+NOTES
+=====
+
+REFERENCES
+==========
+
+SEE ALSO
+========
+
+o )show PermutationGroup
+o )d op wordInStrongGenerators
+
+\end{chunk}
+
+\begin{chunk}{wordInGenerators.help}
+====================================================================
+wordInGenerators from PermutationGroup (PERMGRP)
+====================================================================
+
+NAME
+====
+
+ wordInGenerators
+
+DOMAIN
+======
+
+ PermutationGroup (PERMGRP)
+
+SYNOPSYS
+========
+
+ wordInGenerators : (Permutation Set, %)-> List NonNegativeInteger
+
+ wordInGenerators(p,gp) returns the word for the permutation p
+ in the original generators of the group gp,
+ represented by the indices of the list, given by generators.
+
+DESCRIPTION
+===========
+
+ARGUMENTS
+=========
+
+RETURN VALUE
+============
+
+EXAMPLES
+========
+
+NOTES
+=====
+
+REFERENCES
+==========
+
+SEE ALSO
+========
+
+o )show PermutationGroup
+o )d op wordInGenerators
+
+\end{chunk}
+
+\begin{chunk}{movedPoints.help}
+====================================================================
+movedPoints from PermutationGroup (PERMGRP)
+====================================================================
+
+NAME
+====
+
+ movedPoints
+
+DOMAIN
+======
+
+ PermutationGroup (PERMGRP)
+
+SYNOPSYS
+========
+
+ movedPoints : % -> Set SetCategory
+
+ movedPoints(gp) returns the points moved by the group gp.
+
+DESCRIPTION
+===========
+
+ARGUMENTS
+=========
+
+RETURN VALUE
+============
+
+EXAMPLES
+========
+
+ x : PERM INT := [[1,3,5],[7,11,9]]
+
+ (1 3 5)(7 11 9)
+
+ z : PERM INT := [1,3,11]
+
+ (1 3 11)
+
+ g : PERMGRP INT := [ x , z ]
+
+ <(1 3 5)(7 11 9),(1 3 11)>
+
+ movedPoints g
+
+ {1,3,5,7,9,11}
+
+NOTES
+=====
+
+REFERENCES
+==========
+
+SEE ALSO
+========
+
+o )show PermutationGroup
+o )d op movedPoints
+
+\end{chunk}
+
+\begin{chunk}{initializeGroupForWordProblem.help}
+====================================================================
+initializeGroupForWordProblem from PermutationGroup (PERMGRP)
+====================================================================
+
+NAME
+====
+
+ initializeGroupForWordProblem
+
+DOMAIN
+======
+
+ PermutationGroup (PERMGRP)
+
+SYNOPSYS
+========
+
+ initializeGroupForWordProblem : % -> Void
+
+ initializeGroupForWordProblem(gp) initializes the group gp
+ for the word problem.
+
+DESCRIPTION
+===========
+
+ARGUMENTS
+=========
+
+RETURN VALUE
+============
+
+EXAMPLES
+========
+
+NOTES
+=====
+
+ It calls the other function of this name with parameters
+ 0 and 1: initializeGroupForWordProblem(gp,0,1).
+
+ (1) be careful: invoking this routine will destroy the
+ possibly information about your group (but will recompute it again)
+
+ (2) users need not call this function normally for the soultion of
+ the word problem.
+
+REFERENCES
+==========
+
+SEE ALSO
+========
-See Also:
o )show PermutationGroup
+o )d op initializeGroupForWordProblem
\end{chunk}
@@ -99657,77 +100757,135 @@ PermutationGroup(S:SetCategory): public == private where
public ==> SetCategory with
- coerce : % -> L PERM S
+ coerce : % -> L PERM S
++ coerce(gp) returns the generators of the group gp.
+ ++
+ ++X x : PERM INT := [[1,3,5],[7,11,9]]
+
+ coerce : L PERM S -> %
+ ++ coerce(ls) coerces a list of permutations ls to the group
+ ++ generated by this list.
+ ++
+ ++X y : PERM INT := [[3,5,7,9]]
+ ++X z : PERM INT := [1,3,11]
+ ++X g : PERMGRP INT := [ y , z ]
+
generators : % -> L PERM S
++ generators(gp) returns the generators of the group gp.
+
elt : (%,NNI) -> PERM S
++ elt(gp,i) returns the i-th generator of the group gp.
+
random : (%,I) -> PERM S
++ random(gp,i) returns a random product of maximal i generators
++ of the group gp.
+
random : % -> PERM S
++ random(gp) returns a random product of maximal 20 generators
++ of the group gp.
++ Note: random(gp)=random(gp,20).
+
order : % -> NNI
++ order(gp) returns the order of the group gp.
+ ++
+ ++X x : PERM INT := [[1,3,5],[7,11,9]]
+ ++X y : PERM INT := [[3,5,7,9]]
+ ++X g : PERMGRP INT := [ x , y ]
+ ++X order g
+
degree : % -> NNI
++ degree(gp) returns the number of points moved by all permutations
++ of the group gp.
+ ++
+ ++X y : PERM INT := [[3,5,7,9]]
+ ++X z : PERM INT := [1,3,11]
+ ++X g : PERMGRP INT := [ y , z ]
+ ++X degree g
+
base : % -> L S
++ base(gp) returns a base for the group gp.
+
strongGenerators : % -> L PERM S
++ strongGenerators(gp) returns strong generators for
++ the group gp.
+
wordsForStrongGenerators : % -> L L NNI
++ wordsForStrongGenerators(gp) returns the words for the strong
++ generators of the group gp in the original generators of
++ gp, represented by their indices in the list, given by
++ generators.
- coerce : L PERM S -> %
- ++ coerce(ls) coerces a list of permutations ls to the group
- ++ generated by this list.
+
permutationGroup : L PERM S -> %
++ permutationGroup(ls) coerces a list of permutations ls to
++ the group generated by this list.
+
orbit : (%,S) -> FSET S
++ orbit(gp,el) returns the orbit of the element el under the
++ group gp, i.e. the set of all points gained by applying
++ each group element to el.
- orbits : % -> FSET FSET S
- ++ orbits(gp) returns the orbits of the group gp, i.e.
- ++ it partitions the (finite) of all moved points.
+
orbit : (%,FSET S)-> FSET FSET S
++ orbit(gp,els) returns the orbit of the unordered
++ set els under the group gp.
+
orbit : (%,L S) -> FSET L S
++ orbit(gp,ls) returns the orbit of the ordered
++ list ls under the group gp.
++ Note: return type is L L S temporarily because FSET L S has an error.
- -- (GILT DAS NOCH?)
+ ++
+ ++X x : PERM INT := [[1,3,5],[7,11,9]]
+ ++X y : PERM INT := [[3,5,7,9]]
+ ++X g : PERMGRP INT := [ x , y ]
+ ++X orbit(g, 3)
+
+ orbits : % -> FSET FSET S
+ ++ orbits(gp) returns the orbits of the group gp, i.e.
+ ++ it partitions the (finite) of all moved points.
+ ++
+ ++X y : PERM INT := [[3,5,7,9]]
+ ++X z : PERM INT := [1,3,11]
+ ++X g : PERMGRP INT := [ y , z ]
+ ++X orbits g
+
member? : (PERM S, %)-> B
++ member?(pp,gp) answers the question, whether the
++ permutation pp is in the group gp or not.
+ ++
+ ++X x : PERM INT := [[1,3,5],[7,11,9]]
+ ++X y : PERM INT := [[3,5,7,9]]
+ ++X z : PERM INT := [1,3,11]
+ ++X g : PERMGRP INT := [ x , z ]
+ ++X member? ( y , g )
+
wordInStrongGenerators : (PERM S, %)-> L NNI
++ wordInStrongGenerators(p,gp) returns the word for the
++ permutation p in the strong generators of the group gp,
++ represented by the indices of the list, given by strongGenerators.
+
wordInGenerators : (PERM S, %)-> L NNI
++ wordInGenerators(p,gp) returns the word for the permutation p
++ in the original generators of the group gp,
++ represented by the indices of the list, given by generators.
+
movedPoints : % -> FSET S
++ movedPoints(gp) returns the points moved by the group gp.
+ ++
+ ++X x : PERM INT := [[1,3,5],[7,11,9]]
+ ++X z : PERM INT := [1,3,11]
+ ++X g : PERMGRP INT := [ x , z ]
+ ++X movedPoints g
+
"<" : (%,%) -> B
++ gp1 < gp2 returns true if and only if gp1
++ is a proper subgroup of gp2.
+
"<=" : (%,%) -> B
++ gp1 <= gp2 returns true if and only if gp1
++ is a subgroup of gp2.
++ Note: because of a bug in the parser you have to call this
++ function explicitly by gp1 <=$(PERMGRP S) gp2.
-- (GILT DAS NOCH?)
+
initializeGroupForWordProblem : % -> Void
++ initializeGroupForWordProblem(gp) initializes the group gp
++ for the word problem.
@@ -99737,6 +100895,7 @@ PermutationGroup(S:SetCategory): public == private where
++ possibly information about your group (but will recompute it again)
++ (2) users need not call this function normally for the soultion of
++ the word problem.
+
initializeGroupForWordProblem :(%,I,I) -> Void
++ initializeGroupForWordProblem(gp,m,n) initializes the group
++ gp for the word problem.
diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index c417014..2783275 100644
--- a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ -22,6 +22,22 @@ paragraph for those unfamiliar with the terms.
\section{Algebra Documentation References}
+\index{Sims, Charles}
+\begin{chunk}{axiom.bib}
+@article{Sims71,
+ author = "Sims, Charles",
+ title = "Determining the Conjugacy Classes of a Permutation Group",
+ journal = "Computers in Algebra and Number Theory, SIAM-AMS Proc.",
+ volume = "4",
+ publisher = "American Math. Soc.",
+ year = "1991",
+ pages = "191--195",
+ comment = "documentation for PermutationGroup"
+
+}
+
+\end{chunk}
+
\index{W\"orz-Busekros, A.}
\begin{chunk}{axiom.bib}
@article{Worz80,
@@ -15201,15 +15217,6 @@ Mathematics and Computers in Simulation 42 pp 509-528 (1996)
\end{chunk}
-\index{Sims, Charles}
-\begin{chunk}{ignore}
-\bibitem[Sims 71]{Sims71} Sims, C.
- title = "Determining the Conjugacy Classes of a Permutation Group",
-Computers in Algebra and Number Theory, SIAM-AMS Proc., Vol. 4,
-American Math. Soc., 1991, pp191-195
-
-\end{chunk}
-
\index{Singer, Michael F.}
\begin{chunk}{ignore}
\bibitem[Singer 89]{Sing89} Singer, M.F.
diff --git a/changelog b/changelog
index 2fee24c..19e879d 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20141117 tpd src/axiom-website/patches.html 20141117.02.tpd.patch
+20141117 tpd books/bookvol10.3 help files for PermutationGroup
20141117 tpd src/axiom-website/patches.html 20141117.01.tpd.patch
20141117 tpd books/bookvol5 newHelpSpad2Cmd now recognizes )help abbreviations
20141116 tpd src/axiom-website/patches.html 20141116.03.tpd.patch
diff --git a/patch b/patch
index 18a0aec..8f086ad 100644
--- a/patch
+++ b/patch
@@ -1,5 +1,8 @@
-books/bookvol5 newHelpSpad2Cmd now recognizes )help abbreviations
+books/bookvol10.3 help files for PermutationGroup
The )help command now recognizes
- )help Integer
- )help INT
+ )help PermutationGroup -- the constructor name
+ )help PERMGRP -- the abbreviation
+ )help order -- the function implementations from PERMGRP
+all of which open in an edit window
+
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index 05ef12e..154893b 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -4708,6 +4708,8 @@ books/bookvol10.3 help file for AlgebraGivenByStructuralConstants
src/input/Makefile remove gonshor.input
20141117.01.tpd.patch
books/bookvol5 newHelpSpad2Cmd now recognizes )help abbreviations
+20141117.02.tpd.patch
+books/bookvol10.3 help files for PermutationGroup