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Copy file name to clipboardExpand all lines: doc/cascade.xml
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@@ -30,7 +30,7 @@ Elements of cascade products are <E>cascades</E>, that are tuples of <E>dependen
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<SectionLabel="cascadesgp"><Heading>Cascade semigroups and groups</Heading>
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Cascades can be multiplied together, there exists an identity element for each list of dependency domains and for a permutation cascade the inverse element is also defined. Therefore cascades can be used to form semigroups and groups.
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Cascade semigroups can then be turned into transformation semigroups by using <RefFunc="IsomorphismTransformationSemigroup"BookName="semigroups"/>
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Cascade semigroups can then be turned into transformation semigroups by using <RefFunc="IsomorphismTransformationSemigroup"BookName="ref"/>
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<Example>
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gap> c := Cascade([2,3], [ [[],Transformation([2,2])],
The <RefFunc="Skeleton"BookName="sgpdec"/> already contains lots of information on the components of the decomposition but we still need to put them together in a form of a cascade semigroup.
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The <RefFunc="Skeleton"/> already contains lots of information on the components of the decomposition but we still need to put them together in a form of a cascade semigroup.
<Returns>Transformation as a result of mapping down a cascade transformation <Arg>ct</Arg> in a holonomy decomposition described by its skeleton.</Returns>
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<Description>
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The inverse of <RefFunc="AsHolonomyCascade"BookName="sgpdec"/>
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The inverse of <RefFunc="AsHolonomyCascade"/>
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</Description>
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</ManSection>
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<#/GAPDoc>
@@ -190,7 +190,7 @@ The inverse of <Ref Func="AsHolonomyCoords" BookName="sgpdec"/>
Display a concise textual summary of the FL decomposition components. Works both with a cascade group (that is a result of an FL decomposition) and simply with a subgroup chain.
<Returns>Cascade group isomorphic to <C>G</C>.</Returns>
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<Description>
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The decomposition is done based on a subgroup chain. If the subgroup chain ends in a stabilizer of a point, then the decomposition is isomorphic as a permutation group, i.e. the states are coordinatized as well. In that case the stabilized point needs to be explicitly given. the decomposition will only contain the orbit of this point, so for non-transitive actions the orbits have to be handled separately.
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