The Formal Sequence Constructor
[! x in F | P(x) !]
The Enumerated Sequence Constructor
[ ] : Null -> ESeqEnum
[ U | ] : Str -> SeqEnum
[ e1, e2, ..., en ] : Elt, ..., Elt -> SeqEnum
[ U | e1, e2, ..., em ] : Str, Elt, ..., Elt -> SeqEnum
[ e(x) : x in E | P(x) ]
[ U | e(x) : x in E | P(x) ]
[ e(x1,...,xk) : x1 in E1, ..., xkin Ek | P(x1, ..., xk) ]
[ U | e(x1,...,xk) : x1 in E1, ...,xk in Ek | P(x1, ..., xk) ]
The Arithmetic Progression Constructors
[ i..j ] : RngIntElt, RngIntElt -> SeqEnum
[ i .. j by k ] : RngIntElt, RngIntElt, RngIntElt -> SeqEnum
Example Seq_Progression (H10E1)
Literal Sequences
\[ m1, ..., mn ] : RngIntElt, ..., RngIntElt -> [ RngIntElt ]
Power Sequences
PowerSequence(R) : Str -> PowSeqEnum
S in P : SeqEnum, PowSeqEnum -> BoolElt
P ! S : PowSeqEnum, SeqEnum -> SeqEnum
Example Seq_PowerSequence (H10E2)
Access Functions
# S : SeqEnum -> RngIntElt
Parent(S) : SeqEnum -> Str
Universe(S) : SeqEnum -> Str
S[i] : SeqEnum, RngIntElt -> Elt
Selection Operators on Enumerated Sequences
S[I] : SeqEnum, [RngIntElt] -> SeqEnum
Minimum(S) : SeqEnum -> Elt, RngIntElt
Maximum(S) : SeqEnum -> Elt, RngIntElt
Index(S, x) : SeqEnum, Elt -> RngIntElt
Representative(R) : SeqEnum -> Elt
Random(R) : SeqEnum -> Elt
Explode(R) : SeqEnum -> List
Eltseq(R) : SeqEnum -> SeqEnum
Modifying Enumerated Sequences
Append(~S, x) : SeqEnum, Elt ->
Exclude(~S, x) : SeqEnum, Elt ->
Include(~S, x) : SeqEnum, Elt ->
Insert(~S, i, x) : SeqEnum, RngIntElt, Elt ->
Insert(~S, k, m, T) : SeqEnum, RngIntElt, RngIntElt, SeqEnum ->
Prune(~S) : SeqEnum ->
Remove(~S, i) : SeqEnum, RngIntElt ->
Reverse(~S) : SeqEnum ->
Rotate(~S, p) : SeqEnum, RngIntElt ->
Sort(~S) : SeqEnum ->
Sort(~S, C) : SeqEnum, UserProgram ->
ParallelSort(~S, ~T) : SeqEnum, SeqEnum ->
Undefine(~S, i) : SeqEnum, RngIntElt ->
ChangeUniverse(S, V) : SeqEnum, Str ->
CanChangeUniverse(S, V) : SeqEnum, Str -> Bool, SeqEnum
Example Seq_Farey (H10E3)
Creating New Enumerated Sequences from Existing Ones
S cat T : SeqEnum, SeqEnum -> SeqEnum
S cat:= T : SeqEnum, SeqEnum ->
Partition(S, p) : SeqEnum, RngIntElt -> SeqEnum(SeqEnum)
Partition(S, P) : SeqEnum, [RngIntElt] -> SeqEnum(SeqEnum)
Setseq(S) : SetEnum -> SeqEnum
Seqset(S) : SeqEnum -> SetEnum
Example Seq_EgyptianFractions (H10E4)
Operations on Sequences of Booleans
And(S, T) : [ BoolElt ], [ BoolElt ] -> [BoolElt]
Or(S, T) : [ BoolElt ], [ BoolElt ] -> [ BoolElt ]
Xor(S, T) : [ BoolElt ], [ BoolElt ] -> [ BoolElt ]
Not(S) : [ BoolElt ] -> [ BoolElt ]
Predicates on Sequences
IsComplete(S) : SeqEnum -> BoolElt
IsDefined(S, i) : SeqEnum, RngIntElt -> BoolElt
IsEmpty(S) : SeqEnum -> BoolElt
IsNull(S) : SeqEnum -> BoolElt
Membership Testing
x in S : Elt, SeqEnum -> BoolElt
x notin S : Elt, SeqEnum -> BoolElt
IsSubsequence(S, T) : SeqEnum, SeqEnum -> BoolElt
S eq T : SeqEnum, SeqEnum -> BoolElt
S ne T : SeqEnum, SeqEnum -> BoolElt
Testing Order Relations
S lt T : SeqEnum, SeqEnum -> BoolElt
S le T : SeqEnum, SeqEnum -> BoolElt
S ge T : SeqEnum, SeqEnum -> BoolElt
S gt T : SeqEnum, SeqEnum -> BoolElt
Recursion, Reduction, and Iteration
Recursion
Self(n) : RngIntElt -> Elt
Example Seq_Self (H10E5)
Reduction
& S : Op, SeqEnum -> Elt
Iteration
for x in S do statements; end for;
Example Seq_NestedIteration (H10E6)
Bibliography
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012