Sequences
- Introduction
- Creating Sequences
- The Formal Sequence Constructor
- 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, ..., xₖ in Eₖ | P(x₁, ..., xₖ) ][ U | e(x₁,...,xₖ) : x₁ in E₁, ..., xₖ in Eₖ | P(x₁, ..., xₖ) ]
- The Arithmetic Progression Constructors
- Literal Sequences
- Power Sequences
- Operators on Sequences
- Access Functions
- Selection Operators on Enumerated Sequences
S[I]: SeqEnum, [RngIntElt] → SeqEnumMinimum(S): SeqEnum → Elt, RngIntEltMin(S): SeqEnum → Elt, RngIntEltMaximum(S): SeqEnum → Elt, RngIntEltMax(S): SeqEnum → Elt, RngIntEltIndex(S, x): SeqEnum, Elt → RngIntEltIndex(S, x, f): SeqEnum, Elt, RngIntElt → RngIntEltPosition(S, x): SeqEnum, Elt → RngIntEltPosition(S, x, f): SeqEnum, Elt, RngIntElt → RngIntEltRepresentative(R): SeqEnum → EltRep(R): SeqEnum → EltRandom(R): SeqEnum → EltExplode(R): SeqEnum → ListEltseq(R): SeqEnum → SeqEnum
- Modifying Enumerated Sequences
Append(~S, x): SeqEnum, EltAppend(S, x): SeqEnum, Elt → SeqEnumExclude(~S, x): SeqEnum, EltExclude(S, x): SeqEnum, Elt → SeqEnumInclude(~S, x): SeqEnum, EltInclude(S, x): SeqEnum, Elt → SeqEnumInsert(~S, i, x): SeqEnum, RngIntElt, EltInsert(S, i, x): SeqEnum, RngIntElt, Elt → SeqEnumInsert(~S, k, m, T): SeqEnum, RngIntElt, RngIntElt, SeqEnumInsert(S, k, m, T): SeqEnum, RngIntElt, RngIntElt, SeqEnum → SeqEnumPrune(~S): SeqEnumPrune(S): SeqEnum → SeqEnumRemove(~S, i): SeqEnum, RngIntEltRemove(S, i): SeqEnum, RngIntElt → SeqEnumReverse(~S): SeqEnumReverse(S): SeqEnum → SeqEnumRotate(~S, p): SeqEnum, RngIntEltRotate(S, p): SeqEnum, RngIntElt → SeqEnumSort(~S): SeqEnumSort(S): SeqEnum → SeqEnumSort(~S, C): SeqEnum, UserProgramSort(~S, C, ~p): SeqEnum, UserProgram, GrpPermEltSort(S, C): SeqEnum, UserProgram → SeqEnumParallelSort(~S, ~T): SeqEnum, SeqEnumUndefine(~S, i): SeqEnum, RngIntEltUndefine(S, i): SeqEnum, RngIntElt → SeqEnumChangeUniverse(S, V): SeqEnum, StrChangeUniverse(S, V): SeqEnum, Str → SeqEnumCanChangeUniverse(S, V): SeqEnum, Str → Bool, SeqEnumExample: Farey
- Creating New Enumerated Sequences from Existing Ones
S cat T: SeqEnum, SeqEnum → SeqEnumS cat:= T: SeqEnum, SeqEnumPartition(S, p): SeqEnum, RngIntElt → SeqEnum(SeqEnum)Partition(S, P): SeqEnum, [RngIntElt] → SeqEnum(SeqEnum)Setseq(S): SetEnum → SeqEnumSetToSequence(S): SetEnum → SeqEnumSeqset(S): SeqEnum → SetEnumSequenceToSet(S): SeqEnum → SetEnumExample: Egyptian Fractions- Operations on Sequences of Booleans
And(S, T): [ BoolElt ], [ BoolElt ] → [BoolElt]And(~S, T): [ BoolElt ], [ BoolElt ]Or(S, T): [ BoolElt ], [ BoolElt ] → [ BoolElt ]Or(~S, T): [ BoolElt ], [ BoolElt ]Xor(S, T): [ BoolElt ], [ BoolElt ] → [ BoolElt ]Xor(~S, T): [ BoolElt], [ BoolElt ]Not(S): [ BoolElt ] → [ BoolElt ]Not(~S): [ BoolElt ]
- Predicates on Sequences
- Recursion, Reduction, and Iteration
