[Next] [Prev] [Right] [____] [Up] [Index] [Root] 
Sequences


Sequences




The Magma category SeqEnum consists of
enumerated sequences. A simple example 
of a sequence is  [3, 7, 2]. 


When creating a sequence, it is preferable to 
specify its universe, of which all the terms
are members, as follows:

  [ Integers() | 3, 7, 2]
  [ Sym(5) | (4, 3, 1), (2, 4)(5, 1) ]




An empty sequence is a sequence with no elements: 

  [ UNIVERSE | ] 


A null sequence is an empty sequence with 
no universe:

  [ ]




The sequence constructor 

  [ U | e(x) : x in DOMAIN | P(x) ]


where U is the universe, e(x) and P(x) are 
expressions in the bound identifier x,
and P(x) evaluates to a Boolean, constructs
the enumerated sequence containing all e(x)
where x is in DOMAIN and P(x) is true.
The shorter form

  [ U | e(x) : x in DOMAIN ]


is used when all of DOMAIN is required.


There is also a multivariate version of the
sequence constructor:

  [ U | e(x_1, ..., x_n) : 
    x_1 in DOMAIN_1, ..., x_n in DOMAIN_n | 
    P(x_1, ..., x_n) ]


which works similarly.


The arithmetic progression constructor

  [ s .. t by u ]


where s, t, u evaluate to integers
returns the sequence [ s, s+u, s+2u, ... , t ].
The shorter form

  [ s .. t ]


returns the sequence [ s, s+1, ... , t ].


The terms of a sequence are ordered, in
the order in which they were listed or
constructed from a domain. The i-th element of the
sequence S is S[i], and the position of
element x in S is Index(S, x).  S[i] may
be assigned the value of EXPRESSION with
the statement

  S[i] := EXPRESSION;




A sequence may be recursively defined by means
of Self(), which refers to the sequence under
construction, and Self(i), which refers to its
already-defined i-th term.


The length of a sequence S is #S.  This is the index
of the last term of S whose value is defined. 


Operations on sequences include:
  Universe, IsNull, IsEmpty, Min, Max,
  in, notin, IsSubsequence, eq, ne, lt,
  cat, Include, Exclude, Append, Prune,
  Insert, Remove, Reverse, Rotate, Sort, &.



Example


> proots := [ z : z in GF(10007) | IsPrimitive(z) ];
> print #proots;
5002
> print proots[17];
41


> S1 := [ 84 .. 27 by -5 ];
> Include(~S1, 72);
> print S1;
[ 29, 34, 39, 44, 49, 54, 59, 64, 69, 72, 74, 79, 84 ]
> print &+S1;
750


> fibo := [ i gt 2 select Self(i-2)+Self(i-1) else 1 : i in [1..100] ];
> print fibo[1..10];
[ 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 ]





[Next] [Prev] [Right] [____] [Up] [Index] [Root]