Some more GAP objects

Overview

Teaching: 15 min
Exercises: 5 min
Questions
  • Further examples of immediate and positional objects and operations with them

Objectives
  • See examples of types that are built-in in GAP but may be missing in other systems

  • See examples of list arithmetic

So far we have met three types of GAP types:

In this section, we will demonstrate some other examples of basic objects existing in GAP (the system is extendable, so one can introduce new types of objects, but this is beyond the scope of this lesson!).

Some other immediate objects are floats, cyclotomics and finite field elements:

1.15; Float(1232/3456567);
1.15
0.000356423
E(4); E(4)^2; E(6);
E(4)
-1
-E(3)^2
AsList(GF(2)); Z(5); Z(5)^4;
[ 0*Z(2), Z(2)^0 ]
Z(5)
Z(5)^0

The next type of composite objects are records. While a list contains subobjects indexed by their positions in the list, a record contains subobjects, called record components, which are indexed by their names. Elements of a record are accessed with .

date:= rec(year:= 2015, month:= "Nov", day:= 17);
rec( day := 17, month := "Nov", year := 2015 )
date.year;
2015
date.time:= rec(hour:= 14, minute:= 55, second:= 12);
rec( hour := 14, minute := 55, second := 12 )
date;
rec( day := 17, month := "Nov",
  time := rec( hour := 14, minute := 55, second := 12 ), year := 2015 )
RecNames(date);
[ "time", "year", "month", "day" ]

Next, there are strings and characters. While strings are printed specially by GAP, a string is really just a list of characters, and any function which takes a list will also take a string.

gap> w:="supercalifragilisticexpialidocious"; Length(w);
"supercalifragilisticexpialidocious"
34

Strings are denoted by double quotes, and characters by single ones.

gap> "s" in w; 's' in w; IsSubset(w,"s");  IsSubset(w,['s','f']); ['c','a','t'] = "cat"
false
true
true
true
true

Note that

gap> PositionSublist(w,"sf"); PositionSublist(w,"fr");
fail
10

Be careful that some operations may create a new list, and some may be destructive, for example:

gap> SortedList(w); w;
"aaacccdeefgiiiiiiillloopprrssstuux"
"supercalifragilisticexpialidocious"

but

gap> Sort(w); w;
"aaacccdeefgiiiiiiillloopprrssstuux"

Which letter is occurring in “supercalifragilisticexpialidocious” most often?

gap> c := Collected(w);
[ [ 'a', 3 ], [ 'c', 3 ], [ 'd', 1 ], [ 'e', 2 ], [ 'f', 1 ], [ 'g', 1 ],
  [ 'i', 7 ], [ 'l', 3 ], [ 'o', 2 ], [ 'p', 2 ], [ 'r', 2 ], [ 's', 3 ],
  [ 't', 1 ], [ 'u', 2 ], [ 'x', 1 ] ]
gap> k := Maximum( List( c, v -> v[2] ) ); Filtered( c, v -> v[2] = 7 );
7
[ [ 'i', 7 ] ]

How to find the most occurring letter(s) using one pass over the list c?

The command

k := Maximum( List( c, v -> v[2] ) ); Filtered( c, v -> v[2] = 7 );

iterates over the list c two times (in List and in Filtered), and it also iterates over another list of the same length as c in the call to Maximum. If the list is long, this will impose certain performance and memory penalties. Try to write the code which find the most occurring letter(s) using one pass over the list c without producing an intermediate list.

Key Points

  • GAP has a plethora of variious immediate, positional and component objects.

  • List arithmetic is very flexible and powerful.

  • Objects like lists and records are good to keep structured and related data.