Some more GAP objects

Overview

Teaching: 15 min
Exercises: 5 min

Questions

• Further examples of 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:

• simple objects such as integers, rationals, booleans, permutations;

• composite objects such as lists;

• objects with more complex internal representation, such as groups.

In this section, we will demonstrate some other examples of basic objects that exist 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 simple 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

You already know about lists. Another type of composite objects is 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. In contrast, characters are simple objects like integers.

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! Some operations may create a new list, while others are destructive. For example:

gap> SortedList(w); w;

"aaacccdeefgiiiiiiillloopprrssstuux"
"supercalifragilisticexpialidocious"

but

gap> Sort(w); w;

"aaacccdeefgiiiiiiillloopprrssstuux"

Which letter occurs 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 ] ]

Finding the most common letter(s) in a list using only one pass

The command

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

iterates over the list c twice (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 code that finds the letters that occur most in c without producing an intermediate list.

Key Points

• GAP has a plethora of various 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.