Evolution of a Computer Application

6.b.ii. Top Level Words and Examples

#Set
 (  set -- #ele) Returns number of elements in set. 
2^n
 (  n -- 2^n ) Raise 2 to the input power. (See Singleton.) 
Contains
 (  set1 set2 -- f ) Returns true if set1 contains set2. 
Empty-Set
 ( -- 0 ) Returns the empty set. 
Member!
 (  ele set -- set' ) Make ele a member of set. 
Member?
 (  ele set -- f ) Returns true if ele is a member of set. 
Set-
 (  sub1 sub2 -- sub1-sub2 ) Returns difference of sets. 
Set&
 (  sub1 sub2 -- intersection ) Returns intersection of sets. 
Set*
 (  set1 set2 -- product ) Returns the set of products of elements in set1 set2 in given group. 
Set.
 ( set -- ) Prints set (given as integer bitmap) using letters for elements. 
Set+
 (  sub1 sub2 -- union ) Returns union of sets. 
Set-G
 ( -- gset ) Returns underlying set of current group. 
Singleton
 ( n -- {n} ) Returns set with ele as only member. 
SubGrp.
 (  subg -- ;;;  print subg ) Prints subgroup (bitmap as set) using letters. This is the same as Set.

Examples  

{ ABC} { BC} Contains . -1 (true)
{ ABC} { BD} Contains . 0  (false)
/B { ABC} Member? . -1
/D { ABC} Member? . 0
/D { ABC} Member! 
Set. { A B C D } 
/B Singleton Set. { B }
{ ABC} { BCD} Set- Set. { A }
{ ABC} { BCD} Set+ Set. { A B C D }
{ ABC} { BCD} Set& Set. { B C }
{ ABCD} #Set . 4
8 TABLE
 
  _A_B_C_D_E_F_
A |A B C D E F
B |B C A F D E
C |C A B E F D
D |D E F A B C
E |E F D C A B
F |F D E B C A
Group number 8 of Order 6
    1 elements of order  1:   A
    3 elements of order  2:   D E F
    2 elements of order  3:   B C
    0 elements of order  6:
{ B} Generates Set. { A B C }
{ BD} Generates Set. { A B C D E F }
Center Set. { A }
/B Centralizer Set. { A B C }
{ B} Generates Normalizer Set. { A B C D E F }
{ D} Generates Normalizer Set. { A D }