Hide keyboard shortcuts

Hot-keys on this page

r m x p   toggle line displays

j k   next/prev highlighted chunk

0   (zero) top of page

1   (one) first highlighted chunk

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

r""" 

Finitely generated magmas 

""" 

#***************************************************************************** 

# Copyright (C) 2014 Nicolas M. Thiery <nthiery at users.sf.net> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# http://www.gnu.org/licenses/ 

#****************************************************************************** 

 

from sage.misc.abstract_method import abstract_method 

from sage.categories.category_with_axiom import CategoryWithAxiom 

from sage.categories.magmas import Magmas 

 

class FinitelyGeneratedMagmas(CategoryWithAxiom): 

r""" 

The category of finitely generated (multiplicative) magmas. 

 

See :meth:`Magmas.SubcategoryMethods.FinitelyGeneratedAsMagma` for 

details. 

 

EXAMPLES:: 

 

sage: C = Magmas().FinitelyGeneratedAsMagma(); C 

Category of finitely generated magmas 

sage: C.super_categories() 

[Category of magmas] 

sage: sorted(C.axioms()) 

['FinitelyGeneratedAsMagma'] 

 

TESTS:: 

 

sage: TestSuite(C).run() 

""" 

 

_base_category_class_and_axiom = (Magmas, "FinitelyGeneratedAsMagma") 

 

class ParentMethods: 

 

@abstract_method 

def magma_generators(self): 

""" 

Return distinguished magma generators for ``self``. 

 

OUTPUT: a finite family 

 

This method should be implemented by all 

:class:`finitely generated magmas <FinitelyGeneratedMagmas>`. 

 

EXAMPLES:: 

 

sage: S = FiniteSemigroups().example() 

sage: S.magma_generators() 

Family ('a', 'b', 'c', 'd') 

"""