Sharedsage_worksheets / ADS_Subgroups.sagewsOpen in CoCalc
Author: Ken Levasseur
Description: Worksheets related to Applied Discrete Structures
G=Integers(20)
File: /ext/sage/sage-8.6_1804/local/lib/python2.7/site-packages/sage/categories/monoids.py Signature : G.submonoid(self, generators, category=None) Docstring : Return the multiplicative submonoid generated by "generators". INPUT: * "generators" -- a finite family of elements of "self", or a list, iterable, ... that can be converted into one (see "Family"). * "category" -- a category This is a shorthand for "Semigroups.ParentMethods.subsemigroup()" that specifies that this is a submonoid, and in particular that the unit is "self.one()". EXAMPLES: sage: R = IntegerModRing(15) sage: M = R.submonoid([R(3),R(5)]); M A submonoid of (Ring of integers modulo 15) with 2 generators sage: M.list() [1, 3, 5, 9, 0, 10, 12, 6] Not the presence of the unit, unlike in: sage: S = R.subsemigroup([R(3),R(5)]); S A subsemigroup of (Ring of integers modulo 15) with 2 generators sage: S.list() [3, 5, 9, 0, 10, 12, 6] This method is really a shorthand for subsemigroup: sage: M2 = R.subsemigroup([R(3),R(5)], one=R.one()) sage: M2 is M True
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