Indexed Generators

class sage.structure.indexed_generators.IndexedGenerators(indices, prefix='x', **kwds)

Bases: object

Abstract base class for parents whose elements consist of generators indexed by an arbitrary set.

Options controlling the printing of elements:

  • prefix – string, prefix used for printing elements of this module (optional, default ‘x’). With the default, a monomial indexed by ‘a’ would be printed as x['a'].
  • latex_prefix – string or None, prefix used in the \(\LaTeX\) representation of elements (optional, default None). If this is anything except the empty string, it prints the index as a subscript. If this is None, it uses the setting for prefix, so if prefix is set to “B”, then a monomial indexed by ‘a’ would be printed as B_{a}. If this is the empty string, then don’t print monomials as subscripts: the monomial indexed by ‘a’ would be printed as a, or as [a] if latex_bracket is True.
  • bracketNone, bool, string, or list or tuple of strings (optional, default None): if None, use the value of the attribute self._repr_option_bracket, which has default value True. (self._repr_option_bracket is available for backwards compatibility. Users should set bracket instead. If bracket is set to anything except None, it overrides the value of self._repr_option_bracket.) If False, do not include brackets when printing elements: a monomial indexed by ‘a’ would be printed as B'a', and a monomial indexed by (1,2,3) would be printed as B(1,2,3). If True, use “[” and “]” as brackets. If it is one of “[”, “(”, or “{”, use it and its partner as brackets. If it is any other string, use it as both brackets. If it is a list or tuple of strings, use the first entry as the left bracket and the second entry as the right bracket.
  • latex_bracket – bool, string, or list or tuple of strings (optional, default False): if False, do not include brackets in the LaTeX representation of elements. This option is only relevant if latex_prefix is the empty string; otherwise, brackets are not used regardless. If True, use “left[” and “right]” as brackets. If this is one of “[”, “(”, “\{”, “|”, or “||”, use it and its partner, prepended with “left” and “right”, as brackets. If this is any other string, use it as both brackets. If this is a list or tuple of strings, use the first entry as the left bracket and the second entry as the right bracket.
  • scalar_mult – string to use for scalar multiplication in the print representation (optional, default “*”)
  • latex_scalar_mult – string or None (default: None), string to use for scalar multiplication in the latex representation. If None, use the empty string if scalar_mult is set to “*”, otherwise use the value of scalar_mult.
  • tensor_symbol – string or None (default: None), string to use for tensor product in the print representation. If None, use sage.categories.tensor.symbol.
  • generator_cmp – a comparison function (default: cmp), to use for sorting elements in the output of elements

Note

These print options may also be accessed and modified using the print_options() method, after the parent has been defined.

EXAMPLES:

We demonstrate a variety of the input options:

sage: from sage.structure.indexed_generators import IndexedGenerators
sage: I = IndexedGenerators(ZZ, prefix='A')
sage: I._repr_generator(2)
'A[2]'
sage: I._latex_generator(2)
'A_{2}'

sage: I = IndexedGenerators(ZZ, bracket='(')
sage: I._repr_generator(2)
'x(2)'
sage: I._latex_generator(2)
'x_{2}'

sage: I = IndexedGenerators(ZZ, prefix="", latex_bracket='(')
sage: I._repr_generator(2)
'[2]'
sage: I._latex_generator(2)
\left( 2 \right)

sage: I = IndexedGenerators(ZZ, bracket=['|', '>'])
sage: I._repr_generator(2)
'x|2>'
indices()

Return the indices of self.

EXAMPLES:

sage: F = CombinatorialFreeModule(QQ, ['a', 'b', 'c'])
sage: F.indices()
{'a', 'b', 'c'}
prefix()

Return the prefix used when displaying elements of self.

EXAMPLES:

sage: F = CombinatorialFreeModule(QQ, ['a', 'b', 'c'])
sage: F.prefix()
'B'
sage: X = SchubertPolynomialRing(QQ)
sage: X.prefix()
'X'
print_options(**kwds)

Return the current print options, or set an option.

INPUT: all of the input is optional; if present, it should be in the form of keyword pairs, such as latex_bracket='('. The allowable keywords are:

  • prefix
  • latex_prefix
  • bracket
  • latex_bracket
  • scalar_mult
  • latex_scalar_mult
  • tensor_symbol
  • generator_cmp

See the documentation for CombinatorialFreeModule for descriptions of the effects of setting each of these options.

OUTPUT: if the user provides any input, set the appropriate option(s) and return nothing. Otherwise, return the dictionary of settings for print and LaTeX representations.

EXAMPLES:

sage: F = CombinatorialFreeModule(ZZ, [1,2,3], prefix='x')
sage: F.print_options()
{...'prefix': 'x'...}
sage: F.print_options(bracket='(')
sage: F.print_options()
{...'bracket': '('...}

TESTS:

sage: sorted(F.print_options().items())
[('bracket', '('), ('generator_cmp', <built-in function cmp>),
 ('latex_bracket', False), ('latex_prefix', None),
 ('latex_scalar_mult', None), ('prefix', 'x'),
 ('scalar_mult', '*'), ('tensor_symbol', None)]
sage: F.print_options(bracket='[') # reset

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