def standardize_names_index_set(names=None, index_set=None, ngens=None):
"""
Standardize the ``names`` and ``index_set`` inputs.
INPUT:
- ``names`` -- (optional) the variable names
- ``index_set`` -- (optional) the index set
- ``ngens`` -- (optional) the number of generators
If ``ngens`` is a negative number, then this does not check that
the number of variable names matches the size of the index set.
OUTPUT:
A pair ``(names_std, index_set_std)``, where ``names_std`` is either
``None`` or a tuple of strings, and where ``index_set_std`` is a finite
enumerated set.
The purpose of ``index_set_std`` is to index the generators of some object
(e.g., the basis of a module); the strings in ``names_std``, when they
exist, are used for printing these indices. The ``ngens``
If ``names`` contains exactly one name ``X`` and ``ngens`` is greater than
1, then ``names_std`` are ``Xi`` for ``i`` in ``range(ngens)``.
TESTS::
sage: from sage.structure.indexed_generators import standardize_names_index_set
sage: standardize_names_index_set('x,y')
(('x', 'y'), {'x', 'y'})
sage: standardize_names_index_set(['x','y'])
(('x', 'y'), {'x', 'y'})
sage: standardize_names_index_set(['x','y'], ['a','b'])
(('x', 'y'), {'a', 'b'})
sage: standardize_names_index_set('x,y', ngens=2)
(('x', 'y'), {'x', 'y'})
sage: standardize_names_index_set(index_set=['a','b'], ngens=2)
(None, {'a', 'b'})
sage: standardize_names_index_set('x', ngens=3)
(('x0', 'x1', 'x2'), {'x0', 'x1', 'x2'})
sage: standardize_names_index_set()
Traceback (most recent call last):
...
ValueError: the index_set, names, or number of generators must be specified
sage: standardize_names_index_set(['x'], ['a', 'b'])
Traceback (most recent call last):
...
IndexError: the number of names must equal the size of the indexing set
sage: standardize_names_index_set('x,y', ['a'])
Traceback (most recent call last):
...
IndexError: the number of names must equal the size of the indexing set
sage: standardize_names_index_set('x,y,z', ngens=2)
Traceback (most recent call last):
...
IndexError: the number of names must equal the number of generators
sage: standardize_names_index_set(index_set=['a'], ngens=2)
Traceback (most recent call last):
...
IndexError: the size of the indexing set must equal the number of generators
"""
if names is not None:
if ngens is None or ngens < 0:
names = normalize_names(-1, names)
else:
names = normalize_names(ngens, names)
if index_set is None:
if names is None:
# If neither is specified, we make range(ngens) the index set
if ngens is None:
raise ValueError("the index_set, names, or number of"
" generators must be specified")
index_set = tuple(range(ngens))
else:
# If only the names are specified, then we make the indexing set
# be the names
index_set = tuple(names)
from sage.sets.finite_enumerated_set import FiniteEnumeratedSet
if isinstance(index_set,
dict): # dict of {name: index} -- not likely to be used
if names is not None:
raise ValueError("cannot give index_set as a dict and names")
names = normalize_names(-1, tuple(index_set.keys()))
index_set = FiniteEnumeratedSet([index_set[n] for n in names])
elif isinstance(index_set, str):
index_set = FiniteEnumeratedSet(list(index_set))
elif isinstance(index_set, (tuple, list)):
index_set = FiniteEnumeratedSet(index_set)
if ngens is None or ngens >= 0:
if names is not None:
if len(names) != index_set.cardinality():
raise IndexError("the number of names must equal"
" the size of the indexing set")
if ngens is not None and len(names) != ngens:
raise IndexError("the number of names must equal the"
" number of generators")
elif ngens is not None and index_set.cardinality() != ngens:
raise IndexError("the size of the indexing set must equal"
" the number of generators")
return (names, index_set)
def standardize_names_index_set(names=None, index_set=None, ngens=None):
"""
Standardize the ``names`` and ``index_set`` inputs.
INPUT:
- ``names`` -- (optional) the variable names
- ``index_set`` -- (optional) the index set
- ``ngens`` -- (optional) the number of generators
If ``ngens`` is a negative number, then this does not check that
the number of variable names matches the size of the index set.
OUTPUT:
A pair ``(names_std, index_set_std)``, where ``names_std`` is either
``None`` or a tuple of strings, and where ``index_set_std`` is a finite
enumerated set.
The purpose of ``index_set_std`` is to index the generators of some object
(e.g., the basis of a module); the strings in ``names_std``, when they
exist, are used for printing these indices. The ``ngens``
If ``names`` contains exactly one name ``X`` and ``ngens`` is greater than
1, then ``names_std`` are ``Xi`` for ``i`` in ``range(ngens)``.
TESTS::
sage: from sage.structure.indexed_generators import standardize_names_index_set
sage: standardize_names_index_set('x,y')
(('x', 'y'), {'x', 'y'})
sage: standardize_names_index_set(['x','y'])
(('x', 'y'), {'x', 'y'})
sage: standardize_names_index_set(['x','y'], ['a','b'])
(('x', 'y'), {'a', 'b'})
sage: standardize_names_index_set('x,y', ngens=2)
(('x', 'y'), {'x', 'y'})
sage: standardize_names_index_set(index_set=['a','b'], ngens=2)
(None, {'a', 'b'})
sage: standardize_names_index_set('x', ngens=3)
(('x0', 'x1', 'x2'), {'x0', 'x1', 'x2'})
sage: standardize_names_index_set()
Traceback (most recent call last):
...
ValueError: the index_set, names, or number of generators must be specified
sage: standardize_names_index_set(['x'], ['a', 'b'])
Traceback (most recent call last):
...
IndexError: the number of names must equal the size of the indexing set
sage: standardize_names_index_set('x,y', ['a'])
Traceback (most recent call last):
...
IndexError: the number of names must equal the size of the indexing set
sage: standardize_names_index_set('x,y,z', ngens=2)
Traceback (most recent call last):
...
IndexError: the number of names must equal the number of generators
sage: standardize_names_index_set(index_set=['a'], ngens=2)
Traceback (most recent call last):
...
IndexError: the size of the indexing set must equal the number of generators
"""
if names is not None:
if ngens is None or ngens < 0:
names = normalize_names(-1, names)
else:
names = normalize_names(ngens, names)
if index_set is None:
if names is None:
# If neither is specified, we make range(ngens) the index set
if ngens is None:
raise ValueError("the index_set, names, or number of"
" generators must be specified")
index_set = tuple(range(ngens))
else:
# If only the names are specified, then we make the indexing set
# be the names
index_set = tuple(names)
from sage.sets.finite_enumerated_set import FiniteEnumeratedSet
if isinstance(index_set, dict): # dict of {name: index} -- not likely to be used
if names is not None:
raise ValueError("cannot give index_set as a dict and names")
names = normalize_names(-1, tuple(index_set.keys()))
index_set = FiniteEnumeratedSet([index_set[n] for n in names])
elif isinstance(index_set, str):
index_set = FiniteEnumeratedSet(list(index_set))
elif isinstance(index_set, (tuple, list)):
index_set = FiniteEnumeratedSet(index_set)
if ngens is None or ngens >= 0:
if names is not None:
if len(names) != index_set.cardinality():
raise IndexError("the number of names must equal"
" the size of the indexing set")
if ngens is not None and len(names) != ngens:
raise IndexError("the number of names must equal the"
" number of generators")
elif ngens is not None and index_set.cardinality() != ngens:
raise IndexError("the size of the indexing set must equal"
" the number of generators")
return (names, index_set)
