Dear all,
1. Why important next functions?
k.a_times_b_minus_c
k.a_times_b_plus_c
k.c_minus_a_times_b
sage: k.some_elements ?
...
Returns a collection of elements of this finite field *for use
in unit testing.*
Why this function are defined as public?
2. Also a few misunderstanding functions
- sage: *k.cardinality* ?
Type: builtin_function_or_method
Base Class: <type 'builtin_function_or_method'>
String Form: <built-in method cardinality of
FiniteField_givaro_with_category object at 0xbb0eaac>
Namespace: Interactive
Definition: k.cardinality(self)
Docstring:
Return the order of this finite field (*same as self.order()*).
- sage: *k.cayley_graph() *
---------------------------------------------------------------------------
AttributeError Traceback (most recent call
last)
/home/hamsin/<ipython console> in <module>()
/home/hamsin/bin/sage/local/lib/python2.7/site-packages/sage/categories/semigroups.pyc
in cayley_graph(self, side, simple, elements, generators, connecting_set)
284 generators = connecting_set
285 if generators is None:
--> 286 generators = self.semigroup_generators()
287 if isinstance(generators, (list, tuple)):
288 generators = dict((self(g), self(g)) for g in
generators)
/home/hamsin/bin/sage/local/lib/python2.7/site-packages/sage/structure/parent.so
in sage.structure.parent.Parent.__getattr__ (sage/structure/parent.c:6805)()
/home/hamsin/bin/sage/local/lib/python2.7/site-packages/sage/structure/parent.so
in sage.structure.parent.getattr_from_other_class
(sage/structure/parent.c:3248)()
AttributeError: 'FiniteField_givaro_with_category' object has no
attribute 'semigroup_generators'
- sage: *k.has_base()*
*True*
sage: *k.has_base* ?
Type: builtin_function_or_method
Base Class: <type 'builtin_function_or_method'>
String Form: <built-in method has_base of
FiniteField_givaro_with_category object at 0xbb0eaac>
Namespace: Interactive
Definition: k.has_base(self, category=None)
*??????*
*
*
- sage: *k.ngens* *?*
Type: builtin_function_or_method
Base Class: <type 'builtin_function_or_method'>
String Form: <built-in method ngens of FiniteField_givaro_with_category
object at 0xbb0eaac>
Namespace: Interactive
Definition: k.ngens(self)
Docstring:
The number of generators of the finite field. * Always 1.*
*
*
- sage: *k.normalize_names ?*
Type: builtin_function_or_method
Base Class: <type 'builtin_function_or_method'>
String Form: <built-in method normalize_names of
FiniteField_givaro_with_category object at 0xbb0eaac>
Namespace: Interactive
Definition: k.normalize_names(self, ngens, names=None)
sage: k.normalize_names()
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/home/hamsin/<ipython console> in <module>()
/home/hamsin/bin/sage/local/lib/python2.7/site-packages/sage/structure/category_object.so
in sage.structure.category_object.CategoryObject.normalize_names
(sage/structure/category_object.c:3939)()
TypeError: normalize_names() takes at least 1 positional argument (0
given)
sage: k.normalize_names(1)
*??????*
*
*
- sage: *k.on*
k.one k.one_element
sage: k.one ?
Type: builtin_function_or_method
Base Class: <type 'builtin_function_or_method'>
String Form: <built-in method one_element of
FiniteField_givaro_with_category object at 0xbb0eaac>
Namespace: Interactive
Definition: k.one(self)
Docstring:
Return the one element of this ring (cached), if it exists.
EXAMPLES:
sage: ZZ.*one_element()*
1
sage: QQ.*one_element()*
1
sage: QQ['x'].*one_element()*
1
The result is cached:
sage: ZZ.*one_element() *is *ZZ.one_element()*
True
- sage: *k.zero ? *
Type: builtin_function_or_method
Base Class: <type 'builtin_function_or_method'>
String Form: <built-in method zero_element of
FiniteField_givaro_with_category object at 0xbb0eaac>
Namespace: Interactive
Definition: k.zero(self)
Docstring:
Return the zero element of this ring (cached).
EXAMPLES:
sage: *ZZ.zero_element()*
0
sage: *QQ.zero_element()*
0
sage: QQ['x'].*zero_element()*
0
The result is cached:
sage: ZZ.*zero_element()* is ZZ.*zero_element()*
True
Definition of the field:
sage: R.<x>=ZZ[]
sage: k=GF(2^8,name='a',modulus=x^8+x^4+x^3+x+1)
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