Deprecate is_FiniteField etc., make sage.rings.finite_rings a namespace package

src/.relint.yml

@@ -49,6 +49,6 @@
     Hint: namespace package. Type import_statements("SOME_IDENTIFIER") to find a more specific import,
     Hint: or use 'sage --fiximports' to fix automatically in the source file.
   # Keep in sync with SAGE_ROOT/src/sage/misc/replace_dot_all.py
-  pattern: 'from\s+sage(|[.](arith|categories|combinat|ext|graphs(|[.]decompositions)|interfaces|libs|matrix|misc|numerical(|[.]backends)|rings|sets))[.]all\s+import'
+  pattern: 'from\s+sage(|[.](arith|categories|combinat|ext|graphs(|[.]decompositions)|interfaces|libs|matrix|misc|numerical(|[.]backends)|rings(|[.]finite_rings)|sets))[.]all\s+import'
   filePattern: '.*[.](py|pyx|pxi)$'
   error: false # Make this a warning instead of an error for now

src/sage/crypto/boolean_function.pyx

@@ -38,8 +38,7 @@ from sage.rings.integer_ring import ZZ
 from sage.rings.integer cimport Integer
 from sage.rings.finite_rings.finite_field_constructor import GF
 from sage.rings.polynomial.pbori.pbori import BooleanPolynomial
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
-from sage.rings.finite_rings.finite_field_givaro import FiniteField_givaro
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.polynomial.polynomial_element import Polynomial
 
 from sage.misc.superseded import deprecated_function_alias
@@ -329,11 +328,15 @@ cdef class BooleanFunction(SageObject):
 
         elif isinstance(x, Polynomial):
             K = x.base_ring()
-            if is_FiniteField(K) and K.characteristic() == 2:
+            if isinstance(K, FiniteField) and K.characteristic() == 2:
                 self._nvariables = K.degree()
                 bitset_init(self._truth_table, <mp_bitcnt_t> (1<<self._nvariables))
                 bitset_zero(self._truth_table)
-                if isinstance(K,FiniteField_givaro): #the ordering is not the same in this case
+                try:
+                    from sage.rings.finite_rings.finite_field_givaro import FiniteField_givaro
+                except ImportError:
+                    FiniteField_givaro = ()
+                if isinstance(K, FiniteField_givaro):  # the ordering is not the same in this case
                     for u in K:
                         bitset_set_to(self._truth_table, ZZ(u._vector_().list(),2) , (x(u)).trace())
                 else:

src/sage/crypto/lfsr.py

@@ -129,7 +129,7 @@
 
 from sage.structure.all import Sequence
 from sage.rings.all import Integer, PolynomialRing
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 
 
 def lfsr_sequence(key, fill, n):
@@ -179,7 +179,7 @@ def lfsr_sequence(key, fill, n):
         raise TypeError("key must be a list")
     key = Sequence(key)
     F = key.universe()
-    if not is_FiniteField(F):
+    if not isinstance(F, FiniteField):
         raise TypeError("universe of sequence must be a finite field")
 
     s = fill

src/sage/crypto/mq/rijndael_gf.py

@@ -424,7 +424,8 @@
 
 from sage.matrix.constructor import matrix
 from sage.matrix.constructor import column_matrix
-from sage.structure.element import Matrix
+from sage.structure.element import Element, Matrix
+from sage.rings.finite_rings.finite_field_base import FiniteField as FiniteField_base
 from sage.rings.finite_rings.finite_field_constructor import FiniteField
 from sage.structure.sage_object import SageObject
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
@@ -757,10 +758,9 @@ def _GF_to_hex(self, GF):
             sage: rgf._GF_to_hex(output)
             'e142cd5fcd9d6d94a3340793034391b5'
         """
-        from sage.rings.finite_rings.element_base import is_FiniteFieldElement
         if not isinstance(GF, Matrix) and \
            not isinstance(GF, list) and \
-           not is_FiniteFieldElement(GF):
+           not (isinstance(GF, Element) and isinstance(GF.parent(), FiniteField_base)):
             msg = ("keyword 'GF' must be a matrix over {0}, a list of "
                    "elements from {0}, or a single element from {0}")
             raise TypeError(msg.format(self._F))
@@ -883,10 +883,9 @@ def _GF_to_bin(self, GF):
             sage: rgf._GF_to_bin(output)
             '11011000000111111111100000011011110110000001111111111000000110111101100000011111111110000001101111011000000111111111100000011011'
         """
-        from sage.rings.finite_rings.element_base import is_FiniteFieldElement
         if not isinstance(GF, Matrix) and \
            not isinstance(GF, list) and \
-           not is_FiniteFieldElement(GF):
+           not (isinstance(GF, Element) and isinstance(GF.parent(), FiniteField_base)):
             msg = ("keyword 'GF' must be a matrix over {0}, a list of "
                    "elements from {0}, or a single element from {0}")
             raise TypeError(msg.format(self))

src/sage/crypto/sbox.pyx

@@ -17,7 +17,7 @@ from sage.misc.functional import is_even
 from sage.misc.misc_c import prod as mul
 from sage.misc.superseded import deprecated_function_alias
 from sage.modules.free_module_element import vector
-from sage.rings.finite_rings.element_base import is_FiniteFieldElement
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
 from sage.rings.ideal import FieldIdeal, Ideal
 from sage.rings.integer_ring import ZZ
@@ -195,7 +195,7 @@ cdef class SBox(SageObject):
 
         _S_list = []
         for e in S:
-            if is_FiniteFieldElement(e):
+            if isinstance(e, Element) and isinstance(e.parent(), FiniteField):
                 e = e.polynomial().change_ring(ZZ).subs(e.parent().characteristic())
             _S_list.append(e)
         S = _S_list

src/sage/dynamics/arithmetic_dynamics/affine_ds.py

@@ -43,8 +43,7 @@ class initialization directly.
 from sage.misc.cachefunc import cached_method
 from sage.misc.classcall_metaclass import typecall
 from sage.rings.integer import Integer
-from sage.rings.finite_rings.finite_field_constructor import is_PrimeFiniteField
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.fraction_field import FractionField
 from sage.rings.fraction_field import is_FractionField
 from sage.rings.quotient_ring import is_QuotientRing
@@ -251,7 +250,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None):
                 raise ValueError('domain and codomain do not agree')
             if R not in Fields():
                 return typecall(cls, polys, domain)
-            if is_FiniteField(R):
+            if isinstance(R, FiniteField):
                 return DynamicalSystem_affine_finite_field(polys, domain)
             return DynamicalSystem_affine_field(polys, domain)
         elif isinstance(morphism_or_polys,(list, tuple)):
@@ -299,7 +298,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None):
 
         if R not in Fields():
             return typecall(cls, polys, domain)
-        if is_FiniteField(R):
+        if isinstance(R, FiniteField):
             return DynamicalSystem_affine_finite_field(polys, domain)
         return DynamicalSystem_affine_field(polys, domain)
 
@@ -319,7 +318,8 @@ def __init__(self, polys_or_rat_fncts, domain):
         """
         L = polys_or_rat_fncts
         # Next attribute needed for _fast_eval and _fastpolys
-        self._is_prime_finite_field = is_PrimeFiniteField(L[0].base_ring())
+        R = L[0].base_ring()
+        self._is_prime_finite_field = isinstance(R, FiniteField) and R.is_prime_field()
         DynamicalSystem.__init__(self, L, domain)
 
     def __copy__(self):

src/sage/dynamics/arithmetic_dynamics/generic_ds.py

@@ -33,7 +33,7 @@ class initialization directly.
 from sage.schemes.affine.affine_space import is_AffineSpace
 from sage.schemes.affine.affine_subscheme import AlgebraicScheme_subscheme_affine
 from sage.rings.algebraic_closure_finite_field import AlgebraicClosureFiniteField_generic
-from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.qqbar import AlgebraicField_common
 from sage.schemes.berkovich.berkovich_space import is_Berkovich_Cp
 from sage.rings.rational_field import QQ
@@ -416,7 +416,7 @@ def field_of_definition_critical(self, return_embedding=False, simplify_all=Fals
             CR = CR.ring()
         x = CR.gen(0)
         poly = (g*CR(f).derivative(x) - f*CR(g).derivative(x)).univariate_polynomial()
-        if is_FiniteField(ds.base_ring()):
+        if isinstance(ds.base_ring(), FiniteField):
             return poly.splitting_field(names, map=return_embedding)
         else:
             K = poly.splitting_field(names, map=return_embedding, simplify_all=simplify_all)
@@ -536,7 +536,7 @@ def field_of_definition_periodic(self, n, formal=False, return_embedding=False,
             fn = ds.nth_iterate_map(n)
             f,g = fn[0].numerator(), fn[0].denominator()
             poly = (f - g*x).univariate_polynomial()
-        if is_FiniteField(ds.base_ring()):
+        if isinstance(ds.base_ring(), FiniteField):
             return poly.splitting_field(names, map=return_embedding)
         else:
             K = poly.splitting_field(names, map=return_embedding, simplify_all=simplify_all)
@@ -630,7 +630,7 @@ def field_of_definition_preimage(self, point, n, return_embedding=False, simplif
             #want the polynomial ring not the fraction field
             CR = CR.ring()
         poly = (f*point[1] - g*CR(point[0])).univariate_polynomial()
-        if is_FiniteField(ds.base_ring()):
+        if isinstance(ds.base_ring(), FiniteField):
             return poly.splitting_field(names, map=return_embedding)
         else:
             K = poly.splitting_field(names, map=return_embedding, simplify_all=simplify_all)

src/sage/dynamics/arithmetic_dynamics/projective_ds.py

@@ -72,8 +72,8 @@ class initialization directly.
 from sage.categories.finite_fields import FiniteFields
 from sage.rings.algebraic_closure_finite_field import AlgebraicClosureFiniteField_generic
 from sage.rings.complex_mpfr import ComplexField
-from sage.rings.finite_rings.finite_field_constructor import (is_FiniteField, GF,
-                                                              is_PrimeFiniteField)
+from sage.rings.finite_rings.finite_field_base import FiniteField
+from sage.rings.finite_rings.finite_field_constructor import GF
 from sage.rings.finite_rings.integer_mod_ring import Zmod
 from sage.rings.fraction_field import (FractionField, is_FractionField, FractionField_1poly_field)
 from sage.rings.fraction_field_element import is_FractionFieldElement, FractionFieldElement
@@ -373,7 +373,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None, names=None):
                 raise ValueError('"domain" must be a projective scheme')
             if R not in Fields():
                 return typecall(cls, polys, domain)
-            if is_FiniteField(R):
+            if isinstance(R, FiniteField):
                 return DynamicalSystem_projective_finite_field(polys, domain)
             return DynamicalSystem_projective_field(polys, domain)
 
@@ -432,7 +432,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None, names=None):
                 if not all(split_d == domain._degree(f) for f in split_poly):
                     msg = 'polys (={}) must be multi-homogeneous of the same degrees (by component)'
                     raise TypeError(msg.format(polys))
-            if is_FiniteField(R):
+            if isinstance(R, FiniteField):
                 from sage.dynamics.arithmetic_dynamics.product_projective_ds import DynamicalSystem_product_projective_finite_field
                 return DynamicalSystem_product_projective_finite_field(polys, domain)
             return DynamicalSystem_product_projective(polys, domain)
@@ -450,7 +450,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None, names=None):
             raise ValueError('"domain" must be a projective scheme')
         if R not in Fields():
             return typecall(cls, polys, domain)
-        if is_FiniteField(R):
+        if isinstance(R, FiniteField):
                 return DynamicalSystem_projective_finite_field(polys, domain)
         return DynamicalSystem_projective_field(polys, domain)
 
@@ -469,8 +469,9 @@ def __init__(self, polys, domain):
                     (3/5*x^2 : y^2)
         """
         # Next attribute needed for _fast_eval and _fastpolys
-        self._is_prime_finite_field = is_PrimeFiniteField(polys[0].base_ring())
-        DynamicalSystem.__init__(self,polys,domain)
+        R = polys[0].base_ring()
+        self._is_prime_finite_field = isinstance(R, FiniteField) and R.is_prime_field()
+        DynamicalSystem.__init__(self, polys, domain)
 
     def __copy__(self):
         r"""

src/sage/groups/cubic_braid.py

@@ -1543,10 +1543,10 @@ def as_matrix_group(self, root_bur=None, domain=None, characteristic=None, var='
                 self._classical_invariant_form = herm_form
 
         if unitary:
-            from sage.rings.finite_rings.finite_field_base import is_FiniteField
+            from sage.rings.finite_rings.finite_field_base import FiniteField
             from sage.groups.matrix_gps.unitary import GU
             d, d = herm_form.dimensions()
-            if is_FiniteField(domain):
+            if isinstance(domain, FiniteField):
                 base_group = GU(d, domain, var=domain.gen(), invariant_form=herm_form)
             else:
                 base_group = GU(d, domain, invariant_form=herm_form)

src/sage/groups/matrix_gps/orthogonal.py

@@ -85,7 +85,7 @@
 # ****************************************************************************
 
 from sage.rings.integer_ring import ZZ
-from sage.rings.finite_rings.finite_field_base import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.misc.latex import latex
 from sage.misc.cachefunc import cached_method
 from sage.groups.matrix_gps.named_group import (
@@ -127,7 +127,7 @@ def normalize_args_e(degree, ring, e):
         ...
         ValueError: must have e=-1 or e=1 for even degree
     """
-    if is_FiniteField(ring) and degree%2 == 0:
+    if isinstance(ring, FiniteField) and degree%2 == 0:
         if e not in (-1, +1):
             raise ValueError('must have e=-1 or e=1 for even degree')
     else:
@@ -171,7 +171,7 @@ def _OG(n, R, special, e=0, var='a', invariant_form=None):
     e = normalize_args_e(degree, ring, e)
 
     if invariant_form is not None:
-        if is_FiniteField(ring):
+        if isinstance(ring, FiniteField):
             raise NotImplementedError("invariant_form for finite groups is fixed by GAP")
 
     if e == 0:
@@ -202,7 +202,7 @@ def _OG(n, R, special, e=0, var='a', invariant_form=None):
                                                          latex(ring),
                                                          '+' if e == 1 else '-')
 
-    if is_FiniteField(ring):
+    if isinstance(ring, FiniteField):
         cmd  = '{0}O({1}, {2}, {3})'.format(ltx_prefix, e, degree, ring.order())
         return OrthogonalMatrixGroup_gap(degree, ring, False, name, ltx, cmd)
     else:

src/sage/groups/matrix_gps/symplectic.py

@@ -42,7 +42,7 @@
 
 from sage.misc.latex import latex
 from sage.misc.cachefunc import cached_method
-from sage.rings.finite_rings.finite_field_base import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.groups.matrix_gps.named_group import (
     normalize_args_vectorspace, normalize_args_invariant_form,
     NamedMatrixGroup_generic, NamedMatrixGroup_gap)
@@ -145,7 +145,7 @@ def Sp(n, R, var='a', invariant_form=None):
         raise ValueError('the degree must be even')
 
     if invariant_form is not None:
-        if is_FiniteField(ring):
+        if isinstance(ring, FiniteField):
             raise NotImplementedError("invariant_form for finite groups is fixed by GAP")
 
         invariant_form = normalize_args_invariant_form(ring, degree, invariant_form)

src/sage/groups/matrix_gps/unitary.py

@@ -50,7 +50,7 @@
 # ****************************************************************************
 
 from sage.rings.finite_rings.finite_field_constructor import GF
-from sage.rings.finite_rings.finite_field_base import is_FiniteField
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.misc.latex import latex
 from sage.misc.cachefunc import cached_method
 from sage.groups.matrix_gps.named_group import (
@@ -77,7 +77,7 @@ def finite_field_sqrt(ring):
         sage: finite_field_sqrt(GF(4, 'a'))
         2
     """
-    if not is_FiniteField(ring):
+    if not isinstance(ring, FiniteField):
         raise ValueError('not a finite field')
     q, rem = ring.cardinality().sqrtrem()
     if rem:
@@ -107,7 +107,7 @@ def _UG(n, R, special, var='a', invariant_form=None):
         latex_prefix ='S'
 
     degree, ring = normalize_args_vectorspace(n, R, var=var)
-    if is_FiniteField(ring):
+    if isinstance(ring, FiniteField):
         q = ring.cardinality()
         ring = GF(q**2, name=var)
         if invariant_form is not None:
@@ -134,7 +134,7 @@ def _UG(n, R, special, var='a', invariant_form=None):
         name = '{0} Unitary Group of degree {1} over {2}'.format(prefix, degree, ring)
         ltx  = r'\text{{{0}U}}_{{{1}}}({2})'.format(latex_prefix, degree, latex(ring))
 
-    if is_FiniteField(ring):
+    if isinstance(ring, FiniteField):
         cmd = '{0}U({1}, {2})'.format(latex_prefix, degree, q)
         return UnitaryMatrixGroup_gap(degree, ring, special, name, ltx, cmd)
     else:

src/sage/interfaces/gap.py

@@ -1753,7 +1753,7 @@ def intmod_gap_to_sage(x):
         sage: b.parent()
         Ring of integers modulo 65537
     """
-    from sage.rings.finite_rings.all import FiniteField
+    from sage.rings.finite_rings.finite_field_constructor import FiniteField
     from sage.rings.finite_rings.integer_mod import Mod
     from sage.rings.integer import Integer
     s = str(x)

src/sage/matrix/matrix_space.py

@@ -43,7 +43,7 @@
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
 import sage.rings.integer as integer
-import sage.rings.finite_rings.finite_field_constructor
+from sage.rings.finite_rings.finite_field_base import FiniteField
 import sage.misc.latex as latex
 import sage.modules.free_module
 
@@ -223,7 +223,7 @@ def get_matrix_class(R, nrows, ncols, sparse, implementation):
                     else:
                         return matrix_complex_double_dense.Matrix_complex_double_dense
 
-            elif sage.rings.finite_rings.finite_field_constructor.is_FiniteField(R):
+            elif isinstance(R, FiniteField):
                 if R.order() == 2:
                     try:
                         from . import matrix_mod2_dense

src/sage/modules/free_module.py

@@ -183,7 +183,6 @@
 import sage.misc.latex as latex
 
 from sage.modules.module import Module
-import sage.rings.finite_rings.finite_field_constructor as finite_field
 import sage.rings.ring as ring
 import sage.rings.abc
 import sage.rings.integer_ring
@@ -195,6 +194,7 @@
 from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
 from sage.misc.lazy_attribute import lazy_attribute
 from sage.misc.randstate import current_randstate
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.structure.factory import UniqueFactory
 from sage.structure.sequence import Sequence
 from sage.structure.richcmp import (richcmp_method, rich_to_bool, richcmp,
@@ -6348,7 +6348,7 @@ def _element_constructor_(self, e, *args, **kwds):
         """
         try:
             k = e.parent()
-            if finite_field.is_FiniteField(k) and k.base_ring() == self.base_ring() and k.degree() == self.degree():
+            if isinstance(k, FiniteField) and k.base_ring() == self.base_ring() and k.degree() == self.degree():
                 return self(e._vector_())
         except AttributeError:
             pass