Updated to Python3. Works with Sage 9.0

src/sage/schemes/chow/finite_ring_extension.py

@@ -77,11 +77,11 @@
 # ****************************************************************************
 
 from sage.all import QQ
-from sage.matrix.constructor import matrix
+from sage.matrix.all import matrix
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.quotient_ring import QuotientRing_generic
 from sage.rings.polynomial.term_order import TermOrder
-from sage.libs.singular.function import singular_function, lib as singular_lib
+from sage.libs.singular.function_factory import singular_function, lib as singular_lib
 from sage.rings.polynomial.multi_polynomial_ring_generic import \
     is_MPolynomialRing
 

src/sage/schemes/chow/library/all.py

@@ -1,4 +1,4 @@
 
-from grass import Grass, GrassBundle
-from proj import Proj, ProjBundle
-from twisted_cubics import variety_of_nets_of_quadrics, incidence_variety, map_incidence_to_nets_of_quadrics
+from .grass import Grass, GrassBundle
+from .proj import Proj, ProjBundle
+from .twisted_cubics import variety_of_nets_of_quadrics, incidence_variety, map_incidence_to_nets_of_quadrics

src/sage/schemes/chow/morphism.py

@@ -492,7 +492,7 @@ def upperstar(self, v):
             sage: i.upperstar(Y.tangent_bundle())
             Bundle(X, 3, [1, 12*w])
         """
-        from sheaf import Sheaf, is_sheaf
+        from .sheaf import Sheaf, is_sheaf
         if is_sheaf(v):
             # Return a sheaf if the argument is a sheaf
             if not v.chowscheme() is self.codomain():
@@ -566,7 +566,7 @@ def lowerstar(self, v, normal_bundle=None, verbose=False):
             3
         """
         X, Y = self.domain(), self.codomain()
-        from sheaf import Sheaf, is_sheaf
+        from .sheaf import Sheaf, is_sheaf
         if is_sheaf(v):
             # Return a sheaf if the argument is a sheaf
             if not v.chowscheme() is self.domain():

src/sage/schemes/chow/ring.py

@@ -161,13 +161,12 @@
 
 from sage.all import QQ
 from sage.modules.all import vector
-from sage.matrix.constructor import matrix
+from sage.matrix.all import matrix
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.polynomial.term_order import TermOrder
 from sage.rings.quotient_ring import QuotientRing_generic
-from sage.rings.polynomial.multi_polynomial_ring_generic import \
-    is_MPolynomialRing
-from sage.libs.singular.function import singular_function, lib as singular_lib
+from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
+from sage.libs.singular.function_factory import singular_function, lib as singular_lib
 from sage.misc.cachefunc import cached_method
 from sage.rings.integer import is_Integer
 
@@ -343,10 +342,10 @@ def ChowRing(generators=None, degrees=None, relations=None,
     """
     # Construct a quotient ring by generators and relations.
     if generators:  # Not None neither []
-        if isinstance(generators, basestring):
+        if isinstance(generators, str):
             generators = [generators]
         for gen in generators:
-            if not isinstance(gen, basestring):
+            if not isinstance(gen, str):
                 raise TypeError("Expect list of strings for generators.")
         if is_Integer(degrees) or isinstance(degrees, int):
             degrees = [int(degrees)]
@@ -362,7 +361,7 @@ def ChowRing(generators=None, degrees=None, relations=None,
                            order=TermOrder('wdegrevlex', tuple(degrees)))
         I = R.ideal(0)
         if relations:
-            if isinstance(relations, basestring):
+            if isinstance(relations, str):
                 relations = [relations]
             if not all(isinstance(r, str) for r in relations):
                 raise TypeError("Expect list of strings as relations")
@@ -426,6 +425,12 @@ def __init__(self, R, I, names=None, name=None, latex_name=None):
         self._dimension = None
         self._point_class = None
 
+    def _cache_key(self):
+        return(self.parent(),str(self))
+
+    def __hash__(self):
+        return hash(type(self))
+
     def __eq__(self, other):
         """
         Two ChowRings are considered to be "equal" their dimensions are equal,
@@ -965,7 +970,7 @@ def max_degree(self):
         if self.krull_dimension() != 0:
             return 0
         # Compute max degree:
-        return max([x.lift().degree() for x in self.basis()])
+        return max([self(x).lift().degree() for x in self.basis()])
 
     @cached_method
     def basis_by_degree(self):
@@ -997,7 +1002,7 @@ def basis_by_degree(self):
             return [[1]]
         bbd = [[] for _ in range(self.max_degree() + 1)]
         for e in self.basis():
-            d = e.lift().degree()
+            d = self(e).lift().degree()
             bbd[d].append(e)
         return bbd
 
@@ -1043,7 +1048,6 @@ def intersection_matrix(self):
              for i in range(n) for j in range(n)]
         return matrix(QQ, n, n, m)
 
-    @cached_method
     def dual_basis_slow(self):
         """
         Returns the basis dual to self.basis() with respect to the intersection
@@ -1121,7 +1125,7 @@ def dual_basis(self, verbose=False):
         division = singular_function('division')
         #  We will compute the dictionary degree by degree.
         rbbd, maxdeg = self.basis_by_degree(), len(self.basis_by_degree())
-        for d in range(1 + maxdeg / 2):
+        for d in range(1 + maxdeg // 2):
             # Ring basis in degree d and complementary degree maxdeg - d - 1
             rbd, rbdc, n = rbbd[d], rbbd[maxdeg - d - 1], len(rbbd[d])
             if verbose:

src/sage/schemes/chow/ring_homset.py

@@ -89,7 +89,7 @@ def __call__(self, im_gens, check=True):
             if not im_gens:
                 phi = pi.domain().hom([], self.codomain())
             else:
-                if isinstance(im_gens, basestring):
+                if isinstance(im_gens, str):
                     im_gens = [im_gens]
                 im_gens = [self.codomain()(x) for x in im_gens]
                 phi = pi.domain().hom(im_gens, check=check)

src/sage/schemes/chow/scheme.py

@@ -284,7 +284,7 @@ def _latex_(self):
 
         TESTS::
 
-            sage: P1 = ChowScheme(1, 'h', 1, 'h^2', latex_name='\mathbb{P}^1')
+            sage: P1 = ChowScheme(1, 'h', 1, 'h^2', latex_name='\\mathbb{P}^1')
             sage: P1._latex_()
             '\\mathbb{P}^1'
 
@@ -293,6 +293,12 @@ def _latex_(self):
             return self._latex_name
         return self._repr_()
 
+    def _cache_key(self):
+        return(self.parent(),str(self))
+
+    def __hash__(self):
+        return hash(type(self))
+
     def __eq__(self, other):
         """
         Return True if the two ChowScheme are "equal", e.g. if their underlying
@@ -396,7 +402,7 @@ def __mul__(self, other):
             sage: B.betti_numbers()
             [1, 2, 4, 7, 8, 7, 4, 2, 1]
         """
-        from bundle import Bundle
+        from .bundle import Bundle
         dimension = self.dimension() + other.dimension()
         generators = self.variable_names() + other.variable_names()
         degrees = self.degs() + other.degs()
@@ -1168,7 +1174,7 @@ def o(self, n=0):
         if not isinstance(n, int):
             raise ValueError('Only integers allowed here.')
         if n == 0:
-            from bundle import Bundle
+            from .bundle import Bundle
             return Bundle(self, 1, [1])
 
         if 'o1' not in self.sheaves:

src/sage/schemes/chow/scheme_homset.py

@@ -61,7 +61,7 @@ def create_key_and_extra_args(self, X, Y, category=None,
         if not is_chowScheme(base):
             raise ValueError("Expect a ChowScheme as base")
         if not category:
-            from schemes import ChowSchemes
+            from .schemes import ChowSchemes
             category = ChowSchemes(base)
         key = tuple([id(X), id(Y), category])
         extra = {'X': X, 'Y': Y, 'base_chowscheme': base, 'check': check}

src/sage/schemes/chow/schemes.py

@@ -20,11 +20,9 @@
 
 from sage.categories.category import Category
 from sage.categories.category_types import Category_over_base
-from sage.categories.homsets import HomsetsCategory
 from sage.categories.sets_cat import Sets
 
 
-# noinspection PyAbstractClass
 class ChowSchemes(Category):
     r"""
     Construct a category of ChowSchemes.
@@ -33,7 +31,7 @@ class ChowSchemes(Category):
     @staticmethod
     def __classcall_private__(cls, X=None):
         if X is not None:
-            from scheme import is_chowScheme
+            from .scheme import is_chowScheme
             if not is_chowScheme(X):
                 X = ChowSchemes()(X)
             return ChowSchemes_over_base(X)
@@ -44,20 +42,16 @@ def super_categories(self):
         return [Sets()]
 
     def _call_(self, x):
-        from scheme import is_chowScheme
+        from .scheme import is_chowScheme
         if is_chowScheme(x):
             return x
-        from morphism import is_chowSchemeMorphism
+        from .morphism import is_chowSchemeMorphism
         if is_chowSchemeMorphism(x):
             return x
         else:
             m = "Can't create an object or morphism in %s from %s" % (self, x)
             raise TypeError(m)
 
-    # noinspection PyAbstractClass
-    class HomCategory(HomsetsCategory):
-        def extra_super_categories(self):
-            return []
 
 
 #############################################################