Changeset 7492:22c24fe79fcf

Timestamp:

12/01/07 22:11:13 (5 years ago)

Author:

David Roe <roed@…>

Branch:

default

Message:

Added algebraic closure construction functor.

Location:

sage

Files:

• categories/pushout.py (modified) (2 diffs)
• rings/complex_double.pyx (modified) (2 diffs)
• rings/complex_field.py (modified) (2 diffs)
• rings/real_double.pyx (modified) (1 diff)
• rings/real_mpfr.pyx (modified) (1 diff)

sage/categories/pushout.py

@@ -40 +40 @@
         return False
         
-class CompositConstructionFunctor(ConstructionFunctor):
+class CompositeConstructionFunctor(ConstructionFunctor):
     def __init__(self, first, second):
         Functor.__init__(self, first.domain(), second.codomain())
@@ -254 +254 @@
             c = cmp(self.poly, other.poly)
         return c
+
+class AlgebraicClosureFunctor(ConstructionFunctor):
+    def __init__(self):
+        Functor.__init__(self, Rings(), Rings())
+        self.rank = 3
+    def __call__(self, R):
+        return R.algebraic_closure()
+    def merge(self, other):
+        # Algebraic Closure subsumes Algebraic Extension
+        return self
         
 def BlackBoxConstructionFunctor(ConstructionFunctor):

sage/rings/complex_double.pyx

@@ -277 +277 @@
             sage: parent(a)
             Symbolic Ring
+
+        sage: CDF(1) + RR(1)
+        2.0
         """
         return self._coerce_try(x, [self.real_double_field(),
@@ -339 +342 @@
         """
         return self(3.1415926535897932384626433832)
-    
+
+    def construction(self):
+        """
+        Returns the functorial construction of self, namely,
+        algebraic closure of the real double field.
+        
+        EXAMPLES: 
+            sage: c, S = CDF.construction(); S
+            Real Double Field
+            sage: CDF == c(S)
+            True
+        """
+        from sage.categories.pushout import AlgebraicClosureFunctor
+        return (AlgebraicClosureFunctor(), self.real_double_field())
 
 def new_ComplexDoubleElement():

sage/rings/complex_field.py

@@ -213 +213 @@
            * this MPFR complex field, or any other of higher precision
            * anything that canonically coerces to the mpfr real field with this prec
+
+        EXAMPLES:
+        sage: ComplexField(200)(1) + RealField(90)(1)
+        2.0000000000000000000000000
         """
         try:
@@ -258 +262 @@
         """
         return False
+
+    def construction(self):
+        """
+        Returns the functorial construction of self, namely,
+        algebraic closure of the real field with the same precision.
+        
+        EXAMPLES: 
+            sage: c, S = CC.construction(); S
+            Real Field with 53 bits of precision
+            sage: CC == c(S)
+            True
+        """
+        from sage.categories.pushout import AlgebraicClosureFunctor
+        return (AlgebraicClosureFunctor(), self._real_field())
+
 
     def pi(self):

sage/rings/real_double.pyx

@@ -145 +145 @@
                                   {'type': 'RDF'}),
                sage.rings.rational_field.QQ)
+
+    def algebraic_closure(self):
+        """
+        Returns the algebraic closure of self,
+        ie, the complex double field.
+
+        EXAMPLES:
+        sage: RDF.algebraic_closure()
+        Complex Double Field
+        """
+        from sage.rings.complex_double import CDF
+        return CDF
 
     cdef coerce_map_from_c(self, S):

sage/rings/real_mpfr.pyx

@@ -348 +348 @@
         """
         return sage.rings.complex_field.ComplexField(self.prec())
+
+    def algebraic_closure(self):
+        """
+        Returns the algebraic closure of self, ie the
+        complex field with the same precision.
+        """
+        return self.complex_field()
 
     def ngens(self):