Changeset 7373:5d9964f18f97

Timestamp:

11/19/07 14:31:44 (6 years ago)

Author:

mabshoff@…

Branch:

default

Tags:

2.8.13.alpha1

Message:

patch by Nick Alexander: fix a bug in multipolynomial ideals and makes generic ideals more robust (see #805)

Location:

sage

Files:

• rings/ideal.py (modified) (2 diffs)
• rings/polynomial/multi_polynomial_libsingular.pyx (modified) (1 diff)
• structure/element.pyx (modified) (1 diff)

sage/rings/ideal.py

@@ -187 +187 @@
 
     def __nonzero__(self):
-        return self.gens() != [self.ring()(0)]
+        r"""Return True if this ideal is not (0).
+
+        TESTS:
+
+            sage: I = ZZ.ideal(5)
+            sage: bool(I)
+            True
+
+            sage: I = ZZ['x'].ideal(0)
+            sage: bool(I)
+            False
+
+            sage: I = ZZ['x'].ideal(ZZ['x'].gen()^2)
+            sage: bool(I)
+            True
+
+            sage: I = QQ['x', 'y'].ideal(0)
+            sage: bool(I)
+            False
+        """
+        for g in self.gens():
+            if not g.is_zero():
+                return True
+        return False
 
     def base_ring(self):
@@ -260 +283 @@
         
     def is_trivial(self):
+        r"""Return True if this ideal is (0) or (1).
+
+        TESTS:
+
+            sage: I = ZZ.ideal(5)
+            sage: I.is_trivial()
+            False
+
+            sage: I = ZZ['x'].ideal(-1)
+            sage: I.is_trivial()
+            True
+
+            sage: I = ZZ['x'].ideal(ZZ['x'].gen()^2)
+            sage: I.is_trivial()
+            False
+
+            sage: I = QQ['x', 'y'].ideal(-5)
+            sage: I.is_trivial()
+            True
+
+            sage: I = CC['x'].ideal(0)
+            sage: I.is_trivial()
+            True
+        """
         if self.is_zero():
             return True
-        elif self.is_principal():
-            return self.gen().is_unit()
+        # If self is principal, can give a complete answer
+        if self.is_principal():
+            return self.gens()[0].is_unit()
+        # If self is not principal, can only give an affirmative answer
+        for g in self.gens():
+            if g.is_unit():
+                return True
         raise NotImplementedError
 

sage/rings/polynomial/multi_polynomial_libsingular.pyx

@@ -663 +663 @@
 
         """
+        coerce = kwds.get('coerce', True)
         if len(gens) == 1:
             gens = gens[0]

sage/structure/element.pyx

@@ -1140 +1140 @@
     def __nonzero__(self):
         return True
-    def nonzero(self):
-        return True
-    def is_zero(self):
-        return False
 
 def is_AdditiveGroupElement(x):