Changeset 7454:0cb746e1a4bd

Timestamp:

11/19/07 21:47:51 (6 years ago)

Author:

Mike Hansen <mhansen@…>

Branch:

default

Message:

Fixed #1214

Location:

sage

Files:

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

sage/rings/ideal.py

@@ -365 +365 @@
     
     def __contains__(self, x):
+        """
+        Returns True if x is in the ideal self.
+
+        EXAMPLES:
+            sage: P.<x> = PolynomialRing(ZZ)
+            sage: I = P.ideal(x^2-2)
+            sage: x^2 in I
+            False
+            sage: x^2-2 in I
+            True
+            sage: x^2-3 in I
+            False
+        """
         if self.gen().is_zero():
             return x.is_zero()
@@ -391 +404 @@
         """
         Returns True if self divides other.
+
+        EXAMPLES:
+            sage: P.<x> = PolynomialRing(QQ)
+            sage: I = P.ideal(x)
+            sage: J = P.ideal(x^2)
+            sage: I.divides(J)
+            True
+            sage: J.divides(I)
+            False
         """
         if isinstance(other, Ideal_principal):

sage/structure/element.pyx

@@ -1617 +1617 @@
         """
         raise NotImplementedError
+
+    def divides(self, x):
+        """
+        Return True if self divides x.
+
+        EXAMPLES:
+            sage: P.<x> = PolynomialRing(QQ)
+            sage: x.divides(x^2)
+            True
+            sage: x.divides(x^2+2)
+            False
+            sage: (x^2+2).divides(x)
+            False
+            sage: P.<x> = PolynomialRing(ZZ)
+            sage: x.divides(x^2)
+            True
+            sage: x.divides(x^2+2)
+            False
+            sage: (x^2+2).divides(x)
+            False
+        """
+        return (x % self) == 0
     
     def mod(self, I):