Changeset 7456:f60ec7365b2b

Timestamp:

12/01/07 10:48:42 (6 years ago)

Author:

mabshoff@…

Branch:

default

Parents:

7454:0cb746e1a4bd (diff), 7455:3eda63e6eb1a (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent.

Message:

merge

Files:

• sage/rings/arith.py (modified) (3 diffs)
• sage/rings/arith.py (modified) (5 diffs)

sage/rings/arith.py

@@ -385 +385 @@
 def valuation(m, p):
     """
-    The exact power of p>0 that divides the integer m.
-    We do not require that p be prime, and if m is 0,
-    then this function returns rings.infinity.
-    
-    EXAMPLES::
-
+    The exact power of p that divides m.
+    
+    m should be an integer or rational (but maybe other types
+    work too.)
+
+    This actually just calls the m.valuation() method.
+
+    If m is 0, this function returns rings.infinity.
+
+    EXAMPLES:
         sage: valuation(512,2)
         9
         sage: valuation(1,2)
         0
-
-    Valuation of 0 is defined, but valuation with respect to 0 is not::
-
+        sage: valuation(5/9, 3)
+        -2
+
+    Valuation of 0 is defined, but valuation with respect to 0 is not:
         sage: valuation(0,7)
         +Infinity
@@ -403 +408 @@
         Traceback (most recent call last):
         ...
-        ValueError: valuation at 0 not defined
-
-    Here are some other example::
-    
+        ValueError: You can only compute the valuation with respect to a integer larger than 1.
+
+    Here are some other examples:
         sage: valuation(100,10)
         2
@@ -418 +422 @@
         1
     """
-    if p <= 0:
-        raise ValueError, "valuation at 0 not defined"
-    if m == 0:
-        import sage.rings.all
-        return sage.rings.all.infinity
-    r=0
-    power=p
-    while m%power==0:
-        r += 1
-        power *= p
-    return r
+    return m.valuation(p)
 
 

sage/rings/arith.py

@@ -281 +281 @@
     r"""
     Returns True if $x$ is prime, and False otherwise.  The result
-    is proven correct -- {\em this is NOT a pseudo-primality test!}.
+    is proven correct -- \emph{this is NOT a pseudo-primality test!}.
     
     INPUT:
@@ -317 +317 @@
     r"""
     Returns True if $x$ is a pseudo-prime, and False otherwise.  The result
-    is \em{NOT} proven correct -- {\em this is a pseudo-primality test!}.
+    is \emph{NOT} proven correct -- \emph{this is a pseudo-primality test!}.
     
     INPUT:
@@ -353 +353 @@
     r"""
     Returns True if $x$ is a prime power, and False otherwise.
-    The result is proven correct -- {\em this is NOT a
+    The result is proven correct -- \emph{this is NOT a
     pseudo-primality test!}.
 
@@ -1524 +1524 @@
         The qsieve and ecm commands give access to highly optimized
         implementations of algorithms for doing certain integer
-        factorization problems.  These implementation are not used by
+        factorization problems.  These implementations are not used by
         the generic factor command, which currently just calls PARI
         (note that PARI also implements sieve and ecm algorithms, but
@@ -2386 +2386 @@
         [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1]
         sage: continued_fraction_list(sqrt(4/19))
-        [0, 2, 5, 1, 1, 2, 1, 16, 1, 2, 1, 1, 5, 4, 5, 1, 1, 2, 1, 18]
+        [0, 2, 5, 1, 1, 2, 1, 16, 1, 2, 1, 1, 5, 4, 5, 1, 1, 2, 1, 15, 2]
         sage: continued_fraction_list(RR(pi), partial_convergents=True)
         ([3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 3],