Hi there,
I often come across the situation where I have to construct an integer from
its binary representation and vice versa. So far you do it in SAGE using
strings. I have attached a preliminary patch which allows the following code
to work, i.e. I _replaced_ the binary() method (which returned a string) with
a method that returns a tuple of Python ints.
sage: e = ZZ(10231252).binary(); e
(1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0)
sage: ZZ(e,2)
10231252
I know that this patch has some issues:
* it breaks doctests which rely on strings (fix by replace ZZ.binary() with
ZZ.str(2))
* it returns a tuple of Python ints should return tuple (?) of GF(2) elements
but I didn't want to mess with imports yet
* it can be done faster
* you loose the minus sign: ZZ(-1).binary() is (1,), shall it raise an
exception then?
I am not out for micromanagement but I hesitate to just submit a polished
patch as the Integers are such a central building block of SAGE. So, does
anybody actually like the current behavior of ZZ.binary() which returns a
(signed) string? Any other objections against making the above work?
Martin
--
name: Martin Albrecht
_pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99
_www: http://www.informatik.uni-bremen.de/~malb
_jab: [EMAIL PROTECTED]
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diff -r 813dee35adb8 sage/rings/integer.pyx
--- a/sage/rings/integer.pyx Thu Jun 28 12:53:41 2007 +0200
+++ b/sage/rings/integer.pyx Thu Jun 28 22:53:10 2007 +0200
@@ -265,6 +265,12 @@ cdef class Integer(sage.structure.elemen
# then how do we make Pyrex handle the reference counting?
set_from_Integer(self, (<object> PyObject_GetAttrString(x, "_integer_"))())
+ elif base == 2 and (PY_TYPE_CHECK(x,list) or PY_TYPE_CHECK(x,tuple)):
+ # we are lazy
+ s = "".join([str(e%2) for e in x])
+ if mpz_set_str(self.value, s, 2) != 0:
+ raise TypeError, "Unable to convert bit list to an Integer."
+
else:
raise TypeError, "unable to coerce element to an integer"
@@ -456,19 +462,33 @@ cdef class Integer(sage.structure.elemen
"""
return self.str(16)
+## def binary(self):
+## """
+## Return the binary digits of self as a string.
+
+## EXAMPLES:
+## sage: print Integer(15).binary()
+## 1111
+## sage: print Integer(16).binary()
+## 10000
+## sage: print Integer(16938402384092843092843098243).binary()
+## 1101101011101100011110001110010010100111010001101010001111111000101000000000101111000010000011
+## """
+## return self.str(2)
+
def binary(self):
"""
- Return the binary digits of self as a string.
-
- EXAMPLES:
- sage: print Integer(15).binary()
- 1111
- sage: print Integer(16).binary()
- 10000
- sage: print Integer(16938402384092843092843098243).binary()
- 1101101011101100011110001110010010100111010001101010001111111000101000000000101111000010000011
- """
- return self.str(2)
+ Return the binary digits of self as a tuple in big endian
+ ordering.
+ """
+ cdef long i
+ cdef size_t s = mpz_sizeinbase(self.value, 2)
+ l = [0]*s
+ for i from 0<= i < s:
+ if mpz_tstbit(self.value,i):
+ l[s-i-1] = 1
+ return tuple(l)
+
def set_si(self, signed long int n):
"""
