On 4/3/07, Martin Albrecht <[EMAIL PROTECTED]> wrote:
> On Monday 02 April 2007 22:53, Kate Minola wrote:
> > Would a kind person explain to me why element 1 and element 2
> > are not equal? And what I need to do to test if element 1 is zero
> > in K?
It's a bug.
> > # setup
> > f = conway_polynomial(2,63)
> > K.<a> = GF(2**63, name='a', modulus=f)
> > n = f.degree()
> > m = 3;
> > e = (2^n - 1) / (2^m - 1)
> > c = a^e
> > conway = conway_polynomial(2,m)
> >
> > # element 1
> > print conway(c) # says 0
> > print type(c)
> > print parent(c)
> > print c in K # says True
> >
> > # element 2
> > print K(0) # says 0
> > print type(K(0))
> > print parent(K(0))
> >
> > print conway(c) == K(0) # says False???
>
> This seems to be a bug in the pari.gen.gen class:
>
> sage: e1 = conway(c)
> sage: e2 = K(0)
>
> When compare is called on them, their pari values are compared, these differ
> in their representation.
>
> sage: e1._FiniteField_ext_pariElement__value
> 0
>
> sage: e2._FiniteField_ext_pariElement__value
>
> Mod(Mod(0, 2), Mod(1, 2)*a^63 + Mod(1, 2)*a^24 + Mod(1, 2)*a^23 + Mod(1,
> 2)*a^22 + Mod(1, 2)*a^17 + Mod(1, 2)*a^16 + Mod(1, 2)*a^15 + Mod(1, 2)*a^11 +
> Mod(1, 2)*a^9 + Mod(1, 2)*a^8 + Mod(1, 2)*a^4 + Mod(1, 2)*a^3 + Mod(1, 2)*a^2
> + Mod(1, 2)*a + Mod(1, 2))
>
> Their comparison fails as follows:
>
> e2._FiniteField_ext_pariElement__value._cmp(e1._FiniteField_ext_pariElement__value
> )
> ---------------------------------------------------------------------------
> <class 'gen.PariError'> Traceback (most recent call last)
>
> /home/malb/<ipython console> in <module>()
>
> /home/malb/gen.pyx in gen._pari_trap()
>
> <class 'gen.PariError'>: incorrect type (20)
>
> I openend a ticket on Trac for this.
I've attached a fix. Could you close your trac ticket, since this fix will
be in sage-2.8.1.
William
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# HG changeset patch
# User William Stein <[EMAIL PROTECTED]>
# Date 1187051524 25200
# Node ID c39ca352e774bc61d46e93c63ef159b87cb74b65
# Parent 22fee559b081bc246faa8de71cb08fa0f7d37cdd
Fix a bug in large finite field arithmetic (construction of 0 element wrong in some cases). Also (very slightly!) optimized some arithmetic in finite fields.
diff -r 22fee559b081 -r c39ca352e774 sage/rings/finite_field_element.py
--- a/sage/rings/finite_field_element.py Sun Aug 12 18:14:42 2007 -0700
+++ b/sage/rings/finite_field_element.py Mon Aug 13 17:32:04 2007 -0700
@@ -7,6 +7,18 @@ EXAMPLES:
sage: w = V([0,1,2])
sage: K(1)*w
(0, 1, 0)
+
+We do some arithmetic involving a bigger field and a Conway polynomial,
+i.e., we verify compatibility condition.
+ sage: f = conway_polynomial(2,63)
+ sage: K.<a> = GF(2**63, name='a', modulus=f)
+ sage: n = f.degree()
+ sage: m = 3;
+ sage: e = (2^n - 1) / (2^m - 1)
+ sage: c = a^e
+ sage: conway = conway_polynomial(2,m)
+ sage: conway(c) == 0
+ True
"""
@@ -59,7 +71,7 @@ class FiniteField_ext_pariElement(Finite
sage: loads(a.dumps()) == a
True
"""
- def __init__(self, parent, value):
+ def __init__(self, parent, value, check=True):
"""
Create element of a finite field.
@@ -75,15 +87,33 @@ class FiniteField_ext_pariElement(Finite
self.__parent = parent
if isinstance(value, str):
raise TypeError, "value must not be a string"
+ if not check:
+ if not value: # see comment below about this workaround
+ self.__value = pari(0).Mod(parent._pari_modulus())*parent._pari_one()
+ else:
+ self.__value = value
+ return
try:
if isinstance(value, pari_gen):
- if value.type()[-3:] == "MOD" :
- self.__value = value
- else:
- try:
+ try:
+ # In some cases we get two different versions of
+ # the 0 element of a finite field. This has to do
+ # with how PARI's Mod function works -- it treats
+ # 0 differently. In particular, if value is a a
+ # pari t_POLMOD that is 0, modding it simply
+ # doesn't work correctly. We fix this by changing
+ # the value in the 0 case to the standard pari 0,
+ # which works correctly. Note -- probably all
+ # this code should be replaced by much faster
+ # finite field arithmetic programmed against NTL.
+ if not value:
+ value = pari(0)
+ if value.type() == "t_POLMOD":
+ self.__value = value * parent._pari_one()
+ else:
self.__value = value.Mod(parent._pari_modulus())*parent._pari_one()
- except RuntimeError:
- raise TypeError, "no possible coercion implemented"
+ except RuntimeError:
+ raise TypeError, "no possible coercion implemented"
return
elif isinstance(value, FiniteField_ext_pariElement):
if parent != value.parent():
@@ -271,7 +301,7 @@ class FiniteField_ext_pariElement(Finite
sage: a is a
True
"""
- return FiniteField_ext_pariElement(self.__parent, self.__value)
+ return FiniteField_ext_pariElement(self.__parent, self.__value, check=False)
def _pari_(self, var=None):
"""
@@ -489,18 +519,18 @@ class FiniteField_ext_pariElement(Finite
raise TypeError, "Parents of finite field elements must be equal."
def _add_(self, right):
- return FiniteField_ext_pariElement(self.__parent, self.__value + right.__value)
+ return FiniteField_ext_pariElement(self.__parent, self.__value + right.__value, check=False)
def _sub_(self, right):
- return FiniteField_ext_pariElement(self.__parent, self.__value - right.__value)
+ return FiniteField_ext_pariElement(self.__parent, self.__value - right.__value, check=False)
def _mul_(self, right):
- return FiniteField_ext_pariElement(self.__parent, self.__value * right.__value)
+ return FiniteField_ext_pariElement(self.__parent, self.__value * right.__value, check=False)
def _div_(self, right):
if right.__value == 0:
raise ZeroDivisionError
- return FiniteField_ext_pariElement(self.__parent, self.__value / right.__value)
+ return FiniteField_ext_pariElement(self.__parent, self.__value / right.__value, check=False)
def __int__(self):
try:
@@ -531,10 +561,10 @@ class FiniteField_ext_pariElement(Finite
# right = int(_right)
# if right != _right:
# raise ValueError
- # return FiniteField_ext_pariElement(self.__parent, self.__value**right)
+ # return FiniteField_ext_pariElement(self.__parent, self.__value**right, check=False)
def __neg__(self):
- return FiniteField_ext_pariElement(self.__parent, -self.__value)
+ return FiniteField_ext_pariElement(self.__parent, -self.__value, check=False)
def __pos__(self):
return self
@@ -555,7 +585,7 @@ class FiniteField_ext_pariElement(Finite
if self.__value == 0:
raise ZeroDivisionError, "Cannot invert 0"
- return FiniteField_ext_pariElement(self.__parent, ~self.__value)
+ return FiniteField_ext_pariElement(self.__parent, ~self.__value, check=False)
def lift(self):
"""
