#4738: base_ring of orders in relative number fields is wrong and finding
maximal_orders of relative number fields is very slow
---------------------------------------------------+------------------------
Reporter: ncalexan | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.2.2
Component: number theory | Resolution:
Keywords: base ring relative number field order |
---------------------------------------------------+------------------------
Changes (by ncalexan):
* summary: base_ring of orders in relative number fields is wrong =>
base_ring of orders in relative number fields
is wrong and finding maximal_orders of relative
number fields is very slow
Comment:
While trying to fix this, I discovered that finding orders in relative
number fields is ridiculously slow. I think pari probably will help here,
either but computing it directly or by computing a basis for the absolute
order and then constructing a basis for the relative order from it.
{{{
sage: K.<a,b> = NumberField([x^4 + 1, x^4 - 3])
sage: K.base_field().maximal_order()
Maximal Order in Number Field in b with defining polynomial x^4 - 3
sage: K.absolute_field('c').maximal_order()
Maximal Order in Number Field in c with defining polynomial x^16 - 8*x^12
+ 432*x^8 + 640*x^4 + 256
sage: K.absolute_field('c').maximal_order().basis()
[3/512*c^14 + 3/352*c^12 + 3/128*c^10 + 3/704*c^8 + 1/32*c^6 + 15/176*c^4
+ 1/44, 7/1024*c^15 + 1/512*c^14 + 3/704*c^13 + 1/256*c^12 + 3/256*c^11 +
1/128*c^10 + 3/1408*c^9 + 3/64*c^8 + 1/64*c^7 + 1/32*c^6 + 15/352*c^5 +
1/16*c^4 + 1/88*c, 35/5632*c^14 + 3/256*c^12 + 7/704*c^10 + 3/64*c^8 +
1/88*c^6 + 1/16*c^4 + 1/88*c^2, 79/11264*c^15 + 3/512*c^14 + 7/512*c^13 +
1/128*c^12 + 7/1408*c^11 + 1/128*c^10 + 3/128*c^9 + 1/32*c^8 + 1/176*c^7 +
1/32*c^6 + 1/32*c^5 + 1/176*c^3, 1/128*c^12 + 1/32*c^8 + 1/8*c^4,
1/256*c^15 + 3/256*c^13 + 1/64*c^9 + 1/16*c^5, 1/256*c^14 + 1/64*c^10 +
1/16*c^6, 1/512*c^15 + 1/128*c^13 + 1/128*c^11 + 1/32*c^7, 1/16*c^8,
1/256*c^15 + 1/32*c^9, 1/32*c^10, 1/256*c^15 + 1/128*c^13 + 1/64*c^11,
1/64*c^12, 1/64*c^13, 1/128*c^14, 1/128*c^15]
sage: K.maximal_order()
C-c
C-c---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call
last)
/Users/ncalexan/.sage/temp/pv139196.reshsg.uci.edu/47346/_Users_ncalexan__sage_init_sage_0.py
in <module>()
----> 1
2
3
4
5
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/number_field/number_field.pyc in maximal_order(self)
4894 O = K.maximal_order()
4895 B = [from_K(z) for z in O.basis()]
-> 4896 OK = self.order(B, check_is_integral=False,
check_rank=False)
4897 self.__maximal_order = OK
4898 return OK
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/number_field/number_field.pyc in order(self, *gens,
**kwds)
5630 gens = gens[0]
5631 gens = [self(x) for x in gens]
-> 5632 return order.relative_order_from_ring_generators(gens,
**kwds)
5633
5634
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/number_field/order.pyc in
relative_order_from_ring_generators(gens, check_is_integral, check_rank,
is_maximal, allow_subfield)
1640 module_gens = [to_Kabs(a) for a in gens]
1641 n = [a.absolute_minpoly().degree() for a in gens]
-> 1642 absolute_order_module_gens = monomials(module_gens, n)
1643
1644 abs_order =
absolute_order_from_module_generators(absolute_order_module_gens,
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in monomials(v, n)
52 v = Sequence(v)
53 R = v.universe()
---> 54 return _monomials(v, R, n, 0)
55
56
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in _monomials(gens, R, n, i)
15 nn = list(n)
16 del nn[i]
---> 17 v = monomials(w, nn)
18 k = len(v)
19 for _ in range(n[i]-1):
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in monomials(v, n)
52 v = Sequence(v)
53 R = v.universe()
---> 54 return _monomials(v, R, n, 0)
55
56
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in _monomials(gens, R, n, i)
15 nn = list(n)
16 del nn[i]
---> 17 v = monomials(w, nn)
18 k = len(v)
19 for _ in range(n[i]-1):
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in monomials(v, n)
52 v = Sequence(v)
53 R = v.universe()
---> 54 return _monomials(v, R, n, 0)
55
56
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in _monomials(gens, R, n, i)
15 nn = list(n)
16 del nn[i]
---> 17 v = monomials(w, nn)
18 k = len(v)
19 for _ in range(n[i]-1):
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in monomials(v, n)
52 v = Sequence(v)
53 R = v.universe()
---> 54 return _monomials(v, R, n, 0)
55
56
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in _monomials(gens, R, n, i)
15 nn = list(n)
16 del nn[i]
---> 17 v = monomials(w, nn)
18 k = len(v)
19 for _ in range(n[i]-1):
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in monomials(v, n)
52 v = Sequence(v)
53 R = v.universe()
---> 54 return _monomials(v, R, n, 0)
55
56
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in _monomials(gens, R, n, i)
15 nn = list(n)
16 del nn[i]
---> 17 v = monomials(w, nn)
18 k = len(v)
19 for _ in range(n[i]-1):
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in monomials(v, n)
52 v = Sequence(v)
53 R = v.universe()
---> 54 return _monomials(v, R, n, 0)
55
56
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in _monomials(gens, R, n, i)
15 nn = list(n)
16 del nn[i]
---> 17 v = monomials(w, nn)
18 k = len(v)
19 for _ in range(n[i]-1):
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in monomials(v, n)
52 v = Sequence(v)
53 R = v.universe()
---> 54 return _monomials(v, R, n, 0)
55
56
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in _monomials(gens, R, n, i)
15 nn = list(n)
16 del nn[i]
---> 17 v = monomials(w, nn)
18 k = len(v)
19 for _ in range(n[i]-1):
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in monomials(v, n)
52 v = Sequence(v)
53 R = v.universe()
---> 54 return _monomials(v, R, n, 0)
55
56
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in _monomials(gens, R, n, i)
15 nn = list(n)
16 del nn[i]
---> 17 v = monomials(w, nn)
18 k = len(v)
19 for _ in range(n[i]-1):
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in monomials(v, n)
52 v = Sequence(v)
53 R = v.universe()
---> 54 return _monomials(v, R, n, 0)
55
56
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in _monomials(gens, R, n, i)
15 nn = list(n)
16 del nn[i]
---> 17 v = monomials(w, nn)
18 k = len(v)
19 for _ in range(n[i]-1):
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in monomials(v, n)
52 v = Sequence(v)
53 R = v.universe()
---> 54 return _monomials(v, R, n, 0)
55
56
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in _monomials(gens, R, n, i)
15 nn = list(n)
16 del nn[i]
---> 17 v = monomials(w, nn)
18 k = len(v)
19 for _ in range(n[i]-1):
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in monomials(v, n)
52 v = Sequence(v)
53 R = v.universe()
---> 54 return _monomials(v, R, n, 0)
55
56
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in _monomials(gens, R, n, i)
15 nn = list(n)
16 del nn[i]
---> 17 v = monomials(w, nn)
18 k = len(v)
19 for _ in range(n[i]-1):
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in monomials(v, n)
52 v = Sequence(v)
53 R = v.universe()
---> 54 return _monomials(v, R, n, 0)
55
56
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/monomials.pyc in _monomials(gens, R, n, i)
19 for _ in range(n[i]-1):
20 for j in range(k):
---> 21 v.append(v[j]*z)
22 z *= gens[i]
23 return v
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/interfaces/get_sigs.pyc in my_sigint(x, n)
7
8 def my_sigint(x, n):
----> 9 raise KeyboardInterrupt
10
11 def my_sigfpe(x, n):
KeyboardInterrupt:
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4738#comment:2>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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