#14240: Universal cyclotomic field breaks for moderate order
-----------------------------+----------------------------------------------
Reporter: mraum | Owner: davidloeffler
Type: defect | Status: new
Priority: major | Milestone: sage-5.9
Component: number fields | Keywords: ucf, overflow
Work issues: | Report Upstream: N/A
Reviewers: | Authors:
Merged in: | Dependencies:
Stopgaps: |
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UniversalCyclotomicField seeming is unable to handle moderate orders -
even though I don't see how an overflow could occur when multiplying
elements of order 245. Here is how I found the problem
{{{
UCF.<E> = UniversalCyclotomicField()
K.<rho> = CyclotomicField(245)
h = K.random_element()
h_rho = rho.coordinates_in_terms_of_powers()(h)
h_ucf = sum( c * E(245, i) for (i, c) in enumerate(h_rho) )
h_ucf**2
}}}
The last line gives an OverflowError:
{{{
/home/martin/workspace/sage57/local/lib/python2.7/site-
packages/sage/rings/universal_cyclotomic_field/universal_cyclotomic_field.pyc
in __pow__(self, k)
1506 else:
1507 if k % 2 == 0:
-> 1508 return (self*self).__pow__(k/2)
1509 else:
1510 return self * self.__pow__(k-1)
/home/martin/workspace/sage57/local/lib/python2.7/site-
packages/sage/structure/element.so in
sage.structure.element.RingElement.__mul__
(sage/structure/element.c:14096)()
/home/martin/workspace/sage57/local/lib/python2.7/site-
packages/sage/structure/element.so in
sage.structure.element.RingElement._mul_
(sage/structure/element.c:14222)()
/home/martin/workspace/sage57/local/lib/python2.7/site-
packages/sage/rings/universal_cyclotomic_field/universal_cyclotomic_field.pyc
in _mul_(self, other)
1578 n1,n2 = self.field_order(),other.field_order()
1579 n = LCM_list([n1,n2])
-> 1580 return
F._from_dict(push_down_cython(n,dict_multiplication(D_self, D_other, n1,
n2, n)), remove_zeros=False)
1581
1582 def _sub_(self, other):
/home/martin/workspace/sage57/local/lib/python2.7/site-
packages/sage/rings/universal_cyclotomic_field/universal_cyclotomic_field_c.so
in
sage.rings.universal_cyclotomic_field.universal_cyclotomic_field_c.dict_multiplication
(sage/rings/universal_cyclotomic_field/universal_cyclotomic_field_c.c:12372)()
/home/martin/workspace/sage57/local/lib/python2.7/site-
packages/sage/rings/universal_cyclotomic_field/universal_cyclotomic_field_c.so
in
sage.rings.universal_cyclotomic_field.universal_cyclotomic_field_c.dict_multiplication
(sage/rings/universal_cyclotomic_field/universal_cyclotomic_field_c.c:11381)()
OverflowError: value too large to convert to int
}}}
The element which I have used concretely (but I have tried several random
elements) is
{{{
-2339/36*E(245) + 1/2*E(245)^2 - 155/48*E(245)^3 + 4*E(245)^4 + 3*E(245)^6
+ 3/2*E(245)^8 - 9/2*E(245)^9 - 1/140*E(245)^11 + 1619/330*E(245)^12 +
E(245)^13 + 10*E(245)^16 - 97/12*E(245)^17 - 25/6*E(245)^18 +
17/4*E(245)^19 + 49/2*E(245)^22 - 35*E(245)^23 + 27/4*E(245)^24 +
74/13*E(245)^26 + 3*E(245)^27 + 2*E(245)^28 + 1/5*E(245)^29 - 2*E(245)^31
- 9/4*E(245)^32 + 1/2*E(245)^33 - 20*E(245)^36 - 23/8*E(245)^38 +
11/4*E(245)^41 + 8/3*E(245)^42 - 5/2*E(245)^43 - E(245)^46 + 5*E(245)^47 -
E(245)^48 + 1/2*E(245)^51 - 149/60*E(245)^52 - 35/6*E(245)^53 -
4/5*E(245)^56 - 6*E(245)^57 - 2*E(245)^58 + 21271/4466*E(245)^61 +
5*E(245)^62 + 5/2*E(245)^63 - 16/3*E(245)^66 + 5/6*E(245)^67 +
17/2*E(245)^68 - 5/2*E(245)^69 + 337/13*E(245)^71 - E(245)^72 -
3*E(245)^73 + 89/2*E(245)^74 + 2*E(245)^76 + 2*E(245)^77 + 25/2*E(245)^78
+ 11/2*E(245)^79 - 7/4*E(245)^81 + 29/6*E(245)^82 + 123/244*E(245)^84 -
4/3*E(245)^86 - 13/12*E(245)^87 + 79/20*E(245)^89 - 1/3*E(245)^91 -
5/2*E(245)^92 - 49/4*E(245)^94 + 14/3*E(245)^96 + 6/5*E(245)^97 -
64*E(245)^99 - 2*E(245)^101 + 1/3*E(245)^104 + 1/2*E(245)^106 -
3/2*E(245)^107 - 141/140*E(245)^109 + 6*E(245)^111 - 3/2*E(245)^114 -
19/6*E(245)^116 + 35/6*E(245)^117 - 3/2*E(245)^118 - 1/2*E(245)^119 -
37/12*E(245)^122 - 4*E(245)^123 - 3*E(245)^124 - 5/2*E(245)^126 -
4*E(245)^127 - 1/2*E(245)^128 - 13/4*E(245)^129 + 11/2*E(245)^131 +
5/2*E(245)^133 - 1/2*E(245)^134 - 1/2*E(245)^136 + 19/4*E(245)^138 +
1/2*E(245)^139 - 2*E(245)^141 - 5*E(245)^143 - 7/2*E(245)^144 + E(245)^146
- 129/2*E(245)^148 - 383/2*E(245)^149 + 37*E(245)^151 + 3/2*E(245)^153 -
1/85*E(245)^156 - 1541/140*E(245)^158 + 83/22*E(245)^159 + E(245)^163 -
481/92*E(245)^164 + 11/2*E(245)^166 + 15/34*E(245)^167 + 2*E(245)^168 +
27*E(245)^169 - 2*E(245)^171 - E(245)^172 + 6*E(245)^173 + E(245)^174 -
E(245)^176 + 4*E(245)^177 - 3*E(245)^178 - 11/4*E(245)^179 +
3/2*E(245)^182 - 5/2*E(245)^183 - 5/2*E(245)^184 + 61/12*E(245)^187 +
1/2*E(245)^188 - 1/3*E(245)^189 - 49/12*E(245)^192 - 5*E(245)^193 +
14/3*E(245)^194 - 66*E(245)^197 - 9/4*E(245)^199 + 3*E(245)^202 +
2*E(245)^203 + 3*E(245)^204 - 141/140*E(245)^207 + 105/22*E(245)^208 +
2*E(245)^209 + 2*E(245)^212 - 6*E(245)^213 - 13/6*E(245)^214 -
1/2*E(245)^216 + E(245)^217 + 53/2*E(245)^218 - 1/2*E(245)^219 +
19/3*E(245)^222 + E(245)^223 + 3*E(245)^226 - 25/12*E(245)^227 -
15/4*E(245)^228 + 9/2*E(245)^229 + 1/2*E(245)^231 - 4*E(245)^232 -
2*E(245)^233 - 9/4*E(245)^234 + 19/4*E(245)^236 + 5/2*E(245)^237 +
5/3*E(245)^238 - 4*E(245)^241 - 3*E(245)^242 + 17/3*E(245)^243 -
E(245)^244
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14240>
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