CoCalc Public Filessupport / quotient-ring.ipynb
Author: William A. Stein
Description: Jupyter notebook support/2015-06-04-141749-bokeh.ipynb
In [2]:
f = QQ['t']({16:1, 0:262})
f

t^16 + 262
In [3]:
K.<s> = NumberField(f)
K

Number Field in s with defining polynomial t^16 + 262
In [4]:
R = K.maximal_order()

Maximal Order in Number Field in s with defining polynomial t^16 + 262
In [7]:
I = R.ideal(263,s+1)

In [8]:
I.basis()

[263, s + 1, s^2 + 262, s^3 + 1, s^4 + 262, s^5 + 1, s^6 + 262, s^7 + 1, s^8 + 262, s^9 + 1, s^10 + 262, s^11 + 1, s^12 + 262, s^13 + 1, s^14 + 262, s^15 + 1]
In [6]:
Q = QuotientRing(R, R.ideal(263,s+1))

--------------------------------------------------------------------------- KeyboardInterrupt Traceback (most recent call last) <ipython-input-6-cd6415852f77> in <module>() ----> 1 Q = QuotientRing(R, R.ideal(Integer(263),s+Integer(1))) /projects/sage/sage-7.6/local/lib/python2.7/site-packages/sage/rings/quotient_ring.py in QuotientRing(R, I, names) 284 return R 285 try: --> 286 if I.is_principal(): 287 return R.quotient_by_principal_ideal(I.gen(), names) 288 except (AttributeError, NotImplementedError): /projects/sage/sage-7.6/local/lib/python2.7/site-packages/sage/rings/number_field/number_field_ideal.py in is_principal(self, proof) 1113 self._reduced_generators = self.gens() 1114 return self._is_principal -> 1115 self._cache_bnfisprincipal(proof) 1116 return self._is_principal 1117 /projects/sage/sage-7.6/local/lib/python2.7/site-packages/sage/rings/number_field/number_field_ideal.py in _cache_bnfisprincipal(self, proof, gens_needed) 1056 # We just need to check correctness of pari_bnf(). 1057 proof = get_flag(proof, "number_field") -> 1058 bnf = self.number_field().pari_bnf(proof) 1059 1060 # If we already have _reduced_generators, no need to compute them again /projects/sage/sage-7.6/local/lib/python2.7/site-packages/sage/rings/number_field/number_field.py in pari_bnf(self, proof, units) 3608 f = self.pari_polynomial("y") 3609 if units: -> 3610 self._pari_bnf = f.bnfinit(1) 3611 else: 3612 self._pari_bnf = f.bnfinit() /projects/sage/sage-7.6/local/lib/python2.7/site-packages/sage/libs/cypari2/auto_gen.pxi in sage.libs.cypari2.gen.Gen_auto.bnfinit (/projects/sage/sage-7.6/src/build/cythonized/sage/libs/cypari2/gen.c:18051)() 2986 _tech = (<Gen>tech).g 2987 precision = prec_bits_to_words(precision) -> 2988 sig_on() 2989 cdef GEN _ret = bnfinit0(_P, flag, _tech, precision) 2990 return new_gen(_ret) src/cysignals/signals.pyx in cysignals.signals.sig_raise_exception (build/src/cysignals/signals.c:1303)() KeyboardInterrupt: 
In [12]:
R.free_module() / I.free_module()

Finitely generated module V/W over Integer Ring with invariants (263)
In [13]:
factor(263)

263
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