# HG changeset patch # User Nick Alexander # Date 1241915774 25200 # Branch symbolics_switch # Node ID c2c97977273604df2685527796bb38ab6377973d # Parent 17219f455526ca74bc302d1543fad0e4e3f971b7 [mq]: number_fields.patch diff -r 17219f455526 -r c2c979772736 sage/rings/number_field/number_field.py --- a/sage/rings/number_field/number_field.py Sat May 09 16:32:49 2009 -0700 +++ b/sage/rings/number_field/number_field.py Sat May 09 17:36:14 2009 -0700 @@ -6778,16 +6778,18 @@ # crash Sage: see #5316). Overwrite them with correct values. self._zero_element = self(0) self._one_element = self(1) - if self.coerce_embedding() is None: + + emb = self.coerce_embedding() + if emb is None: self._standard_embedding = True else: rootD = number_field_element_quadratic.NumberFieldElement_quadratic(self, (QQ(0),QQ(1))) if D > 0: from sage.rings.real_double import RDF - self._standard_embedding = RDF(rootD) > 0 + self._standard_embedding = RDF.has_coerce_map_from(self) and RDF(rootD) > 0 else: from sage.rings.complex_double import CDF - self._standard_embedding = CDF(rootD).imag() > 0 + self._standard_embedding = CDF.has_coerce_map_from(self) and CDF(rootD).imag() > 0 def _coerce_map_from_(self, K): """ diff -r 17219f455526 -r c2c979772736 sage/rings/number_field/number_field_base.pyx --- a/sage/rings/number_field/number_field_base.pyx Sat May 09 16:32:49 2009 -0700 +++ b/sage/rings/number_field/number_field_base.pyx Sat May 09 17:36:14 2009 -0700 @@ -138,7 +138,7 @@ We compute the Minkowski bound for $\QQ[\sqrt[3]{2}]$: sage: K = QQ[2^(1/3)] sage: B = K.minkowski_bound(); B - 16*sqrt(3)/(3*pi) + 16/3*sqrt(3)/pi sage: B.n() 2.94042077558289 sage: int(B) @@ -184,7 +184,7 @@ field, where the Minkowski bound is much better: sage: K = QQ[sqrt(5)] sage: K.minkowski_bound() - sqrt(5)/2 + 1/2*sqrt(5) sage: K.minkowski_bound().n() 1.11803398874989 sage: K.bach_bound() @@ -196,7 +196,7 @@ degree field, where the Bach bound is much better: sage: K = CyclotomicField(37) sage: K.minkowski_bound().n() - 7.50857335698545e14 + 7.50857335698544e14 sage: K.bach_bound().n() 191669.304126267 diff -r 17219f455526 -r c2c979772736 sage/rings/number_field/number_field_element.pyx --- a/sage/rings/number_field/number_field_element.pyx Sat May 09 16:32:49 2009 -0700 +++ b/sage/rings/number_field/number_field_element.pyx Sat May 09 17:36:14 2009 -0700 @@ -1323,7 +1323,8 @@ sage: K. = NumberField(x^3 + x - 1, embedding=0.68) sage: b = SR(a); b - (sqrt(31)/(6*sqrt(3)) + 1/2)^(1/3) - 1/(3*(sqrt(31)/(6*sqrt(3)) + 1/2)^(1/3)) + (1/18*sqrt(3)*sqrt(31) + 1/2)^(1/3) - 1/3/(1/18*sqrt(3)*sqrt(31) + 1/2)^(1/3) + sage: (b^3 + b - 1).simplify_radical() 0 @@ -1338,9 +1339,14 @@ sage: K. = CyclotomicField(19) sage: SR(zeta) - e^(2*I*pi/19) + e^(2/19*I*pi) + sage: CC(zeta) + 0.945817241700635 + 0.324699469204683*I + sage: CC(SR(zeta)) + 0.945817241700635 + 0.324699469204683*I + sage: SR(zeta^5 + 2) - e^(10*I*pi/19) + 2 + e^(2/19*I*pi)*e^(8/19*I*pi) + 2 For degree greater than 5, sometimes Galois theory prevents a closed-form solution:: @@ -1355,7 +1361,7 @@ sage: K. = NumberField(x^6-x^3-1, embedding=1) sage: SR(a) - (sqrt(5) + 1)^(1/3)/2^(1/3) + 1/2*(sqrt(5) + 1)^(1/3)*2^(2/3) """ if self.__symbolic is None: @@ -1377,11 +1383,9 @@ if isinstance(K, number_field.NumberField_cyclotomic): # solution by radicals may be difficult, but we have a closed form - from sage.functions.all import exp - from sage.rings.complex_field import ComplexField - from sage.rings.real_mpfr import RR + from sage.all import exp, I, pi, ComplexField, RR CC = ComplexField(53) - two_pi_i = 2 * SR.pi()*SR(-1).sqrt() + two_pi_i = 2 * pi * I k = ( K._n()*CC(K.gen()).log() / CC(two_pi_i) ).real().round() # n ln z / (2 pi i) gen_image = exp(k*two_pi_i/K._n()) if self is gen: diff -r 17219f455526 -r c2c979772736 sage/rings/number_field/number_field_element_quadratic.pyx --- a/sage/rings/number_field/number_field_element_quadratic.pyx Sat May 09 16:32:49 2009 -0700 +++ b/sage/rings/number_field/number_field_element_quadratic.pyx Sat May 09 17:36:14 2009 -0700 @@ -873,7 +873,7 @@ sage: a.real() -1/2 sage: SR(a) - (sqrt(3)*I - 1)/2 + 1/2*I*sqrt(3) - 1/2 sage: bool(I*a.imag() + a.real() == a) True diff -r 17219f455526 -r c2c979772736 sage/rings/polynomial/polynomial_element.pyx --- a/sage/rings/polynomial/polynomial_element.pyx Sat May 09 16:32:49 2009 -0700 +++ b/sage/rings/polynomial/polynomial_element.pyx Sat May 09 17:36:14 2009 -0700 @@ -3824,7 +3824,7 @@ sage: X = var('X') sage: f = expand((X-1)*(X-I)^3*(X^2 - sqrt(2))); f - X^6 - (3*I - 1)*X^5 - X^4*sqrt(2) + (3*I - 3)*X^4 + (3*I + 1)*X^3*sqrt(2) + (I + 3)*X^3 - (3*I + 3)*X^2*sqrt(2) - I*X^2 - (I - 3)*X*sqrt(2) + I*sqrt(2) + -sqrt(2)*X^4 + I*sqrt(2) + X^6 - (3*I - 1)*X^5 + (3*I - 3)*X^4 + (3*I + 1)*sqrt(2)*X^3 + (I + 3)*X^3 - (3*I + 3)*sqrt(2)*X^2 - I*X^2 - (I - 3)*sqrt(2)*X sage: print f.roots() [(I, 3), (-2^(1/4), 1), (2^(1/4), 1), (1, 1)] @@ -4019,7 +4019,7 @@ sage: p.roots(ring=RR, algorithm='numpy') Traceback (most recent call last): ... - ValueError: array must not contain infs or NaNs + LinAlgError: Array must not contain infs or NaNs sage: p.roots(ring=RR, algorithm='pari') [(-3.50746621104340e451, 1)] sage: p.roots(ring=AA) @@ -4028,7 +4028,7 @@ [(-3.5074662110434039?e451, 1)] sage: p = bigc*x + 1 sage: p.roots(ring=RR) - [(0.000000000000000, 1)] + [(-0.000000000000000, 1)] sage: p.roots(ring=AA) [(-2.8510609648967059?e-452, 1)] sage: p.roots(ring=QQbar)