diff --git a/src/doc/de/thematische_anleitungen/sage_gymnasium.rst b/src/doc/de/thematische_anleitungen/sage_gymnasium.rst index 5a150a0..f9ede06 100644 --- a/src/doc/de/thematische_anleitungen/sage_gymnasium.rst +++ b/src/doc/de/thematische_anleitungen/sage_gymnasium.rst @@ -716,7 +716,7 @@ die ähnliche Funktion ``canonicalize_radical``:: Diese Gesetze können auch umgekehrt verwendet werden, wie in diesem Beispiel:: sage: (5*log(2) + 5*log(5)).simplify_log() - log(100000) + 5*log(10) Es geben weitere mögliche Vereinfachungen, die wir hier nicht weiter erwähnen. diff --git a/src/sage/coding/code_bounds.py b/src/sage/coding/code_bounds.py index 7935bbf..64ac455 100644 --- a/src/sage/coding/code_bounds.py +++ b/src/sage/coding/code_bounds.py @@ -577,8 +577,8 @@ def entropy(x, q=2): sage: codes.bounds.entropy(0, 2) 0 - sage: codes.bounds.entropy(1/5,4) - 1/5*log(3)/log(4) - 4/5*log(4/5)/log(4) - 1/5*log(1/5)/log(4) + sage: codes.bounds.entropy(1/5,4).factor() + 1/10*(log(3) - 4*log(4/5) - log(1/5))/log(2) sage: codes.bounds.entropy(1, 3) log(2)/log(3) diff --git a/src/sage/functions/log.py b/src/sage/functions/log.py index 15e3dbf..64d898c 100644 --- a/src/sage/functions/log.py +++ b/src/sage/functions/log.py @@ -121,12 +121,12 @@ class Function_exp(GinacFunction): sage: model_exp = exp(II)**a*(b) sage: sol1_l={b: 5.0, a: 1.1} sage: model_exp.subs(sol1_l) - 5.00000000000000*(e^II)^1.10000000000000 + 5.00000000000000*e^(1.10000000000000*II) :: sage: exp(3)^II*exp(x) - (e^3)^II*e^x + e^(3*II + x) sage: exp(x)*exp(x) e^(2*x) sage: exp(x)*exp(a) @@ -137,7 +137,7 @@ class Function_exp(GinacFunction): Another instance of the same problem (:trac:`7394`):: sage: 2*sqrt(e) - 2*sqrt(e) + 2*e^(1/2) Check that :trac:`19918` is fixed:: @@ -271,7 +271,7 @@ class Function_log(GinacFunction): sage: RDF(log(1024, 2)) 10.0 sage: log(10, 4) - log(10)/log(4) + 1/2*log(10)/log(2) sage: RDF(log(10, 4)) 1.6609640474436813 sage: log(10, 2) diff --git a/src/sage/functions/orthogonal_polys.py b/src/sage/functions/orthogonal_polys.py index 5db9871..c877454 100644 --- a/src/sage/functions/orthogonal_polys.py +++ b/src/sage/functions/orthogonal_polys.py @@ -1666,7 +1666,7 @@ class Func_assoc_legendre_Q(BuiltinFunction): EXAMPLES:: sage: gen_legendre_Q(2,1,3) - -1/4*sqrt(-2)*(-36*I*pi + 36*log(4) - 36*log(2) - 25) + -1/4*sqrt(-2)*(-36*I*pi + 36*log(2) - 25) """ ret = self._eval_special_values_(n, m, x) if ret is not None: diff --git a/src/sage/libs/pynac/pynac.pxd b/src/sage/libs/pynac/pynac.pxd index 9e37f08..1d19fdd 100644 --- a/src/sage/libs/pynac/pynac.pxd +++ b/src/sage/libs/pynac/pynac.pxd @@ -97,6 +97,7 @@ cdef extern from "sage/libs/pynac/wrap.h": cdef cppclass GEx "ex": GEx() + GEx(GNumeric o) GEx(GSymbol m) GEx(GEx m) GEx(long n) @@ -127,8 +128,8 @@ cdef extern from "sage/libs/pynac/wrap.h": GEx numer() except + GEx denom() except + GEx numer_denom() except + - int degree(GEx expr) except + - int ldegree(GEx expr) except + + GNumeric degree(GEx expr) except + + GNumeric ldegree(GEx expr) except + GEx unit(GEx expr) except + GEx content(GEx expr) except + GEx primpart(GEx expr) except + @@ -161,6 +162,7 @@ cdef extern from "sage/libs/pynac/wrap.h": # Algorithms GEx g_gcd "gcd"(GEx a, GEx b) except + + bint g_factor "factor"(GEx expr, GEx res) except + GEx g_gosper_term "gosper_term"(GEx the_ex, GEx n) except + GEx g_gosper_sum_definite "gosper_sum_definite"(GEx the_ex, GEx n, GEx a, GEx b, int* p) except + diff --git a/src/sage/rings/asymptotic/asymptotic_ring.py b/src/sage/rings/asymptotic/asymptotic_ring.py index 0b03a4a..9de56a6 100644 --- a/src/sage/rings/asymptotic/asymptotic_ring.py +++ b/src/sage/rings/asymptotic/asymptotic_ring.py @@ -2485,7 +2485,7 @@ class AsymptoticExpansion(CommutativeAlgebraElement): :: sage: (x^2 + log(x)).subs(x=4*x+2).truncate(5) - 16*x^2 + 16*x + log(x) + log(4) + 4 + 1/2*x^(-1) + O(x^(-2)) + 16*x^2 + 16*x + log(x) + 2*log(2) + 4 + 1/2*x^(-1) + O(x^(-2)) sage: _.parent() Asymptotic Ring <(e^x)^QQ * x^ZZ * log(x)^ZZ> over Symbolic Ring diff --git a/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py b/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py index 9a6f67a..de61ed3 100644 --- a/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py +++ b/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py @@ -60,9 +60,15 @@ A univariate smooth point example:: sage: decomp = F.asymptotic_decomposition(alpha) sage: decomp (0, []) + - (-1/2*(x^2 + 6*x + 9)*r^2/(x^5 + 9*x^4 + 27*x^3 + 27*x^2) - - 1/2*(5*x^2 + 24*x + 27)*r/(x^5 + 9*x^4 + 27*x^3 + 27*x^2) - - 3*(x^2 + 3*x + 3)/(x^5 + 9*x^4 + 27*x^3 + 27*x^2), + (-1/2*r^2*(x^2/(x^5 + 9*x^4 + 27*x^3 + 27*x^2) + + 6*x/(x^5 + 9*x^4 + 27*x^3 + 27*x^2) + + 9/(x^5 + 9*x^4 + 27*x^3 + 27*x^2)) + - 1/2*r*(5*x^2/(x^5 + 9*x^4 + 27*x^3 + 27*x^2) + + 24*x/(x^5 + 9*x^4 + 27*x^3 + 27*x^2) + + 27/(x^5 + 9*x^4 + 27*x^3 + 27*x^2)) + - 3*x^2/(x^5 + 9*x^4 + 27*x^3 + 27*x^2) + - 9*x/(x^5 + 9*x^4 + 27*x^3 + 27*x^2) + - 9/(x^5 + 9*x^4 + 27*x^3 + 27*x^2), [(x - 1/2, 1)]) sage: F1 = decomp[1] sage: p = {x: 1/2} @@ -139,9 +145,9 @@ A multiple point example (Example 6.5 of [RaWi2012]_):: sage: alpha = (var('a'), var('b')) sage: decomp = F.asymptotic_decomposition(alpha); decomp (0, []) + - (-1/9*(2*b^2*x^2 - 5*a*b*x*y + 2*a^2*y^2)*r^2/(x^2*y^2) - - 1/9*(6*b*x^2 - 5*(a + b)*x*y + 6*a*y^2)*r/(x^2*y^2) - - 1/9*(4*x^2 - 5*x*y + 4*y^2)/(x^2*y^2), + (-1/9*r^2*(2*a^2/x^2 + 2*b^2/y^2 - 5*a*b/(x*y)) + - 1/9*r*(6*a/x^2 + 6*b/y^2 - 5*a/(x*y) - 5*b/(x*y)) + - 4/9/x^2 - 4/9/y^2 + 5/9/(x*y), [(x + 2*y - 1, 1), (2*x + y - 1, 1)]) sage: F1 = decomp[1] sage: F1.asymptotics(p, alpha, 2) @@ -1480,9 +1486,9 @@ class FractionWithFactoredDenominator(RingElement): sage: alpha = [var('a')] sage: F.asymptotic_decomposition(alpha) (0, []) + - (1/54*(5*a^2*x^2 + 2*a^2*x + 11*a^2)*r^2/x^2 - - 1/54*(5*a*x^2 - 2*a*x - 33*a)*r/x^2 + 11/27/x^2, [(x - 1, 1)]) + - (-5/27, [(x + 2, 1)]) + (1/54*(5*a^2 + 2*a^2/x + 11*a^2/x^2)*r^2 + - 1/54*(5*a - 2*a/x - 33*a/x^2)*r + 11/27/x^2, + [(x - 1, 1)]) + (-5/27, [(x + 2, 1)]) :: @@ -1495,7 +1501,7 @@ class FractionWithFactoredDenominator(RingElement): sage: alpha = var('a, b') sage: F.asymptotic_decomposition(alpha) (0, []) + - (1/3*(2*b*x - a*y)*r/(x*y) + 1/3*(2*x - y)/(x*y), + (-1/3*r*(a/x - 2*b/y) - 1/3/x + 2/3/y, [(x + 2*y - 1, 1), (2*x + y - 1, 1)]) """ R = self.denominator_ring @@ -1600,7 +1606,7 @@ class FractionWithFactoredDenominator(RingElement): (1, [(x*y + x + y - 1, 2)]) sage: alpha = [4, 3] sage: decomp = F.asymptotic_decomposition(alpha); decomp - (0, []) + (-3/2*r*(y + 1)/y - 1/2*(y + 1)/y, [(x*y + x + y - 1, 1)]) + (0, []) + (-3/2*r*(1/y + 1) - 1/2/y - 1/2, [(x*y + x + y - 1, 1)]) sage: F1 = decomp[1] sage: p = {y: 1/3, x: 1/2} sage: asy = F1.asymptotics(p, alpha, 2, verbose=True) @@ -1634,7 +1640,7 @@ class FractionWithFactoredDenominator(RingElement): sage: alpha = [3, 3, 2] sage: decomp = F.asymptotic_decomposition(alpha); decomp (0, []) + - (16*r*(4*y - 3*z)/(y*z) + 16*(2*y - z)/(y*z), + (-16*r*(3/y - 4/z) - 16/y + 32/z, [(x + 2*y + z - 4, 1), (2*x + y + z - 4, 1)]) sage: F1 = decomp[1] sage: p = {x: 1, y: 1, z: 1} diff --git a/src/sage/rings/asymptotic/term_monoid.py b/src/sage/rings/asymptotic/term_monoid.py index b879639..ded7f02 100644 --- a/src/sage/rings/asymptotic/term_monoid.py +++ b/src/sage/rings/asymptotic/term_monoid.py @@ -3339,7 +3339,7 @@ class ExactTerm(TermWithCoefficient): sage: T(x^1234).log_term() (1234*log(x),) sage: T(49*x^7).log_term(base=7) - (log(49)/log(7), 7/log(7)*log(x)) + (2, 7/log(7)*log(x)) :: @@ -3347,7 +3347,7 @@ class ExactTerm(TermWithCoefficient): sage: T('x * y').log_term() (log(x), log(y)) sage: T('4 * x * y').log_term(base=2) - (log(4)/log(2), 1/log(2)*log(x), 1/log(2)*log(y)) + (2, 1/log(2)*log(x), 1/log(2)*log(y)) .. SEEALSO:: diff --git a/src/sage/rings/integer.pyx b/src/sage/rings/integer.pyx index 0b8a3bd..cdc34a2 100644 --- a/src/sage/rings/integer.pyx +++ b/src/sage/rings/integer.pyx @@ -2532,7 +2532,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement): sage: Integer(125).log(5,prec=53) 3.00000000000000 sage: log(Integer(125)) - log(125) + 3*log(5) For extremely large numbers, this works:: diff --git a/src/sage/rings/rational.pyx b/src/sage/rings/rational.pyx index 36af3a5..857081b 100644 --- a/src/sage/rings/rational.pyx +++ b/src/sage/rings/rational.pyx @@ -3075,11 +3075,11 @@ cdef class Rational(sage.structure.element.FieldElement): sage: (124/345).log(5,100) -0.63578895682825611710391773754 sage: log(QQ(125)) - log(125) + 3*log(5) sage: log(QQ(125), 5) 3 sage: log(QQ(125), 3) - log(125)/log(3) + 3*log(5)/log(3) sage: QQ(8).log(1/2) -3 sage: (1/8).log(1/2) diff --git a/src/sage/schemes/elliptic_curves/ell_point.py b/src/sage/schemes/elliptic_curves/ell_point.py index 8009421..9ec892e 100644 --- a/src/sage/schemes/elliptic_curves/ell_point.py +++ b/src/sage/schemes/elliptic_curves/ell_point.py @@ -2886,7 +2886,7 @@ class EllipticCurvePoint_number_field(EllipticCurvePoint_field): sage: Q.non_archimedean_local_height(K.ideal(1-2*i)) 0 sage: Q.non_archimedean_local_height() - 1/2*log(16) + 2*log(2) An example over the rational numbers:: diff --git a/src/sage/symbolic/constants_c.pyx b/src/sage/symbolic/constants_c.pyx index 8eb61f5..38e8db6 100644 --- a/src/sage/symbolic/constants_c.pyx +++ b/src/sage/symbolic/constants_c.pyx @@ -145,14 +145,14 @@ cdef class E(Expression): sage: t.operands() [a] - As opposed to:: + This applies to the unit argument as well:: sage: u = SR(1).exp()^a; u e^a sage: u.operator() - + exp sage: u.operands() - [e, a] + [a] It also works with matrices (see :trac:`4735`):: diff --git a/src/sage/symbolic/expression.pyx b/src/sage/symbolic/expression.pyx index 94252ea..3e06201 100644 --- a/src/sage/symbolic/expression.pyx +++ b/src/sage/symbolic/expression.pyx @@ -3247,11 +3247,8 @@ cdef class Expression(CommutativeRingElement): -1 sage: b = -x*A; c = b*b; c 1/4*x^2*(sqrt(5) + I*sqrt(2*sqrt(5) + 10) - 1) - - Products of non integer powers of exp are not simplified:: - sage: exp(x)^I*exp(z)^(2.5) - (e^x)^I*(e^z)^2.50000000000000 + e^(I*x + 2.50000000000000*z) :: @@ -6311,7 +6308,7 @@ cdef class Expression(CommutativeRingElement): 0 """ cdef Expression ss = self.coerce_in(s) - return self._gobj.ldegree(ss._gobj) + return new_Expression_from_GEx(self._parent, GEx(self._gobj.ldegree(ss._gobj))) def degree(self, s): """ @@ -6337,7 +6334,7 @@ cdef class Expression(CommutativeRingElement): 0 """ cdef Expression ss = self.coerce_in(s) - return self._gobj.degree(ss._gobj) + return new_Expression_from_GEx(self._parent, GEx(self._gobj.degree(ss._gobj))) def unit(self, s): """ @@ -7185,12 +7182,12 @@ cdef class Expression(CommutativeRingElement): sage: f.collect(z) (x^2*y^2 + 4)*z^2 + 4*x*y + 20*y^2 + (x + 21*y)*z - Sometimes, we do have to call :meth:`expand()` on the - expression first to achieve the desired result:: + The terms are collected, whether the expression + is expanded or not:: sage: f = (x + y)*(x - z) sage: f.collect(x) - x^2 + x*y - x*z - y*z + x^2 + x*(y - z) - y*z sage: f.expand().collect(x) x^2 + x*(y - z) - y*z @@ -10433,9 +10430,9 @@ cdef class Expression(CommutativeRingElement): ``x*log(9)`` is contracted only if ``algorithm`` is ``'all'``:: sage: (x*log(9)).simplify_log() - x*log(9) + 2*x*log(3) sage: (x*log(9)).simplify_log('all') - log(9^x) + log(3^(2*x)) TESTS: @@ -10550,7 +10547,7 @@ cdef class Expression(CommutativeRingElement): To expand also log(3/4) use ``algorithm='all'``:: sage: (log(3/4*x^pi)).log_expand('all') - pi*log(x) - log(4) + log(3) + pi*log(x) + log(3) - 2*log(2) To expand only the power use ``algorithm='powers'``.:: @@ -10573,7 +10570,7 @@ cdef class Expression(CommutativeRingElement): pi*log(x) + log(3/4) sage: (log(3/4*x^pi)).log_expand('all') - pi*log(x) - log(4) + log(3) + pi*log(x) + log(3) - 2*log(2) sage: (log(3/4*x^pi)).log_expand() pi*log(x) + log(3/4) diff --git a/src/sage/tests/french_book/calculus_doctest.py b/src/sage/tests/french_book/calculus_doctest.py index 0d40cae..ffe5d4b 100644 --- a/src/sage/tests/french_book/calculus_doctest.py +++ b/src/sage/tests/french_book/calculus_doctest.py @@ -331,7 +331,7 @@ Sage example in ./calculus.tex, line 914:: Sage example in ./calculus.tex, line 929:: sage: v(x) = diff(u(x), x); sol = solve(v(x) == 0, x); sol - [x == 100/log(100), x == 0] + [x == 50/log(10), x == 0] sage: floor(sol[0].rhs()) 21