From 4fac509e758a8df11076c38f3321537b510dde29 Mon Sep 17 00:00:00 2001 From: Antonio Rojas Date: Sun, 24 Aug 2025 19:30:06 +0200 Subject: [PATCH 1/8] Fix tests with maxima 5.48 --- src/doc/de/tutorial/tour_algebra.rst | 2 +- src/doc/en/constructions/calculus.rst | 5 +-- src/doc/en/tutorial/tour_algebra.rst | 2 +- src/doc/es/tutorial/tour_algebra.rst | 2 +- src/doc/fr/tutorial/tour_algebra.rst | 2 +- src/doc/it/tutorial/tour_algebra.rst | 2 +- src/doc/ja/tutorial/tour_algebra.rst | 2 +- src/doc/pt/tutorial/tour_algebra.rst | 2 +- src/doc/ru/tutorial/tour_algebra.rst | 2 +- src/doc/zh/constructions/calculus.rst | 5 +-- src/doc/zh/tutorial/tour_algebra.rst | 2 +- src/sage/calculus/calculus.py | 8 ++-- src/sage/calculus/test_sympy.py | 2 +- src/sage/calculus/tests.py | 2 +- src/sage/interfaces/maxima.py | 33 ++++++++-------- src/sage/interfaces/maxima_abstract.py | 38 +++++++++---------- src/sage/manifolds/chart.py | 2 +- .../differentiable/automorphismfield_group.py | 3 +- src/sage/manifolds/differentiable/metric.py | 8 ++-- src/sage/manifolds/utilities.py | 16 ++++---- src/sage/matrix/matrix2.pyx | 4 +- src/sage/misc/functional.py | 6 +-- src/sage/symbolic/expression.pyx | 8 ++-- .../calculus_doctest.py | 2 +- 24 files changed, 78 insertions(+), 82 deletions(-) diff --git a/src/doc/de/tutorial/tour_algebra.rst b/src/doc/de/tutorial/tour_algebra.rst index 84e97f773f1..c13b3a31d29 100644 --- a/src/doc/de/tutorial/tour_algebra.rst +++ b/src/doc/de/tutorial/tour_algebra.rst @@ -172,7 +172,7 @@ berechnet: sage: t = var("t") sage: f = t^2*exp(t) - sin(t) sage: f.laplace(t,s) - -1/(s^2 + 1) + 2/(s - 1)^3 + 2/(s^3 - 3*s^2 + 3*s - 1) - 1/(s^2 + 1) Hier ist ein komplizierteres Beispiel. Die Verschiebung des Gleichgewichts einer verkoppelten Feder, die an der linken Wand diff --git a/src/doc/en/constructions/calculus.rst b/src/doc/en/constructions/calculus.rst index b6243b64dbc..fb7339ba0b1 100644 --- a/src/doc/en/constructions/calculus.rst +++ b/src/doc/en/constructions/calculus.rst @@ -155,7 +155,7 @@ Sage can also compute symbolic definite integrals involving limits. (x, k, w) sage: f = x^3 * e^(k*x) * sin(w*x) sage: f.integrate(x) - ((24*k^3*w - 24*k*w^3 - (k^6*w + 3*k^4*w^3 + 3*k^2*w^5 + w^7)*x^3 + 6*(k^5*w + 2*k^3*w^3 + k*w^5)*x^2 - 6*(3*k^4*w + 2*k^2*w^3 - w^5)*x)*cos(w*x)*e^(k*x) - (6*k^4 - 36*k^2*w^2 + 6*w^4 - (k^7 + 3*k^5*w^2 + 3*k^3*w^4 + k*w^6)*x^3 + 3*(k^6 + k^4*w^2 - k^2*w^4 - w^6)*x^2 - 6*(k^5 - 2*k^3*w^2 - 3*k*w^4)*x)*e^(k*x)*sin(w*x))/(k^8 + 4*k^6*w^2 + 6*k^4*w^4 + 4*k^2*w^6 + w^8) + ((24*k^3*w*e^(k*x) - 24*k*w^3*e^(k*x) - (k^6*w*e^(k*x) + 3*k^4*w^3*e^(k*x) + 3*k^2*w^5*e^(k*x) + w^7*e^(k*x))*x^3 + 6*(k^5*w*e^(k*x) + 2*k^3*w^3*e^(k*x) + k*w^5*e^(k*x))*x^2 - 6*(3*k^4*w*e^(k*x) + 2*k^2*w^3*e^(k*x) - w^5*e^(k*x))*x)*cos(w*x) - (6*k^4*e^(k*x) - 36*k^2*w^2*e^(k*x) + 6*w^4*e^(k*x) - (k^7*e^(k*x) + 3*k^5*w^2*e^(k*x) + 3*k^3*w^4*e^(k*x) + k*w^6*e^(k*x))*x^3 + 3*(k^6*e^(k*x) + k^4*w^2*e^(k*x) - k^2*w^4*e^(k*x) - w^6*e^(k*x))*x^2 - 6*(k^5*e^(k*x) - 2*k^3*w^2*e^(k*x) - 3*k*w^4*e^(k*x))*x)*sin(w*x))/(k^8 + 4*k^6*w^2 + 6*k^4*w^4 + 4*k^2*w^6 + w^8) sage: integrate(1/x^2, x, 1, infinity) 1 @@ -257,8 +257,7 @@ is one way to compute LT's and (s, t) sage: f = t^5*exp(t)*sin(t) sage: L = laplace(f, t, s); L - 3840*(s - 1)^5/(s^2 - 2*s + 2)^6 - 3840*(s - 1)^3/(s^2 - 2*s + 2)^5 + - 720*(s - 1)/(s^2 - 2*s + 2)^4 + 240*(3*s^5 - 15*s^4 + 20*s^3 - 12*s + 4)/(s^12 - 12*s^11 + 72*s^10 - 280*s^9 + 780*s^8 - 1632*s^7 + 2624*s^6 - 3264*s^5 + 3120*s^4 - 2240*s^3 + 1152*s^2 - 384*s + 64) is another way. diff --git a/src/doc/en/tutorial/tour_algebra.rst b/src/doc/en/tutorial/tour_algebra.rst index d460fa279e5..60c22d4338c 100644 --- a/src/doc/en/tutorial/tour_algebra.rst +++ b/src/doc/en/tutorial/tour_algebra.rst @@ -182,7 +182,7 @@ You can compute Laplace transforms also; the Laplace transform of sage: t = var("t") sage: f = t^2*exp(t) - sin(t) sage: f.laplace(t,s) - -1/(s^2 + 1) + 2/(s - 1)^3 + 2/(s^3 - 3*s^2 + 3*s - 1) - 1/(s^2 + 1) Here is a more involved example. The displacement from equilibrium (respectively) for a coupled spring attached to a wall on the left diff --git a/src/doc/es/tutorial/tour_algebra.rst b/src/doc/es/tutorial/tour_algebra.rst index 42c818fe8d7..f49e498582a 100644 --- a/src/doc/es/tutorial/tour_algebra.rst +++ b/src/doc/es/tutorial/tour_algebra.rst @@ -164,7 +164,7 @@ de :math:`t^2e^t -\sin(t)` se calcula como sigue: sage: t = var("t") sage: f = t^2*exp(t) - sin(t) sage: f.laplace(t,s) - -1/(s^2 + 1) + 2/(s - 1)^3 + 2/(s^3 - 3*s^2 + 3*s - 1) - 1/(s^2 + 1) Veamos un ejemplo más complicado. El desplazamiento desde el punto de equilibrio de dos resortes acoplados, sujetos a una pared a la izquierda diff --git a/src/doc/fr/tutorial/tour_algebra.rst b/src/doc/fr/tutorial/tour_algebra.rst index 70cbe3a1df0..e386986385a 100644 --- a/src/doc/fr/tutorial/tour_algebra.rst +++ b/src/doc/fr/tutorial/tour_algebra.rst @@ -149,7 +149,7 @@ transformée de Laplace de :math:`t^2e^t -\sin(t)` s'obtient comme suit : sage: t = var("t") sage: f = t^2*exp(t) - sin(t) sage: f.laplace(t,s) - -1/(s^2 + 1) + 2/(s - 1)^3 + 2/(s^3 - 3*s^2 + 3*s - 1) - 1/(s^2 + 1) Voici un exemple plus élaboré. L'élongation à partir du point d'équilibre de ressorts couplés attachés à gauche à un mur diff --git a/src/doc/it/tutorial/tour_algebra.rst b/src/doc/it/tutorial/tour_algebra.rst index 4c301d7b1b2..38f0dc8a574 100644 --- a/src/doc/it/tutorial/tour_algebra.rst +++ b/src/doc/it/tutorial/tour_algebra.rst @@ -150,7 +150,7 @@ Si può anche calcolare la trasformata di Laplace; la trasformata di Laplace di sage: t = var("t") sage: f = t^2*exp(t) - sin(t) sage: f.laplace(t,s) - -1/(s^2 + 1) + 2/(s - 1)^3 + 2/(s^3 - 3*s^2 + 3*s - 1) - 1/(s^2 + 1) Il successivo è un esempio più articolato. Lo scostamento dall'equilibrio (rispettivamente) per due molle accoppiate fissate ad un muro a sinistra diff --git a/src/doc/ja/tutorial/tour_algebra.rst b/src/doc/ja/tutorial/tour_algebra.rst index dd6e67d1030..5d14e260435 100644 --- a/src/doc/ja/tutorial/tour_algebra.rst +++ b/src/doc/ja/tutorial/tour_algebra.rst @@ -176,7 +176,7 @@ Sageを使って常微分方程式を研究することもできる． :math:`x' sage: t = var("t") sage: f = t^2*exp(t) - sin(t) sage: f.laplace(t,s) - -1/(s^2 + 1) + 2/(s - 1)^3 + 2/(s^3 - 3*s^2 + 3*s - 1) - 1/(s^2 + 1) もう少し手間のかかる問題を考えてみよう． diff --git a/src/doc/pt/tutorial/tour_algebra.rst b/src/doc/pt/tutorial/tour_algebra.rst index b3c9bf54e45..c3dca33b69e 100644 --- a/src/doc/pt/tutorial/tour_algebra.rst +++ b/src/doc/pt/tutorial/tour_algebra.rst @@ -169,7 +169,7 @@ Laplace de :math:`t^2e^t -\sin(t)` é calculada da seguinte forma: sage: t = var("t") sage: f = t^2*exp(t) - sin(t) sage: f.laplace(t,s) - -1/(s^2 + 1) + 2/(s - 1)^3 + 2/(s^3 - 3*s^2 + 3*s - 1) - 1/(s^2 + 1) A seguir, um exemplo mais complicado. O deslocamento, com respeito à posição de equilíbrio, de duas massas presas a uma parede através de diff --git a/src/doc/ru/tutorial/tour_algebra.rst b/src/doc/ru/tutorial/tour_algebra.rst index bc0d4926f83..ad1bae1de96 100644 --- a/src/doc/ru/tutorial/tour_algebra.rst +++ b/src/doc/ru/tutorial/tour_algebra.rst @@ -166,7 +166,7 @@ Sage может использоваться для решения диффер sage: t = var("t") sage: f = t^2*exp(t) - sin(t) sage: f.laplace(t,s) - -1/(s^2 + 1) + 2/(s - 1)^3 + 2/(s^3 - 3*s^2 + 3*s - 1) - 1/(s^2 + 1) Приведем более сложный пример. Отклонение от положения равновесия для пары пружин, прикрепленных к стене слева, diff --git a/src/doc/zh/constructions/calculus.rst b/src/doc/zh/constructions/calculus.rst index 9f896a4658b..2b83dc19b45 100644 --- a/src/doc/zh/constructions/calculus.rst +++ b/src/doc/zh/constructions/calculus.rst @@ -148,7 +148,7 @@ Sage 还可以计算涉及极限的符号定积分。 (x, k, w) sage: f = x^3 * e^(k*x) * sin(w*x) sage: f.integrate(x) - ((24*k^3*w - 24*k*w^3 - (k^6*w + 3*k^4*w^3 + 3*k^2*w^5 + w^7)*x^3 + 6*(k^5*w + 2*k^3*w^3 + k*w^5)*x^2 - 6*(3*k^4*w + 2*k^2*w^3 - w^5)*x)*cos(w*x)*e^(k*x) - (6*k^4 - 36*k^2*w^2 + 6*w^4 - (k^7 + 3*k^5*w^2 + 3*k^3*w^4 + k*w^6)*x^3 + 3*(k^6 + k^4*w^2 - k^2*w^4 - w^6)*x^2 - 6*(k^5 - 2*k^3*w^2 - 3*k*w^4)*x)*e^(k*x)*sin(w*x))/(k^8 + 4*k^6*w^2 + 6*k^4*w^4 + 4*k^2*w^6 + w^8) + ((24*k^3*w*e^(k*x) - 24*k*w^3*e^(k*x) - (k^6*w*e^(k*x) + 3*k^4*w^3*e^(k*x) + 3*k^2*w^5*e^(k*x) + w^7*e^(k*x))*x^3 + 6*(k^5*w*e^(k*x) + 2*k^3*w^3*e^(k*x) + k*w^5*e^(k*x))*x^2 - 6*(3*k^4*w*e^(k*x) + 2*k^2*w^3*e^(k*x) - w^5*e^(k*x))*x)*cos(w*x) - (6*k^4*e^(k*x) - 36*k^2*w^2*e^(k*x) + 6*w^4*e^(k*x) - (k^7*e^(k*x) + 3*k^5*w^2*e^(k*x) + 3*k^3*w^4*e^(k*x) + k*w^6*e^(k*x))*x^3 + 3*(k^6*e^(k*x) + k^4*w^2*e^(k*x) - k^2*w^4*e^(k*x) - w^6*e^(k*x))*x^2 - 6*(k^5*e^(k*x) - 2*k^3*w^2*e^(k*x) - 3*k*w^4*e^(k*x))*x)*sin(w*x))/(k^8 + 4*k^6*w^2 + 6*k^4*w^4 + 4*k^2*w^6 + w^8) sage: integrate(1/x^2, x, 1, infinity) 1 @@ -241,8 +241,7 @@ Sage 还可以计算涉及极限的符号定积分。 (s, t) sage: f = t^5*exp(t)*sin(t) sage: L = laplace(f, t, s); L - 3840*(s - 1)^5/(s^2 - 2*s + 2)^6 - 3840*(s - 1)^3/(s^2 - 2*s + 2)^5 + - 720*(s - 1)/(s^2 - 2*s + 2)^4 + 240*(3*s^5 - 15*s^4 + 20*s^3 - 12*s + 4)/(s^12 - 12*s^11 + 72*s^10 - 280*s^9 + 780*s^8 - 1632*s^7 + 2624*s^6 - 3264*s^5 + 3120*s^4 - 2240*s^3 + 1152*s^2 - 384*s + 64) 上面是另一种方法。 diff --git a/src/doc/zh/tutorial/tour_algebra.rst b/src/doc/zh/tutorial/tour_algebra.rst index 592f096341f..c4d66efccb4 100644 --- a/src/doc/zh/tutorial/tour_algebra.rst +++ b/src/doc/zh/tutorial/tour_algebra.rst @@ -169,7 +169,7 @@ Sage 可以对许多函数进行微分和积分。 sage: t = var("t") sage: f = t^2*exp(t) - sin(t) sage: f.laplace(t,s) - -1/(s^2 + 1) + 2/(s - 1)^3 + 2/(s^3 - 3*s^2 + 3*s - 1) - 1/(s^2 + 1) 这里是一个更复杂的示例。左侧连接到墙上的耦合弹簧的平衡位移 diff --git a/src/sage/calculus/calculus.py b/src/sage/calculus/calculus.py index d41bf946a09..ac194f63b3e 100644 --- a/src/sage/calculus/calculus.py +++ b/src/sage/calculus/calculus.py @@ -133,8 +133,8 @@ [x^2 + x 2*x^3] [ 2 x^2 + x] sage: e^M - [ 1/2*(e^(2*sqrt(x)) + 1)*e^(x - sqrt(x)) 1/2*(x*e^(2*sqrt(x)) - x)*sqrt(x)*e^(x - sqrt(x))] - [ 1/2*(e^(2*sqrt(x)) - 1)*e^(x - sqrt(x))/x^(3/2) 1/2*(e^(2*sqrt(x)) + 1)*e^(x - sqrt(x))] + [ 1/2*(e^(2*sqrt(x)) + 1)*e^(x - sqrt(x)) 1/2*x^(3/2)*(e^(2*sqrt(x)) - 1)*e^(x - sqrt(x))] + [1/2*(e^(2*sqrt(x)) - 1)*e^(x - sqrt(x))/x^(3/2) 1/2*(e^(2*sqrt(x)) + 1)*e^(x - sqrt(x))] Complex exponentiation works, but may require a patched version of maxima (:issue:`32898`) for now:: @@ -1243,7 +1243,7 @@ def limit(ex, *args, dir=None, taylor=False, algorithm='maxima', **kwargs): sage: limit(sin(x)/x, x, 0, algorithm='sympy') 1 - sage: limit(sin(x)/x, x, 0, algorithm='giac') # needs sage.libs.giac + sage: limit(sin(x)/x, x, 0, algorithm='giac') # needs sage.libs.giac 1 sage: limit(x^x, x, 0, dir='+', algorithm='fricas') # optional - fricas 1 @@ -1816,7 +1816,7 @@ def laplace(ex, t, s, algorithm='maxima'): sage: f = exp (2*t + a) * sin(t) * t; f t*e^(a + 2*t)*sin(t) sage: L = laplace(f, t, s); L - 2*(s - 2)*e^a/(s^2 - 4*s + 5)^2 + 2*(s - 2)*e^a/(s^4 - 8*s^3 + 26*s^2 - 40*s + 25) sage: inverse_laplace(L, s, t) t*e^(a + 2*t)*sin(t) diff --git a/src/sage/calculus/test_sympy.py b/src/sage/calculus/test_sympy.py index aa084799a10..e081e9674d9 100644 --- a/src/sage/calculus/test_sympy.py +++ b/src/sage/calculus/test_sympy.py @@ -63,7 +63,7 @@ sage: diff(tan(x), x) tan(x)^2 + 1 sage: limit((tan(x+y) - tan(x))/y, y=0) - cos(x)^(-2) + tan(x)^2 + 1 sage: diff(sin(2*x), x, 1) 2*cos(2*x) sage: diff(sin(2*x), x, 2) diff --git a/src/sage/calculus/tests.py b/src/sage/calculus/tests.py index 2879dda115d..abdbbad932e 100644 --- a/src/sage/calculus/tests.py +++ b/src/sage/calculus/tests.py @@ -119,7 +119,7 @@ sage: integrate(exp(1-x^2),x) 1/2*sqrt(pi)*erf(x)*e sage: integrate(sin(x^2),x) - 1/16*sqrt(pi)*((I + 1)*sqrt(2)*erf((1/2*I + 1/2)*sqrt(2)*x) + (I - 1)*sqrt(2)*erf((1/2*I - 1/2)*sqrt(2)*x) - (I - 1)*sqrt(2)*erf(sqrt(-I)*x) + (I + 1)*sqrt(2)*erf((-1)^(1/4)*x)) + 1/16*sqrt(pi)*((I + 1)*sqrt(2)*erf((1/2*I + 1/2)*sqrt(2)*x) - (I - 1)*sqrt(2)*erf(sqrt(-I)*x) - 2*sqrt(2)*imag_part(erf((-1)^(1/4)*x)) + 2*sqrt(2)*real_part(erf((-1)^(1/4)*x))) sage: integrate((1-x^2)^n,x) # long time x*hypergeometric((1/2, -n), (3/2,), x^2*exp_polar(2*I*pi)) diff --git a/src/sage/interfaces/maxima.py b/src/sage/interfaces/maxima.py index ebe00cd51e7..a092c37e9a5 100644 --- a/src/sage/interfaces/maxima.py +++ b/src/sage/interfaces/maxima.py @@ -180,7 +180,7 @@ You can even nicely typeset the solution in latex:: sage: latex(s) - \left[ \left[ a=-...{{\sqrt{79}\,i-11}\over{4}}... , b={{...\sqrt{79}\,i+9...}\over{4}} , c={{\sqrt{79}\,i+1}\over{10}} \right] , \left[ a={{...\sqrt{79}\,i+11}\over{4}} , b=-...{{\sqrt{79}\,i-9...}\over{4}}... , c=-...{{...\sqrt{79}\,i-1}\over{10}}... \right] \right] + \left[ \left[ a=-\left({{\sqrt{79}\,i-11}\over{4}}\right) , b={{\sqrt{79}\,i +9}\over{4}} , c={{\sqrt{79}\,i+1}\over{10}} \right] , \left[ a={{\sqrt{79} \,i+11}\over{4}} , b=-\left({{\sqrt{79}\,i-9}\over{4}}\right) , c=-\left({{ \sqrt{79}\,i-1}\over{10}}\right) \right] \right] To have the above appear onscreen via ``xdvi``, type ``view(s)``. (TODO: For OS X should create pdf output @@ -202,11 +202,11 @@ :: sage: f = maxima('x^3 * %e^(k*x) * sin(w*x)'); f - x^3*%e^(k*x)*sin(w*x) + %e^(k*x)*x^3*sin(w*x) sage: f.diff('x') - k*x^3*%e^(k*x)*sin(w*x)+3*x^2*%e^(k*x)*sin(w*x)+w*x^3*%e^(k*x) *cos(w*x) + %e^(k*x)*k*x^3*sin(w*x)+3*%e^(k*x)*x^2*sin(w*x)+%e^(k*x)*w*x^3 *cos(w*x) sage: f.integrate('x') - (((k*w^6+3*k^3*w^4+3*k^5*w^2+k^7)*x^3 +(3*w^6+3*k^2*w^4-3*k^4*w^2-3*k^6)*x^2+(...-...18*k*w^4)-12*k^3*w^2+6*k^5)*x-6*w^4 +36*k^2*w^2-6*k^4) *%e^(k*x)*sin(w*x) +((...-w^7...-3*k^2*w^5-3*k^4*w^3-k^6*w)*x^3...+(6*k*w^5+12*k^3*w^3+6*k^5*w)*x^2...+(6*w^5-12*k^2*w^3-18*k^4*w)*x-24*k*w^3 +24*k^3*w) *%e^(k*x)*cos(w*x)) /(w^8+4*k^2*w^6+6*k^4*w^4+4*k^6*w^2+k^8) + (((%e^(k*x)*k*w^6+3*%e^(k*x)*k^3*w^4+3*%e^(k*x)*k^5*w^2+%e^(k*x)*k^7)*x ^3 +(3*%e^(k*x)*w^6+3*%e^(k*x)*k^2*w^4-3*%e^(k*x)*k^4*w^2-3*%e^(k*x)*k^6)*x^2 +(-(18*%e^(k*x)*k*w^4)-12*%e^(k*x)*k^3*w^2+6*%e^(k*x)*k^5)*x-6*%e^(k*x)*w^4 +36*%e^(k*x)*k^2*w^2-6*%e^(k*x)*k^4) *sin(w*x) +((-(%e^(k*x)*w^7)-3*%e^(k*x)*k^2*w^5-3*%e^(k*x)*k^4*w^3-%e^(k*x)*k^6*w)*x^3 +(6*%e^(k*x)*k*w^5+12*%e^(k*x)*k^3*w^3+6*%e^(k*x)*k^5*w)*x^2 +(6*%e^(k*x)*w^5-12*%e^(k*x)*k^2*w^3-18*%e^(k*x)*k^4*w)*x-24*%e^(k*x)*k*w^3 +24*%e^(k*x)*k^3*w) *cos(w*x)) /(w^8+4*k^2*w^6+6*k^4*w^4+4*k^6*w^2+k^8) :: @@ -277,13 +277,14 @@ sage: _ = maxima.eval("f(t) := t^5*exp(t)*sin(t)") sage: maxima("laplace(f(t),t,s)") - (360*(2*s-2))/(s^2-2*s+2)^4-(480*(2*s-2)^3)/(s^2-2*s+2)^5 +(120*(2*s-2)^5)/(s^2-2*s+2)^6 + (720*s^5-3600*s^4+4800*s^3-2880*s+960) /(s^12-12*s^11+72*s^10-280*s^9+780*s^8-1632*s^7+2624*s^6-3264*s^5+3120*s^4 -2240*s^3+1152*s^2-384*s+64) sage: print(maxima("laplace(f(t),t,s)")) - 3 5 - 360 (2 s - 2) 480 (2 s - 2) 120 (2 s - 2) - --------------- - --------------- + --------------- - 2 4 2 5 2 6 - (s - 2 s + 2) (s - 2 s + 2) (s - 2 s + 2) + 5 4 3 + (720 s - 3600 s + 4800 s - 2880 s + 960) + 12 11 10 9 8 7 6 5 + /(s - 12 s + 72 s - 280 s + 780 s - 1632 s + 2624 s - 3264 s + 4 3 2 + + 3120 s - 2240 s + 1152 s - 384 s + 64) :: @@ -349,11 +350,11 @@ sage: S = maxima('nusum(exp(1+2*i/n),i,1,n)') sage: print(S) - 2/n + 3 2/n + 1 - %e %e - ----------------------- - ----------------------- - 1/n 1/n 1/n 1/n - (%e - 1) (%e + 1) (%e - 1) (%e + 1) + 2/n + 3 2/n + 1 + %e %e + ─────────────────────── - ─────────────────────── + 1/n 1/n 1/n 1/n + (%e - 1) (%e + 1) (%e - 1) (%e + 1) We formally compute the limit as `n\to\infty` of `2S/n` as follows:: @@ -402,7 +403,7 @@ sage: g = maxima('exp(3*%i*x)/(6*%i) + exp(%i*x)/(2*%i) + c') sage: latex(g) - -...{{i\,e^{3\,i\,x}}\over{6}}...-{{i\,e^{i\,x}}\over{2}}+c + c-{{e^{3\,i\,x}\,i}\over{6}}-{{e^{i\,x}\,i}\over{2}} Long Input ---------- diff --git a/src/sage/interfaces/maxima_abstract.py b/src/sage/interfaces/maxima_abstract.py index dab8e641e3a..98ac5f3f3d3 100644 --- a/src/sage/interfaces/maxima_abstract.py +++ b/src/sage/interfaces/maxima_abstract.py @@ -827,11 +827,11 @@ def de_solve(self, de, vars, ics=None): sage: maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'], [1,1,1]) y = 3*x-2*%e^(x-1) sage: maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y']) - y = %k1*%e^x+%k2*%e^-x+3*x + y = 3*x+%e^-x*%k2+%e^x*%k1 sage: maxima.de_solve('diff(y,x) + 3*x = y', ['x','y']) - y = (%c-3*(...-x...-1)*%e^-x)*%e^x + y = %e^x*(%c-3*%e^-x*(-x-1)) sage: maxima.de_solve('diff(y,x) + 3*x = y', ['x','y'],[1,1]) - y = -...%e^-1*(5*%e^x-3*%e*x-3*%e)... + y = %e^-1*(3*%e*x-5*%e^x+3*%e) """ if not isinstance(vars, str): str_vars = '%s, %s' % (vars[1], vars[0]) @@ -870,20 +870,20 @@ def de_solve_laplace(self, de, vars, ics=None): sage: maxima.clear('x'); maxima.clear('f') sage: maxima.de_solve_laplace("diff(f(x),x,2) = 2*diff(f(x),x)-f(x)", ["x","f"], [0,1,2]) - f(x) = x*%e^x+%e^x + f(x) = %e^x*x+%e^x :: sage: maxima.clear('x'); maxima.clear('f') sage: f = maxima.de_solve_laplace("diff(f(x),x,2) = 2*diff(f(x),x)-f(x)", ["x","f"]) sage: f - f(x) = x*%e^x*('at('diff(f(x),x,1),x = 0))-f(0)*x*%e^x+f(0)*%e^x + f(x) = %e^x*x*('at('diff(f(x),x,1),x = 0))-%e^x*f(0)*x+%e^x*f(0) sage: print(f) - ! - x d ! x x - f(x) = x %e (-- (f(x))! ) - f(0) x %e + f(0) %e - dx ! - !x = 0 + │ + x d │ x x + f(x) = %e x (── (f(x))│ ) - %e f(0) x + %e f(0) + dx │ + │x = 0 .. NOTE:: @@ -1094,10 +1094,10 @@ def __str__(self): sage: f = maxima('1/(x-1)^3'); f 1/(x-1)^3 sage: print(f) - 1 - -------- - 3 - (x - 1) + 1 + ──────── + 3 + (x - 1) """ return self.display2d(onscreen=False) @@ -1713,9 +1713,9 @@ def _latex_(self): sage: y,d = var('y,d') sage: f = function('f') sage: latex(maxima(derivative(f(x*y), x))) - \left(\left.{{{\it \partial}}\over{{\it \partial}\, {\it \_symbol}_{0}}}\,f\left( {\it \_symbol}_{0}\right)\right|_{ {\it \_symbol}_{0}={\it x}\, {\it y}}\right)\,{\it y} + \left(\left.{{{\it \partial}}\over{{\it \partial}\, {\it \_symbol}_{0}}}\,f\left({\it \_symbol}_{0} \right)\right|_{{\it \_symbol}_{0}={\it x}\, {\it y}}\right)\,{\it y} sage: latex(maxima(derivative(f(x,y,d), d,x,x,y))) - {{{\it \partial}^4}\over{{\it \partial}\,{\it d}\, {\it \partial}\,{\it x}^2\,{\it \partial}\, {\it y}}}\,f\left({\it x} , {\it y} , {\it d}\right) + {{{\it \partial}^4}\over{{\it \partial}\,{\it d}\, {\it \partial}\,{\it x}^2\,{\it \partial}\,{\it y} }}\,f\left({\it x} , {\it y} , {\it d} \right) sage: latex(maxima(d/(d-2))) {{{\it d}}\over{{\it d}-2}} """ @@ -1826,9 +1826,9 @@ def partial_fraction_decomposition(self, var='x'): sage: f.partial_fraction_decomposition('x') 1/(2*(x-1))-1/(2*(x+1)) sage: print(f.partial_fraction_decomposition('x')) - 1 1 - --------- - --------- - 2 (x - 1) 2 (x + 1) + 1 1 + ───────── - ───────── + 2 (x - 1) 2 (x + 1) """ return self.partfrac(var) diff --git a/src/sage/manifolds/chart.py b/src/sage/manifolds/chart.py index c9bc4c802f1..eeed8d5da00 100644 --- a/src/sage/manifolds/chart.py +++ b/src/sage/manifolds/chart.py @@ -3807,7 +3807,7 @@ def set_inverse(self, *transformations, **kwds): sage: spher_to_cart.set_inverse(sqrt(x^3+y^2), atan2(y,x)) Check of the inverse coordinate transformation: - r == sqrt(r*cos(ph)^3 + sin(ph)^2)*r **failed** + r == r*sqrt(abs(r*cos(ph)^3 + sin(ph)^2)) **failed** ph == arctan2(r*sin(ph), r*cos(ph)) **failed** x == sqrt(x^3 + y^2)*x/sqrt(x^2 + y^2) **failed** y == sqrt(x^3 + y^2)*y/sqrt(x^2 + y^2) **failed** diff --git a/src/sage/manifolds/differentiable/automorphismfield_group.py b/src/sage/manifolds/differentiable/automorphismfield_group.py index 45a2fad087a..11a548a0317 100644 --- a/src/sage/manifolds/differentiable/automorphismfield_group.py +++ b/src/sage/manifolds/differentiable/automorphismfield_group.py @@ -535,8 +535,7 @@ class AutomorphismFieldParalGroup(FreeModuleLinearGroup): Field of tangent-space automorphisms t^(-1) on the 2-dimensional differentiable manifold M sage: (t1^(-1)).display() - t^(-1) = 1/(e^y + 1) ∂/∂x⊗dx - x*y/(x^2 + (x^2 + 1)*e^y + 1) ∂/∂x⊗dy - + 1/(x^2 + 1) ∂/∂y⊗dy + t^(-1) = 1/(e^y + 1) ∂/∂x⊗dx - x*y/(x^2*(e^y + 1) + e^y + 1) ∂/∂x⊗dy + 1/(x^2 + 1) ∂/∂y⊗dy Since any automorphism field can be considered as a tensor field of type-`(1,1)` on ``M``, there is a coercion map from ``G`` to the diff --git a/src/sage/manifolds/differentiable/metric.py b/src/sage/manifolds/differentiable/metric.py index 01b48ef9724..43758ba7e73 100644 --- a/src/sage/manifolds/differentiable/metric.py +++ b/src/sage/manifolds/differentiable/metric.py @@ -1556,9 +1556,9 @@ def sqrt_abs_det(self, frame=None): [ 1/8*u^2 - 1/8*v^2 + 1/4*v + 1/2 1/4*u] [ 1/4*u -1/8*u^2 + 1/8*v^2 + 1/4*v + 1/2] sage: g.sqrt_abs_det(Y.frame()).expr() - 1/2*sqrt(-x^2*y^2 - (x + 1)*y + x + 1) + 1/2*sqrt(abs(x^2*y^2 + (x + 1)*y - x - 1)) sage: g.sqrt_abs_det(Y.frame()).expr(Y) - 1/8*sqrt(-u^4 - v^4 + 2*(u^2 + 2)*v^2 - 4*u^2 + 16*v + 16) + 1/8*sqrt(abs(u^4 + v^4 - 2*(u^2 + 2)*v^2 + 4*u^2 - 16*v - 16)) A chart can be passed instead of a frame:: @@ -1578,9 +1578,9 @@ def sqrt_abs_det(self, frame=None): sage: g.sqrt_abs_det().expr() sqrt(-x**2*y**2 - x*y + x - y + 1) sage: g.sqrt_abs_det(Y.frame()).expr() - sqrt(-x**2*y**2 - x*y + x - y + 1)/2 + sqrt(Abs(x**2*y**2 + x*y - x + y - 1))/2 sage: g.sqrt_abs_det(Y.frame()).expr(Y) - sqrt(-u**4 + 2*u**2*v**2 - 4*u**2 - v**4 + 4*v**2 + 16*v + 16)/8 + sqrt(Abs(-u**4 + 2*u**2*v**2 - 4*u**2 - v**4 + 4*v**2 + 16*v + 16))/8 """ dom = self._domain if frame is None: diff --git a/src/sage/manifolds/utilities.py b/src/sage/manifolds/utilities.py index b1eed3b8b2e..57b35bef6cc 100644 --- a/src/sage/manifolds/utilities.py +++ b/src/sage/manifolds/utilities.py @@ -225,10 +225,10 @@ class SimplifyAbsTrig(ExpressionTreeWalker): sage: a = abs(cos(x)) + abs(sin(x)) The method :meth:`~sage.symbolic.expression.Expression.simplify_full()` - is ineffective on such an expression:: + works on such an expression:: sage: a.simplify_full() - abs(cos(x)) + abs(sin(x)) + -cos(x) + sin(x) We construct a :class:`SimplifyAbsTrig` object ``s`` from the symbolic expression ``a``:: @@ -436,9 +436,9 @@ def simplify_abs_trig(expr): sage: s = abs(sin(x)) + abs(sin(y)) + abs(sin(3*z)) sage: s.simplify_trig() - abs(4*cos(-z)^2 - 1)*abs(sin(-z)) + abs(sin(x)) + abs(sin(y)) + -4*sin(-z)^3 + abs(sin(x)) + sin(y) + 3*sin(-z) sage: s.simplify_full() - abs(4*cos(-z)^2 - 1)*abs(sin(-z)) + abs(sin(x)) + abs(sin(y)) + -4*sin(-z)^3 + abs(sin(x)) + sin(y) + 3*sin(-z) despite the following assumptions hold:: @@ -571,10 +571,10 @@ def simplify_chain_real(expr): sage: s = abs(sin(pi*x)) sage: simplify_chain_real(s) # correct output since x in (0,1) sin(pi*x) - sage: s.simplify_real() # unsimplified output - abs(sin(pi*x)) - sage: s.simplify_full() # unsimplified output - abs(sin(pi*x)) + sage: s.simplify_real() # simplified output with maxima>=5.48 + sin(pi*x) + sage: s.simplify_full() # simplified output with maxima>=5.48 + sin(pi*x) :: diff --git a/src/sage/matrix/matrix2.pyx b/src/sage/matrix/matrix2.pyx index a6fbac8b102..9474f6b48b4 100644 --- a/src/sage/matrix/matrix2.pyx +++ b/src/sage/matrix/matrix2.pyx @@ -16693,8 +16693,8 @@ cdef class Matrix(Matrix1): sage: # needs sage.symbolic sage: a = matrix([[1,2], [3,4]]) sage: a.exp() - [-1/22*((sqrt(33) - 11)*e^sqrt(33) - sqrt(33) - 11)*e^(-1/2*sqrt(33) + 5/2) 2/33*(sqrt(33)*e^sqrt(33) - sqrt(33))*e^(-1/2*sqrt(33) + 5/2)] - [ 1/11*(sqrt(33)*e^sqrt(33) - sqrt(33))*e^(-1/2*sqrt(33) + 5/2) 1/22*((sqrt(33) + 11)*e^sqrt(33) - sqrt(33) + 11)*e^(-1/2*sqrt(33) + 5/2)] + [ 1/22*((sqrt(33) + 11)*e^2 - (sqrt(33) - 11)*e^(sqrt(33) + 2))*e^(-1/2*sqrt(33) + 1/2) -2/33*(sqrt(33)*e^2 - sqrt(33)*e^(sqrt(33) + 2))*e^(-1/2*sqrt(33) + 1/2)] + [ -1/11*(sqrt(33)*e^2 - sqrt(33)*e^(sqrt(33) + 2))*e^(-1/2*sqrt(33) + 1/2) -1/22*((sqrt(33) - 11)*e^2 - (sqrt(33) + 11)*e^(sqrt(33) + 2))*e^(-1/2*sqrt(33) + 1/2)] sage: type(a.exp()) # needs sage.symbolic diff --git a/src/sage/misc/functional.py b/src/sage/misc/functional.py index 07170cde870..9ac3a8b6658 100644 --- a/src/sage/misc/functional.py +++ b/src/sage/misc/functional.py @@ -721,9 +721,7 @@ def integral(x, *args, **kwds): real sage: f = exp(-x) * sinh(sqrt(x)) sage: t = integrate(f, x, 0, Infinity); t # long time - 1/4*sqrt(pi)*(erf(1) - 1)*e^(1/4) - - 1/4*(sqrt(pi)*(erf(1) - 1) - sqrt(pi) + 2*e^(-1) - 2)*e^(1/4) - + 1/4*sqrt(pi)*e^(1/4) - 1/2*e^(1/4) + 1/2*e^(-3/4) + 1/2*sqrt(pi)*e^(1/4) sage: t.canonicalize_radical() # long time 1/2*sqrt(pi)*e^(1/4) sage: sage.calculus.calculus.maxima('domain: complex') @@ -932,7 +930,7 @@ def krull_dimension(x): 0 sage: ZZ.krull_dimension() 1 - sage: ZZ[sqrt(5)].krull_dimension() # needs sage.rings.number_field sage.symbolic + sage: ZZ[sqrt(5)].krull_dimension() # needs sage.rings.number_field sage.symbolic 1 sage: U. = PolynomialRing(ZZ, 3); U Multivariate Polynomial Ring in x, y, z over Integer Ring diff --git a/src/sage/symbolic/expression.pyx b/src/sage/symbolic/expression.pyx index ad57fb7be20..3820b5146b3 100644 --- a/src/sage/symbolic/expression.pyx +++ b/src/sage/symbolic/expression.pyx @@ -13016,21 +13016,21 @@ cdef class Expression(Expression_abc): Check that the sum in :issue:`10682` is done right:: sage: sum(binomial(n,k)*k^2, k, 2, n) - 1/4*(n^2 + n)*2^n - n + 1/4*2^n*n^2 + 1/4*(2^n - 4)*n This sum used to give a wrong result (:issue:`9635`) but now gives correct results with all relevant assumptions:: sage: (n,k,j)=var('n,k,j') sage: sum(binomial(n,k)*binomial(k-1,j)*(-1)**(k-1-j),k,j+1,n) - -(-1)^j*sum((-1)^k*binomial(k - 1, j)*binomial(n, k), k, j + 1, n) + -sum((-1)^(-j + k)*binomial(k - 1, j)*binomial(n, k), k, j + 1, n) sage: assume(j>-1) sage: sum(binomial(n,k)*binomial(k-1,j)*(-1)**(k-1-j),k,j+1,n) 1 sage: forget() sage: assume(n>=j) sage: sum(binomial(n,k)*binomial(k-1,j)*(-1)**(k-1-j),k,j+1,n) - -(-1)^j*sum((-1)^k*binomial(k - 1, j)*binomial(n, k), k, j + 1, n) + -sum((-1)^(-j + k)*binomial(k - 1, j)*binomial(n, k), k, j + 1, n) sage: forget() sage: assume(j==-1) sage: sum(binomial(n,k)*binomial(k-1,j)*(-1)**(k-1-j),k,j+1,n) @@ -13038,7 +13038,7 @@ cdef class Expression(Expression_abc): sage: forget() sage: assume(j<-1) sage: sum(binomial(n,k)*binomial(k-1,j)*(-1)**(k-1-j),k,j+1,n) - -(-1)^j*sum((-1)^k*binomial(k - 1, j)*binomial(n, k), k, j + 1, n) + -sum((-1)^(-j + k)*binomial(k - 1, j)*binomial(n, k), k, j + 1, n) sage: forget() Check that :issue:`16176` is fixed:: diff --git a/src/sage/tests/books/computational-mathematics-with-sagemath/calculus_doctest.py b/src/sage/tests/books/computational-mathematics-with-sagemath/calculus_doctest.py index b5531b112b4..15f74fe5779 100644 --- a/src/sage/tests/books/computational-mathematics-with-sagemath/calculus_doctest.py +++ b/src/sage/tests/books/computational-mathematics-with-sagemath/calculus_doctest.py @@ -256,7 +256,7 @@ Sage example in ./calculus.tex, line 1086:: sage: solve(x^(1/x)==(1/x)^x, x) - [(1/x)^x == x^(1/x)] + [x^(1/x) == (1/x)^x] Sage example in ./calculus.tex, line 1124:: From 515647d122874e4714d05e61c4cfa36885d8c33a Mon Sep 17 00:00:00 2001 From: Antonio Rojas Date: Sun, 24 Aug 2025 19:31:02 +0200 Subject: [PATCH 2/8] Add correspondences for real part and imaginary part functions --- src/sage/interfaces/maxima_lib.py | 2 ++ 1 file changed, 2 insertions(+) diff --git a/src/sage/interfaces/maxima_lib.py b/src/sage/interfaces/maxima_lib.py index 760c15ecc5b..c4fd10ca599 100644 --- a/src/sage/interfaces/maxima_lib.py +++ b/src/sage/interfaces/maxima_lib.py @@ -1245,6 +1245,8 @@ def reduce_load_MaximaLib(): sage.functions.error.erf: "%ERF", sage.functions.gamma.gamma_inc: "%GAMMA_INCOMPLETE", sage.functions.other.conjugate: "$CONJUGATE", + sage.functions.other.imag_part: "%IMAGPART", + sage.functions.other.real_part: "%REALPART", } # we compile the dictionary sage_op_dict = {k: EclObject(sage_op_dict[k]) for k in sage_op_dict} From 2857c8376818575a1517e4b114946f6be8300e42 Mon Sep 17 00:00:00 2001 From: Antonio Rojas Date: Sun, 24 Aug 2025 23:44:37 +0200 Subject: [PATCH 3/8] Adapt to upstream rename of pcprntd --- src/sage/interfaces/maxima_lib.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/sage/interfaces/maxima_lib.py b/src/sage/interfaces/maxima_lib.py index c4fd10ca599..adabe1b0aea 100644 --- a/src/sage/interfaces/maxima_lib.py +++ b/src/sage/interfaces/maxima_lib.py @@ -164,7 +164,7 @@ ecl_eval("(initialize-runtime-globals)") ecl_eval("(setq $nolabels t))") ecl_eval("(defun add-lineinfo (x) x)") -ecl_eval('(defun principal nil (cond ($noprincipal (diverg)) ((not pcprntd) (merror "Divergent Integral"))))') +ecl_eval('(defun principal nil (cond ($noprincipal (diverg)) ((not *pcprntd*) (merror "Divergent Integral"))))') ecl_eval("(remprop 'mfactorial 'grind)") # don't use ! for factorials (#11539) ecl_eval("(setf $errormsg nil)") From 53290d02dfe4ff3f3106c488a34e341508c6fb43 Mon Sep 17 00:00:00 2001 From: Antonio Rojas Date: Sun, 24 Aug 2025 23:49:15 +0200 Subject: [PATCH 4/8] More test fixes --- src/sage/functions/bessel.py | 10 +++++----- src/sage/symbolic/integration/external.py | 7 +------ src/sage/symbolic/integration/integral.py | 7 ++----- 3 files changed, 8 insertions(+), 16 deletions(-) diff --git a/src/sage/functions/bessel.py b/src/sage/functions/bessel.py index 1cd132b3a45..4ead3c47c45 100644 --- a/src/sage/functions/bessel.py +++ b/src/sage/functions/bessel.py @@ -1673,7 +1673,7 @@ class SphericalBesselJ(BuiltinFunction): sage: spherical_bessel_J(4, x).simplify() -((45/x^2 - 105/x^4 - 1)*sin(x) + 5*(21/x^2 - 2)*cos(x)/x)/x sage: integrate(spherical_bessel_J(1,x)^2,(x,0,oo)) - 1/6*pi + 0 sage: latex(spherical_bessel_J(4, x)) j_{4}\left(x\right) @@ -1772,7 +1772,7 @@ class SphericalBesselY(BuiltinFunction): sage: integrate(spherical_bessel_Y(0, x), x) -1/2*Ei(I*x) - 1/2*Ei(-I*x) sage: integrate(spherical_bessel_Y(1,x)^2,(x,0,oo)) - -1/6*pi + 0 sage: latex(spherical_bessel_Y(0, x)) y_{0}\left(x\right) @@ -1867,7 +1867,7 @@ class SphericalHankel1(BuiltinFunction): sage: spherical_hankel1(3 + 0.2 * I, 3) 0.201654587512037 - 0.531281544239273*I sage: spherical_hankel1(1, x).simplify() - -(x + I)*e^(I*x)/x^2 + -I*(-I*x + 1)*e^(I*x)/x^2 sage: spherical_hankel1(3 + 2 * I, 5 - 0.2 * I) 1.25375216869913 - 0.518011435921789*I sage: integrate(spherical_hankel1(3, x), x) @@ -1965,11 +1965,11 @@ class SphericalHankel2(BuiltinFunction): sage: spherical_hankel2(3 + 0.2 * I, 3) 0.0998874108557565 + 0.479149050937147*I sage: spherical_hankel2(1, x).simplify() - -(x - I)*e^(-I*x)/x^2 + I*(I*x + 1)*e^(-I*x)/x^2 sage: spherical_hankel2(2,i).simplify() -e sage: spherical_hankel2(2,x).simplify() - (-I*x^2 - 3*x + 3*I)*e^(-I*x)/x^3 + -I*(x^2 - 3*I*x - 3)*e^(-I*x)/x^3 sage: spherical_hankel2(3 + 2*I, 5 - 0.2*I) 0.0217627632692163 + 0.0224001906110906*I sage: integrate(spherical_hankel2(3, x), x) diff --git a/src/sage/symbolic/integration/external.py b/src/sage/symbolic/integration/external.py index 1390c524300..4d52d4ab963 100644 --- a/src/sage/symbolic/integration/external.py +++ b/src/sage/symbolic/integration/external.py @@ -30,12 +30,7 @@ def maxima_integrator(expression, v, a=None, b=None): Check that :issue:`25817` is fixed:: sage: maxima_integrator(log(e^x*log(x)*sin(x))/x^2, x) - 1/2*(x*(Ei(-log(x)) + conjugate(Ei(-log(x)))) - - 2*x*integrate(sin(x)/(x*cos(x)^2 + x*sin(x)^2 - + 2*x*cos(x) + x), x) + 2*x*integrate(sin(x)/(x*cos(x)^2 - + x*sin(x)^2 - 2*x*cos(x) + x), x) + 2*x*log(x) + 2*log(2) - - log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - log(cos(x)^2 - + sin(x)^2 - 2*cos(x) + 1) - 2*log(log(x)))/x + -1/2*(2*x*integrate(sin(x)/(x*cos(x)^2 + x*sin(x)^2 + 2*x*cos(x) + x), x) - 2*x*integrate(sin(x)/(x*cos(x)^2 + x*sin(x)^2 - 2*x*cos(x) + x), x) - 2*x*log(x) - 2*x*real_part(Ei(-log(x))) - 2*log(2) + log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) + 2*log(log(x)))/x """ from sage.calculus.calculus import maxima if not isinstance(expression, Expression): diff --git a/src/sage/symbolic/integration/integral.py b/src/sage/symbolic/integration/integral.py index 4a70d373516..096ca779a71 100644 --- a/src/sage/symbolic/integration/integral.py +++ b/src/sage/symbolic/integration/integral.py @@ -614,10 +614,7 @@ def integrate(expression, v=None, a=None, b=None, algorithm=None, hold=False): x y + Sqrt[--] FresnelS[Sqrt[--] x] 2 Pi sage: print(f.integral(x)) - x*y^z + 1/16*sqrt(pi)*((I + 1)*sqrt(2)*erf((1/2*I + 1/2)*sqrt(2)*x) - + (I - 1)*sqrt(2)*erf((1/2*I - 1/2)*sqrt(2)*x) - - (I - 1)*sqrt(2)*erf(sqrt(-I)*x) - + (I + 1)*sqrt(2)*erf((-1)^(1/4)*x)) + x*y^z + 1/16*sqrt(pi)*((I + 1)*sqrt(2)*erf((1/2*I + 1/2)*sqrt(2)*x) - (I - 1)*sqrt(2)*erf(sqrt(-I)*x) - 2*sqrt(2)*imag_part(erf((-1)^(1/4)*x)) + 2*sqrt(2)*real_part(erf((-1)^(1/4)*x))) Alternatively, just use algorithm='mathematica_free' to integrate via Mathematica over the internet (does NOT require a Mathematica license!):: @@ -1076,7 +1073,7 @@ def integrate(expression, v=None, a=None, b=None, algorithm=None, hold=False): sage: assume(a > 0) sage: assume(a < 1) sage: integrate(x*log(1/(a*x+(1-x)^2)), x, 0, 1, algorithm='maxima') - 1/4*a^2*log(a) + 1/2*sqrt(-a^2 + 4*a)*a*arctan(sqrt(-a^2 + 4*a)*(a - 2)/(a^2 - 4*a)) - 1/2*sqrt(-a^2 + 4*a)*a*arctan(sqrt(-a^2 + 4*a)/(a - 4)) - a*log(a) - sqrt(-a^2 + 4*a)*arctan(sqrt(-a^2 + 4*a)*(a - 2)/(a^2 - 4*a)) + sqrt(-a^2 + 4*a)*arctan(sqrt(-a^2 + 4*a)/(a - 4)) - 1/2*a + 3/2 + 1/4*a^2*log(a) - 1/2*sqrt(-a^2 + 4*a)*a*arctan(sqrt(-a^2 + 4*a)/(a - 4)) + 1/2*sqrt(-a^2 + 4*a)*a*arctan(sqrt(-a^2 + 4*a)*(a - 2)/((a - 4)*a)) - a*log(a) + sqrt(-a^2 + 4*a)*arctan(sqrt(-a^2 + 4*a)/(a - 4)) - sqrt(-a^2 + 4*a)*arctan(sqrt(-a^2 + 4*a)*(a - 2)/((a - 4)*a)) - 1/2*a + 3/2 Check that :issue:`25905` is fixed:: From 9aa8aefc7c29191f39641af7caf43df61a6936eb Mon Sep 17 00:00:00 2001 From: Antonio Rojas Date: Sun, 24 Aug 2025 23:53:00 +0200 Subject: [PATCH 5/8] Update maxima to 5.48.1 --- build/pkgs/maxima/checksums.ini | 4 ++-- build/pkgs/maxima/package-version.txt | 2 +- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/build/pkgs/maxima/checksums.ini b/build/pkgs/maxima/checksums.ini index 2b0e2828df0..e764b01f4a6 100644 --- a/build/pkgs/maxima/checksums.ini +++ b/build/pkgs/maxima/checksums.ini @@ -1,4 +1,4 @@ tarball=maxima-VERSION.tar.gz -sha1=fff13f4c010e6daab65fbc8a6895c2bd79925177 -sha256=9104021b24fd53e8c03a983509cb42e937a925e8c0c85c335d7709a14fd40f7a +sha1=c560b853864f333e999e475607de77facb9f358e +sha256=b0916b5fb37b6eeaae400083175e68e28f80b9a1ab580c106a05448cf1c496b2 upstream_url=https://sourceforge.net/projects/maxima/files/Maxima-source/VERSION-source/maxima-VERSION.tar.gz/download diff --git a/build/pkgs/maxima/package-version.txt b/build/pkgs/maxima/package-version.txt index 5ddc1d087c6..297c7a9e65d 100644 --- a/build/pkgs/maxima/package-version.txt +++ b/build/pkgs/maxima/package-version.txt @@ -1 +1 @@ -5.47.0 +5.48.1 From a51e99eb4095625fe0f90acfd29c721f659c5a45 Mon Sep 17 00:00:00 2001 From: Antonio Rojas Date: Sun, 24 Aug 2025 23:59:06 +0200 Subject: [PATCH 6/8] Fix ruff --- src/sage/interfaces/maxima.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/sage/interfaces/maxima.py b/src/sage/interfaces/maxima.py index a092c37e9a5..a916796341b 100644 --- a/src/sage/interfaces/maxima.py +++ b/src/sage/interfaces/maxima.py @@ -180,7 +180,7 @@ You can even nicely typeset the solution in latex:: sage: latex(s) - \left[ \left[ a=-\left({{\sqrt{79}\,i-11}\over{4}}\right) , b={{\sqrt{79}\,i +9}\over{4}} , c={{\sqrt{79}\,i+1}\over{10}} \right] , \left[ a={{\sqrt{79} \,i+11}\over{4}} , b=-\left({{\sqrt{79}\,i-9}\over{4}}\right) , c=-\left({{ \sqrt{79}\,i-1}\over{10}}\right) \right] \right] + \left[ \left[ a=-\left({{\sqrt{79}\,i-11}\over{4}}\right) , b={{\sqrt{79}\,i +9}\over{4}} , c={{\sqrt{79}\,i+1}\over{10}} \right] , \left[ a={{\sqrt{79} \,i+11}\over{4}} , b=-\left({{\sqrt{79}\,i-9}\over{4}}\right) , c=-\left({{ \sqrt{79}\,i-1}\over{10}}\right) \right] \right] To have the above appear onscreen via ``xdvi``, type ``view(s)``. (TODO: For OS X should create pdf output From 53d01616c277233f6fee1069cc14074db236e8fe Mon Sep 17 00:00:00 2001 From: Antonio Rojas Date: Tue, 26 Aug 2025 09:54:28 +0200 Subject: [PATCH 7/8] Drop `principal` redefinition It seems to be no longer needed, and requires divergent code for different maxima versions --- src/sage/interfaces/maxima_lib.py | 1 - 1 file changed, 1 deletion(-) diff --git a/src/sage/interfaces/maxima_lib.py b/src/sage/interfaces/maxima_lib.py index adabe1b0aea..93ccf8e3ea6 100644 --- a/src/sage/interfaces/maxima_lib.py +++ b/src/sage/interfaces/maxima_lib.py @@ -164,7 +164,6 @@ ecl_eval("(initialize-runtime-globals)") ecl_eval("(setq $nolabels t))") ecl_eval("(defun add-lineinfo (x) x)") -ecl_eval('(defun principal nil (cond ($noprincipal (diverg)) ((not *pcprntd*) (merror "Divergent Integral"))))') ecl_eval("(remprop 'mfactorial 'grind)") # don't use ! for factorials (#11539) ecl_eval("(setf $errormsg nil)") From a58c077426d4a3f0a410f2acabaa2ef16769891c Mon Sep 17 00:00:00 2001 From: Antonio Rojas Date: Tue, 26 Aug 2025 11:54:14 +0200 Subject: [PATCH 8/8] Revert "Drop `principal` redefinition" This reverts commit 66f2485cccf63f5f28cc2f0cad68a7c323adc7b2. --- src/sage/interfaces/maxima_lib.py | 1 + 1 file changed, 1 insertion(+) diff --git a/src/sage/interfaces/maxima_lib.py b/src/sage/interfaces/maxima_lib.py index 93ccf8e3ea6..adabe1b0aea 100644 --- a/src/sage/interfaces/maxima_lib.py +++ b/src/sage/interfaces/maxima_lib.py @@ -164,6 +164,7 @@ ecl_eval("(initialize-runtime-globals)") ecl_eval("(setq $nolabels t))") ecl_eval("(defun add-lineinfo (x) x)") +ecl_eval('(defun principal nil (cond ($noprincipal (diverg)) ((not *pcprntd*) (merror "Divergent Integral"))))') ecl_eval("(remprop 'mfactorial 'grind)") # don't use ! for factorials (#11539) ecl_eval("(setf $errormsg nil)")