Fix tests with maxima 5.48

antonio-rojas · antonio-rojas · commit c6e034cc84df · 2025-08-24T19:30:06.000+02:00
diff --git 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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
diff --git a/src/sage/matrix/matrix2.pyx b/src/sage/matrix/matrix2.pyx
diff --git a/src/sage/misc/functional.py b/src/sage/misc/functional.py
diff --git a/src/sage/symbolic/expression.pyx b/src/sage/symbolic/expression.pyx
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
