40679-Update_to_maxima_5.49.patch

diff --git a/src/sage/calculus/calculus.py b/src/sage/calculus/calculus.py
index 270e3c49058..0f64e09e18b 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::
@@ -1247,7 +1247,7 @@ 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
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/functions/bessel.py b/src/sage/functions/bessel.py
index db32eebe381..056bceaf49c 100644
--- a/src/sage/functions/bessel.py
+++ b/src/sage/functions/bessel.py
@@ -1864,7 +1864,7 @@ 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)
@@ -1962,11 +1962,11 @@ 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/interfaces/maxima.py b/src/sage/interfaces/maxima.py
index 154a2cc34e0..1eebc46e03a 100644
--- a/src/sage/interfaces/maxima.py
+++ b/src/sage/interfaces/maxima.py
@@ -194,7 +194,7 @@
 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
@@ -216,11 +216,11 @@
 ::
 
     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)
 
 ::
 
@@ -291,13 +291,14 @@
 
     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)
 
 ::
 
@@ -363,11 +364,11 @@
 
     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::
@@ -418,7 +419,7 @@
     sage: from sage.interfaces.maxima import maxima
     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 5866b955bb0..e7c1da2a277 100644
--- a/src/sage/interfaces/maxima_abstract.py
+++ b/src/sage/interfaces/maxima_abstract.py
@@ -866,11 +866,11 @@ 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])
@@ -910,20 +910,20 @@ def de_solve_laplace(self, de, vars, ics=None):
             sage: from sage.interfaces.maxima_lib import maxima
             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::
 
@@ -1136,10 +1136,10 @@ 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)
 
@@ -1798,9 +1798,9 @@ 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}}
         """
@@ -1929,9 +1929,9 @@ 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/interfaces/maxima_lib.py b/src/sage/interfaces/maxima_lib.py
index 637ef29a6f2..fff2a6ee39c 100644
--- a/src/sage/interfaces/maxima_lib.py
+++ b/src/sage/interfaces/maxima_lib.py
@@ -164,7 +164,7 @@
 ecl_eval("(setq $nolabels t))")
 ecl_eval("(defun add-lineinfo (x) x)")
 ecl_eval(r"(defun tex-derivative (x l r) (tex (if $derivabbrev (tex-dabbrev x) (tex-d x '\\partial)) l r lop rop ))")
-ecl_eval('(defun principal nil (cond ($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)")
 
@@ -1224,6 +1224,8 @@ 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}
diff --git a/src/sage/manifolds/chart.py b/src/sage/manifolds/chart.py
index 7232f0c4ddb..1240fe5ad83 100644
--- a/src/sage/manifolds/chart.py
+++ b/src/sage/manifolds/chart.py
@@ -3761,7 +3761,7 @@ def set_inverse(self, *transformations, **kwds):
             sage: spher_to_cart.set_inverse(sqrt(x^2+y^2), atan2(y,x))
             Check of the inverse coordinate transformation:
               r == r  *passed*
-              ph == arctan2(r*sin(ph), r*cos(ph))  **failed**
+              ph == -2*pi*ceil(-1/2*(pi - ph)/pi) + ph  **failed**
               x == x  *passed*
               y == y  *passed*
             NB: a failed report can reflect a mere lack of simplification.
@@ -3798,8 +3798,8 @@ 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**
-              ph == arctan2(r*sin(ph), r*cos(ph))  **failed**
+              r == r*sqrt(abs(r*cos(ph)^3 + sin(ph)^2))  **failed**
+              ph == -2*pi*ceil(-1/2*(pi - ph)/pi) + 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**
             NB: a failed report can reflect a mere lack of simplification.
diff --git a/src/sage/manifolds/continuous_map.py b/src/sage/manifolds/continuous_map.py
index e673f0ced6d..bd9db2f3e2b 100644
--- a/src/sage/manifolds/continuous_map.py
+++ b/src/sage/manifolds/continuous_map.py
@@ -1578,7 +1578,7 @@ def expr(self, chart1=None, chart2=None):
             sage: ch_spher_cart.set_inverse(sqrt(x^2+y^2), atan2(y,x))
             Check of the inverse coordinate transformation:
               r == r  *passed*
-              ph == arctan2(r*sin(ph), r*cos(ph))  **failed**
+              ph == -2*pi*ceil(-1/2*(pi - ph)/pi) + ph  **failed**
               x == x  *passed*
               y == y  *passed*
             NB: a failed report can reflect a mere lack of simplification.
@@ -1627,7 +1627,7 @@ def set_expr(self, chart1, chart2, coord_functions):
               x == x  *passed*
               y == y  *passed*
               r == r  *passed*
-              ph == arctan2(r*sin(ph), r*cos(ph))  **failed**
+              ph == -2*pi*ceil(-1/2*(pi - ph)/pi) + ph  **failed**
             NB: a failed report can reflect a mere lack of simplification.
             sage: rot = U.continuous_map(U, ((x - sqrt(3)*y)/2, (sqrt(3)*x + y)/2),
             ....:                        name='R')
@@ -1681,7 +1681,7 @@ def set_expr(self, chart1, chart2, coord_functions):
               x == x  *passed*
               y == y  *passed*
               r == r  *passed*
-              ph == arctan2(r*sin(ph), r*cos(ph))  **failed**
+              ph == -2*pi*ceil(-1/2*(pi - ph)/pi) + ph  **failed**
             NB: a failed report can reflect a mere lack of simplification.
             sage: rot = U.continuous_map(U, ((x - sqrt(3)*y)/2, (sqrt(3)*x + y)/2),
             ....:                        name='R')
@@ -1770,7 +1770,7 @@ def add_expr(self, chart1, chart2, coord_functions):
               x == x  *passed*
               y == y  *passed*
               r == r  *passed*
-              ph == arctan2(r*sin(ph), r*cos(ph))  **failed**
+              ph == -2*pi*ceil(-1/2*(pi - ph)/pi) + ph  **failed**
             NB: a failed report can reflect a mere lack of simplification.
             sage: rot = U.continuous_map(U, ((x - sqrt(3)*y)/2, (sqrt(3)*x + y)/2),
             ....:                        name='R')
@@ -1784,7 +1784,7 @@ def add_expr(self, chart1, chart2, coord_functions):
 
             sage: rot.display(c_spher, c_spher)
             R: U → U
-               (r, ph) ↦ (r, arctan2(1/2*(sqrt(3)*cos(ph) + sin(ph))*r, -1/2*(sqrt(3)*sin(ph) - cos(ph))*r))
+               (r, ph) ↦ (r, arctan2(1/2*sqrt(3)*cos(ph) + 1/2*sin(ph), -1/2*sqrt(3)*sin(ph) + 1/2*cos(ph)))
 
         Therefore, we use the method :meth:`add_expr` to set the
         spherical-coordinate expression by hand::
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/curve.py b/src/sage/manifolds/differentiable/curve.py
index 8a1cfc2e77e..9c1d518acc3 100644
--- a/src/sage/manifolds/differentiable/curve.py
+++ b/src/sage/manifolds/differentiable/curve.py
@@ -466,7 +466,7 @@ def coord_expr(self, chart=None):
               x == x  *passed*
               y == y  *passed*
               r == r  *passed*
-              ph == arctan2(r*sin(ph), r*cos(ph))  **failed**
+              ph == -2*pi*ceil(-1/2*(pi - ph)/pi) + ph  **failed**
             NB: a failed report can reflect a mere lack of simplification.
             sage: R.<t> = manifolds.RealLine()
             sage: c = U.curve({c_spher: (1,t)}, (t, 0, 2*pi), name='c')
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/differentiable/pseudo_riemannian_submanifold.py b/src/sage/manifolds/differentiable/pseudo_riemannian_submanifold.py
index 57dc1c99862..e7c7aaebeea 100644
--- a/src/sage/manifolds/differentiable/pseudo_riemannian_submanifold.py
+++ b/src/sage/manifolds/differentiable/pseudo_riemannian_submanifold.py
@@ -819,8 +819,7 @@ def normal(self):
             ....:                              atan2(-y,-x)+pi)
             Check of the inverse coordinate transformation:
               the == 2*arctan(sqrt(-cos(the) + 1)/sqrt(cos(the) + 1))  **failed**
-              phi == pi + arctan2(sin(phi)*sin(the)/(cos(the) - 1),
-                                  cos(phi)*sin(the)/(cos(the) - 1))  **failed**
+              phi == pi + arctan2(cos(the)*sin(phi) - sin(phi), cos(phi)*cos(the) - cos(phi))  **failed**
               x == x  *passed*
               y == y  *passed*
             NB: a failed report can reflect a mere lack of simplification.
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 7ff5a3a95bc..6c057a23bbe 100644
--- a/src/sage/matrix/matrix2.pyx
+++ b/src/sage/matrix/matrix2.pyx
@@ -16669,8 +16669,8 @@ 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
             <class 'sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense'>
diff --git a/src/sage/misc/functional.py b/src/sage/misc/functional.py
index 65a35b45a53..74ecc2198a6 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.<x,y,z> = 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 691acf2c947..07b191522c9 100644
--- a/src/sage/symbolic/expression.pyx
+++ b/src/sage/symbolic/expression.pyx
@@ -13019,21 +13019,21 @@ 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)
@@ -13041,7 +13041,7 @@ 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/symbolic/integration/external.py b/src/sage/symbolic/integration/external.py
index c99676c0b88..105e8e3bbbd 100644
--- a/src/sage/symbolic/integration/external.py
+++ b/src/sage/symbolic/integration/external.py
@@ -31,12 +31,7 @@ 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 b3d1dd1c2bf..1002343e884 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!)::
@@ -1011,8 +1008,8 @@ def integrate(expression, v=None, a=None, b=None, algorithm=None, hold=False):
         sage: f = log(sin(x))*sin(x)^2
         sage: g = integrate(f, x) ; g
         1/4*I*x^2
+        - 1/2*I*x*arctan2(-sin(x), -cos(x) + 1)
         - 1/2*I*x*arctan2(sin(x), cos(x) + 1)
-        + 1/2*I*x*arctan2(sin(x), -cos(x) + 1)
         - 1/4*x*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)
         - 1/4*x*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)
         + 1/4*(2*x - sin(2*x))*log(sin(x))
@@ -1036,7 +1033,7 @@ 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::
 
diff --git a/src/sage/symbolic/relation.py b/src/sage/symbolic/relation.py
index 8fada2b4e9b..02cfc43f282 100644
--- a/src/sage/symbolic/relation.py
+++ b/src/sage/symbolic/relation.py
@@ -1338,20 +1338,6 @@ def _solve_expression(f, x, explicit_solutions, multiplicities,
         sage: (x^2>1).solve(x)
         [[x < -1], [x > 1]]
 
-    Catch error message from Maxima::
-
-        sage: solve(acot(x),x)
-        Traceback (most recent call last):
-        ...
-        TypeError: ECL says: cot: argument 0 isn't in the domain of cot.
-
-    ::
-
-        sage: solve(acot(x),x,to_poly_solve=True)
-        Traceback (most recent call last):
-        ...
-        TypeError: ECL says: cot: argument 0 isn't in the domain of cot.
-
     :issue:`7491` fixed::
 
         sage: y = var('y')
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::