gh-35707: Make Sage work with maxima 5.47

    
Maxima 5.47 has been released. The main change that affects Sage is http
s://sourceforge.net/p/maxima/code/ci/f5ca00582c24cfedca53a664335f6c13e1e
40cf9, which makes the maxima ecl library crash because the `e-val`
variable is unassigned. We fix this by running the `initialize-runtime-
globals` function on load.

The remaining issues are a few harmless test failures caused by
numerical noise and output format changes (such as additional
parentheses near minus signs)
    
URL: #35707
Reported by: Antonio Rojas
Reviewer(s): Antonio Rojas, Gonzalo Tornaría, Michael Orlitzky

src/doc/de/tutorial/interfaces.rst

@@ -272,8 +272,8 @@ deren :math:`i,j` Eintrag gerade :math:`i/j` ist, für :math:`i,j=1,\ldots,4`.
     matrix([1,1/2,1/3,1/4],[0,0,0,0],[0,0,0,0],[0,0,0,0])
     sage: A.eigenvalues()
     [[0,4],[3,1]]
-    sage: A.eigenvectors()
-    [[[0,4],[3,1]],[[[1,0,0,-4],[0,1,0,-2],[0,0,1,-4/3]],[[1,2,3,4]]]]
+    sage: A.eigenvectors().sage()
+    [[[0, 4], [3, 1]], [[[1, 0, 0, -4], [0, 1, 0, -2], [0, 0, 1, -4/3]], [[1, 2, 3, 4]]]]
 
 Hier ein anderes Beispiel:
 
@@ -332,12 +332,9 @@ Und der letzte ist die berühmte Kleinsche Flasche:
 
 ::
 
-    sage: maxima("expr_1: 5*cos(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0) - 10.0")
-    5*cos(x)*(sin(x/2)*sin(2*y)+cos(x/2)*cos(y)+3.0)-10.0
-    sage: maxima("expr_2: -5*sin(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0)")
-    -5*sin(x)*(sin(x/2)*sin(2*y)+cos(x/2)*cos(y)+3.0)
-    sage: maxima("expr_3: 5*(-sin(x/2)*cos(y) + cos(x/2)*sin(2*y))")
-    5*(cos(x/2)*sin(2*y)-sin(x/2)*cos(y))
+    sage: _ = maxima("expr_1: 5*cos(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0) - 10.0")
+    sage: _ = maxima("expr_2: -5*sin(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0)")
+    sage: _ = maxima("expr_3: 5*(-sin(x/2)*cos(y) + cos(x/2)*sin(2*y))")
     sage: maxima.plot3d ("[expr_1, expr_2, expr_3]", "[x, -%pi, %pi]", # not tested
     ....:     "[y, -%pi, %pi]", "['grid, 40, 40]",
     ....:     '[plot_format, openmath]')

src/doc/de/tutorial/tour_algebra.rst

@@ -209,9 +209,12 @@ Lösung: Berechnen Sie die Laplace-Transformierte der ersten Gleichung
 
 ::
 
-    sage: de1 = maxima("2*diff(x(t),t, 2) + 6*x(t) - 2*y(t)")
-    sage: lde1 = de1.laplace("t","s"); lde1
-    2*((-%at('diff(x(t),t,1),t = 0))+s^2*'laplace(x(t),t,s)-x(0)*s) -2*'laplace(y(t),t,s)+6*'laplace(x(t),t,s)
+    sage: t,s = SR.var('t,s')
+    sage: x = function('x')
+    sage: y = function('y')
+    sage: f = 2*x(t).diff(t,2) + 6*x(t) - 2*y(t)
+    sage: f.laplace(t,s)
+    2*s^2*laplace(x(t), t, s) - 2*s*x(0) + 6*laplace(x(t), t, s) - 2*laplace(y(t), t, s) - 2*D[0](x)(0)
 
 Das ist schwierig zu lesen, es besagt jedoch, dass
 
@@ -226,8 +229,8 @@ Laplace-Transformierte der zweiten Gleichung:
 ::
 
     sage: de2 = maxima("diff(y(t),t, 2) + 2*y(t) - 2*x(t)")
-    sage: lde2 = de2.laplace("t","s"); lde2
-    (-%at('diff(y(t),t,1),t = 0))+s^2*'laplace(y(t),t,s) +2*'laplace(y(t),t,s)-2*'laplace(x(t),t,s) -y(0)*s
+    sage: lde2 = de2.laplace("t","s"); lde2.sage()
+    s^2*laplace(y(t), t, s) - s*y(0) - 2*laplace(x(t), t, s) + 2*laplace(y(t), t, s) - D[0](y)(0)
 
 Dies besagt
 

src/doc/en/constructions/linear_algebra.rst

@@ -277,8 +277,8 @@ Another approach is to use the interface with Maxima:
 
     sage: A = maxima("matrix ([1, -4], [1, -1])")
     sage: eig = A.eigenvectors()
-    sage: eig
-    [[[-sqrt(3)*%i,sqrt(3)*%i],[1,1]], [[[1,(sqrt(3)*%i+1)/4]],[[1,-(sqrt(3)*%i-1)/4]]]]
+    sage: eig.sage()
+    [[[-I*sqrt(3), I*sqrt(3)], [1, 1]], [[[1, 1/4*I*sqrt(3) + 1/4]], [[1, -1/4*I*sqrt(3) + 1/4]]]]
 
 This tells us that :math:`\vec{v}_1 = [1,(\sqrt{3}i + 1)/4]` is
 an eigenvector of :math:`\lambda_1 = - \sqrt{3}i` (which occurs

src/doc/en/tutorial/interfaces.rst

@@ -267,8 +267,8 @@ whose :math:`i,j` entry is :math:`i/j`, for
     matrix([1,1/2,1/3,1/4],[0,0,0,0],[0,0,0,0],[0,0,0,0])
     sage: A.eigenvalues()
     [[0,4],[3,1]]
-    sage: A.eigenvectors()
-    [[[0,4],[3,1]],[[[1,0,0,-4],[0,1,0,-2],[0,0,1,-4/3]],[[1,2,3,4]]]]
+    sage: A.eigenvectors().sage()
+    [[[0, 4], [3, 1]], [[[1, 0, 0, -4], [0, 1, 0, -2], [0, 0, 1, -4/3]], [[1, 2, 3, 4]]]]
 
 Here's another example:
 
@@ -320,8 +320,8 @@ The next plot is the famous Klein bottle (do not type the ``....:``)::
 
     sage: maxima("expr_1: 5*cos(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0) - 10.0")
     5*cos(x)*(sin(x/2)*sin(2*y)+cos(x/2)*cos(y)+3.0)-10.0
-    sage: maxima("expr_2: -5*sin(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0)")
-    -5*sin(x)*(sin(x/2)*sin(2*y)+cos(x/2)*cos(y)+3.0)
+    sage: maxima("expr_2: -5*sin(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0)").sage()
+    -5*(cos(1/2*x)*cos(y) + sin(1/2*x)*sin(2*y) + 3.0)*sin(x)
     sage: maxima("expr_3: 5*(-sin(x/2)*cos(y) + cos(x/2)*sin(2*y))")
     5*(cos(x/2)*sin(2*y)-sin(x/2)*cos(y))
     sage: maxima.plot3d ("[expr_1, expr_2, expr_3]", "[x, -%pi, %pi]",  # not tested

src/doc/en/tutorial/tour_algebra.rst

@@ -216,9 +216,12 @@ the notation :math:`x=x_{1}`, :math:`y=x_{2}`):
 
 ::
 
-    sage: de1 = maxima("2*diff(x(t),t, 2) + 6*x(t) - 2*y(t)")
-    sage: lde1 = de1.laplace("t","s"); lde1
-    2*((-%at('diff(x(t),t,1),t = 0))+s^2*'laplace(x(t),t,s)-x(0)*s) -2*'laplace(y(t),t,s)+6*'laplace(x(t),t,s)
+    sage: t,s = SR.var('t,s')
+    sage: x = function('x')
+    sage: y = function('y')
+    sage: f = 2*x(t).diff(t,2) + 6*x(t) - 2*y(t)
+    sage: f.laplace(t,s)
+    2*s^2*laplace(x(t), t, s) - 2*s*x(0) + 6*laplace(x(t), t, s) - 2*laplace(y(t), t, s) - 2*D[0](x)(0)
 
 This is hard to read, but it says that
 
@@ -232,8 +235,8 @@ Laplace transform of the second equation:
 ::
 
     sage: de2 = maxima("diff(y(t),t, 2) + 2*y(t) - 2*x(t)")
-    sage: lde2 = de2.laplace("t","s"); lde2
-    (-%at('diff(y(t),t,1),t = 0))+s^2*'laplace(y(t),t,s) +2*'laplace(y(t),t,s)-2*'laplace(x(t),t,s) -y(0)*s
+    sage: lde2 = de2.laplace("t","s"); lde2.sage()
+    s^2*laplace(y(t), t, s) - s*y(0) - 2*laplace(x(t), t, s) + 2*laplace(y(t), t, s) - D[0](y)(0)
 
 This says
 

src/doc/es/tutorial/tour_algebra.rst

@@ -197,8 +197,8 @@ la notación :math:`x=x_{1}`, :math:`y=x_{2}`):
 ::
 
     sage: de1 = maxima("2*diff(x(t),t, 2) + 6*x(t) - 2*y(t)")
-    sage: lde1 = de1.laplace("t","s"); lde1
-    2*((-%at('diff(x(t),t,1),t = 0))+s^2*'laplace(x(t),t,s)-x(0)*s) -2*'laplace(y(t),t,s)+6*'laplace(x(t),t,s)
+    sage: lde1 = de1.laplace("t","s"); lde1.sage()
+    2*s^2*laplace(x(t), t, s) - 2*s*x(0) + 6*laplace(x(t), t, s) - 2*laplace(y(t), t, s) - 2*D[0](x)(0)
 
 El resultado puede ser difícil de leer, pero significa que
 
@@ -211,9 +211,12 @@ Toma la transformada de Laplace de la segunda ecuación:
 
 ::
 
-    sage: de2 = maxima("diff(y(t),t, 2) + 2*y(t) - 2*x(t)")
-    sage: lde2 = de2.laplace("t","s"); lde2
-    (-%at('diff(y(t),t,1),t = 0))+s^2*'laplace(y(t),t,s) +2*'laplace(y(t),t,s)-2*'laplace(x(t),t,s) -y(0)*s
+    sage: t,s = SR.var('t,s')
+    sage: x = function('x')
+    sage: y = function('y')
+    sage: f = 2*x(t).diff(t,2) + 6*x(t) - 2*y(t)
+    sage: f.laplace(t,s)
+    2*s^2*laplace(x(t), t, s) - 2*s*x(0) + 6*laplace(x(t), t, s) - 2*laplace(y(t), t, s) - 2*D[0](x)(0)
 
 Esto dice
 

src/doc/fr/tutorial/interfaces.rst

@@ -273,8 +273,8 @@ pour :math:`i,j=1,\ldots,4`.
     matrix([1,1/2,1/3,1/4],[0,0,0,0],[0,0,0,0],[0,0,0,0])
     sage: A.eigenvalues()
     [[0,4],[3,1]]
-    sage: A.eigenvectors()
-    [[[0,4],[3,1]],[[[1,0,0,-4],[0,1,0,-2],[0,0,1,-4/3]],[[1,2,3,4]]]]
+    sage: A.eigenvectors().sage()
+    [[[0, 4], [3, 1]], [[[1, 0, 0, -4], [0, 1, 0, -2], [0, 0, 1, -4/3]], [[1, 2, 3, 4]]]]
 
 Un deuxième exemple :
 
@@ -334,12 +334,9 @@ Et la fameuse bouteille de Klein (n'entrez pas les ``....:``):
 
 ::
 
-    sage: maxima("expr_1: 5*cos(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0) - 10.0")
-    5*cos(x)*(sin(x/2)*sin(2*y)+cos(x/2)*cos(y)+3.0)-10.0
-    sage: maxima("expr_2: -5*sin(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0)")
-    -5*sin(x)*(sin(x/2)*sin(2*y)+cos(x/2)*cos(y)+3.0)
-    sage: maxima("expr_3: 5*(-sin(x/2)*cos(y) + cos(x/2)*sin(2*y))")
-    5*(cos(x/2)*sin(2*y)-sin(x/2)*cos(y))
+    sage: _ = maxima("expr_1: 5*cos(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0) - 10.0")
+    sage: _ = maxima("expr_2: -5*sin(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0)")
+    sage: _ = maxima("expr_3: 5*(-sin(x/2)*cos(y) + cos(x/2)*sin(2*y))")
     sage: maxima.plot3d ("[expr_1, expr_2, expr_3]", "[x, -%pi, %pi]", # not tested
     ....:     "[y, -%pi, %pi]", "['grid, 40, 40]",
     ....:     '[plot_format, openmath]')

src/doc/fr/tutorial/tour_algebra.rst

@@ -182,8 +182,8 @@ Solution : Considérons la transformée de Laplace de la première équation
 ::
 
     sage: de1 = maxima("2*diff(x(t),t, 2) + 6*x(t) - 2*y(t)")
-    sage: lde1 = de1.laplace("t","s"); lde1
-    2*((-%at('diff(x(t),t,1),t = 0))+s^2*'laplace(x(t),t,s)-x(0)*s) -2*'laplace(y(t),t,s)+6*'laplace(x(t),t,s)
+    sage: lde1 = de1.laplace("t","s"); lde1.sage()
+    2*s^2*laplace(x(t), t, s) - 2*s*x(0) + 6*laplace(x(t), t, s) - 2*laplace(y(t), t, s) - 2*D[0](x)(0)
 
 La réponse n'est pas très lisible, mais elle signifie que
 
@@ -196,9 +196,12 @@ la seconde équation :
 
 ::
 
-    sage: de2 = maxima("diff(y(t),t, 2) + 2*y(t) - 2*x(t)")
-    sage: lde2 = de2.laplace("t","s"); lde2
-    (-%at('diff(y(t),t,1),t = 0))+s^2*'laplace(y(t),t,s) +2*'laplace(y(t),t,s)-2*'laplace(x(t),t,s) -y(0)*s
+    sage: t,s = SR.var('t,s')
+    sage: x = function('x')
+    sage: y = function('y')
+    sage: f = 2*x(t).diff(t,2) + 6*x(t) - 2*y(t)
+    sage: f.laplace(t,s)
+    2*s^2*laplace(x(t), t, s) - 2*s*x(0) + 6*laplace(x(t), t, s) - 2*laplace(y(t), t, s) - 2*D[0](x)(0)
 
 Ceci signifie
 

src/doc/it/tutorial/tour_algebra.rst

@@ -183,8 +183,8 @@ la notazione :math:`x=x_{1}`, :math:`y=x_{2}`:
 ::
 
     sage: de1 = maxima("2*diff(x(t),t, 2) + 6*x(t) - 2*y(t)")
-    sage: lde1 = de1.laplace("t","s"); lde1
-    2*((-%at('diff(x(t),t,1),t = 0))+s^2*'laplace(x(t),t,s)-x(0)*s) -2*'laplace(y(t),t,s)+6*'laplace(x(t),t,s)
+    sage: lde1 = de1.laplace("t","s"); lde1.sage()
+    2*s^2*laplace(x(t), t, s) - 2*s*x(0) + 6*laplace(x(t), t, s) - 2*laplace(y(t), t, s) - 2*D[0](x)(0)
 
 Questo è di difficile lettura, ma dice che
 
@@ -197,9 +197,12 @@ trasformata di Laplace della seconda equazione:
 
 ::
 
-    sage: de2 = maxima("diff(y(t),t, 2) + 2*y(t) - 2*x(t)")
-    sage: lde2 = de2.laplace("t","s"); lde2
-    (-%at('diff(y(t),t,1),t = 0))+s^2*'laplace(y(t),t,s) +2*'laplace(y(t),t,s)-2*'laplace(x(t),t,s) -y(0)*s
+    sage: t,s = SR.var('t,s')
+    sage: x = function('x')
+    sage: y = function('y')
+    sage: f = 2*x(t).diff(t,2) + 6*x(t) - 2*y(t)
+    sage: f.laplace(t,s)
+    2*s^2*laplace(x(t), t, s) - 2*s*x(0) + 6*laplace(x(t), t, s) - 2*laplace(y(t), t, s) - 2*D[0](x)(0)
 
 che significa
 

src/doc/ja/tutorial/interfaces.rst

@@ -239,8 +239,8 @@ Sage/Maximaインターフェイスの使い方を例示するため，ここで
     matrix([1,1/2,1/3,1/4],[0,0,0,0],[0,0,0,0],[0,0,0,0])
     sage: A.eigenvalues()
     [[0,4],[3,1]]
-    sage: A.eigenvectors()
-    [[[0,4],[3,1]],[[[1,0,0,-4],[0,1,0,-2],[0,0,1,-4/3]],[[1,2,3,4]]]]
+    sage: A.eigenvectors().sage()
+    [[[0, 4], [3, 1]], [[[1, 0, 0, -4], [0, 1, 0, -2], [0, 0, 1, -4/3]], [[1, 2, 3, 4]]]]
 
 
 使用例をもう一つ示す:
@@ -299,11 +299,8 @@ Sage/Maximaインターフェイスの使い方を例示するため，ここで
 
 ::
 
-    sage: maxima("expr_1: 5*cos(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0) - 10.0")
-    5*cos(x)*(sin(x/2)*sin(2*y)+cos(x/2)*cos(y)+3.0)-10.0
-    sage: maxima("expr_2: -5*sin(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0)")
-    -5*sin(x)*(sin(x/2)*sin(2*y)+cos(x/2)*cos(y)+3.0)
-    sage: maxima("expr_3: 5*(-sin(x/2)*cos(y) + cos(x/2)*sin(2*y))")
-    5*(cos(x/2)*sin(2*y)-sin(x/2)*cos(y))
+    sage: _ = maxima("expr_1: 5*cos(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0) - 10.0")
+    sage: _ = maxima("expr_2: -5*sin(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0)")
+    sage: _ = maxima("expr_3: 5*(-sin(x/2)*cos(y) + cos(x/2)*sin(2*y))")
     sage: maxima.plot3d ("[expr_1, expr_2, expr_3]", "[x, -%pi, %pi]",  # not tested
     ....:     "[y, -%pi, %pi]", "['grid, 40, 40]", '[plot_format, openmath]')

src/doc/ja/tutorial/tour_algebra.rst

@@ -213,8 +213,8 @@ 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: de1 = maxima("2*diff(x(t),t, 2) + 6*x(t) - 2*y(t)")
-    sage: lde1 = de1.laplace("t","s"); lde1
-    2*((-%at('diff(x(t),t,1),t = 0))+s^2*'laplace(x(t),t,s)-x(0)*s) -2*'laplace(y(t),t,s)+6*'laplace(x(t),t,s)
+    sage: lde1 = de1.laplace("t","s"); lde1.sage()
+    2*s^2*laplace(x(t), t, s) - 2*s*x(0) + 6*laplace(x(t), t, s) - 2*laplace(y(t), t, s) - 2*D[0](x)(0)
 
 この出力は読みにくいけれども，意味しているのは
 
@@ -226,9 +226,12 @@ 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: de2 = maxima("diff(y(t),t, 2) + 2*y(t) - 2*x(t)")
-    sage: lde2 = de2.laplace("t","s"); lde2
-    (-%at('diff(y(t),t,1),t = 0))+s^2*'laplace(y(t),t,s) +2*'laplace(y(t),t,s)-2*'laplace(x(t),t,s) -y(0)*s
+    sage: t,s = SR.var('t,s')
+    sage: x = function('x')
+    sage: y = function('y')
+    sage: f = 2*x(t).diff(t,2) + 6*x(t) - 2*y(t)
+    sage: f.laplace(t,s)
+    2*s^2*laplace(x(t), t, s) - 2*s*x(0) + 6*laplace(x(t), t, s) - 2*laplace(y(t), t, s) - 2*D[0](x)(0)
 
 意味するところは
 

src/doc/pt/tutorial/interfaces.rst

@@ -269,8 +269,8 @@ entrada :math:`i,j` é :math:`i/j`, para :math:`i,j=1,\ldots,4`.
     matrix([1,1/2,1/3,1/4],[0,0,0,0],[0,0,0,0],[0,0,0,0])
     sage: A.eigenvalues()
     [[0,4],[3,1]]
-    sage: A.eigenvectors()
-    [[[0,4],[3,1]],[[[1,0,0,-4],[0,1,0,-2],[0,0,1,-4/3]],[[1,2,3,4]]]]
+    sage: A.eigenvectors().sage()
+    [[[0, 4], [3, 1]], [[[1, 0, 0, -4], [0, 1, 0, -2], [0, 0, 1, -4/3]], [[1, 2, 3, 4]]]]
 
 Aqui vai outro exemplo:
 
@@ -330,13 +330,10 @@ E agora a famosa garrafa de Klein:
 
 ::
 
-    sage: maxima("expr_1: 5*cos(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0)"
+    sage: _ = maxima("expr_1: 5*cos(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0)"
     ....:        "- 10.0")
-    5*cos(x)*(sin(x/2)*sin(2*y)+cos(x/2)*cos(y)+3.0)-10.0
-    sage: maxima("expr_2: -5*sin(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0)")
-    -5*sin(x)*(sin(x/2)*sin(2*y)+cos(x/2)*cos(y)+3.0)
-    sage: maxima("expr_3: 5*(-sin(x/2)*cos(y) + cos(x/2)*sin(2*y))")
-    5*(cos(x/2)*sin(2*y)-sin(x/2)*cos(y))
+    sage: _ = maxima("expr_2: -5*sin(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0)")
+    sage: _ = maxima("expr_3: 5*(-sin(x/2)*cos(y) + cos(x/2)*sin(2*y))")
     sage: maxima.plot3d("[expr_1, expr_2, expr_3]", "[x, -%pi, %pi]", # not tested
     ....:               "[y, -%pi, %pi]", "['grid, 40, 40]",
     ....:               '[plot_format, openmath]')

src/doc/pt/tutorial/tour_algebra.rst

@@ -205,8 +205,8 @@ equação (usando a notação :math:`x=x_{1}`, :math:`y=x_{2}`):
 ::
 
     sage: de1 = maxima("2*diff(x(t),t, 2) + 6*x(t) - 2*y(t)")
-    sage: lde1 = de1.laplace("t","s"); lde1
-    2*((-%at('diff(x(t),t,1),t = 0))+s^2*'laplace(x(t),t,s)-x(0)*s) -2*'laplace(y(t),t,s)+6*'laplace(x(t),t,s)
+    sage: lde1 = de1.laplace("t","s"); lde1.sage()
+    2*s^2*laplace(x(t), t, s) - 2*s*x(0) + 6*laplace(x(t), t, s) - 2*laplace(y(t), t, s) - 2*D[0](x)(0)
 
 O resultado é um pouco difícil de ler, mas diz que
 
@@ -219,9 +219,12 @@ calcule a transformada de Laplace da segunda equação:
 
 ::
 
-    sage: de2 = maxima("diff(y(t),t, 2) + 2*y(t) - 2*x(t)")
-    sage: lde2 = de2.laplace("t","s"); lde2
-    (-%at('diff(y(t),t,1),t = 0))+s^2*'laplace(y(t),t,s) +2*'laplace(y(t),t,s)-2*'laplace(x(t),t,s) -y(0)*s
+    sage: t,s = SR.var('t,s')
+    sage: x = function('x')
+    sage: y = function('y')
+    sage: f = 2*x(t).diff(t,2) + 6*x(t) - 2*y(t)
+    sage: f.laplace(t,s)
+    2*s^2*laplace(x(t), t, s) - 2*s*x(0) + 6*laplace(x(t), t, s) - 2*laplace(y(t), t, s) - 2*D[0](x)(0)
 
 O resultado significa que
 

src/doc/ru/tutorial/interfaces.rst

@@ -264,8 +264,8 @@ gnuplot, имеет методы решения и манипуляции мат
     matrix([1,1/2,1/3,1/4],[0,0,0,0],[0,0,0,0],[0,0,0,0])
     sage: A.eigenvalues()
     [[0,4],[3,1]]
-    sage: A.eigenvectors()
-    [[[0,4],[3,1]],[[[1,0,0,-4],[0,1,0,-2],[0,0,1,-4/3]],[[1,2,3,4]]]]
+    sage: A.eigenvectors().sage()
+    [[[0, 4], [3, 1]], [[[1, 0, 0, -4], [0, 1, 0, -2], [0, 0, 1, -4/3]], [[1, 2, 3, 4]]]]
 
 Вот другой пример:
 
@@ -323,12 +323,9 @@ gnuplot, имеет методы решения и манипуляции мат
 
 ::
 
-    sage: maxima("expr_1: 5*cos(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0) - 10.0")
-    5*cos(x)*(sin(x/2)*sin(2*y)+cos(x/2)*cos(y)+3.0)-10.0
-    sage: maxima("expr_2: -5*sin(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0)")
-    -5*sin(x)*(sin(x/2)*sin(2*y)+cos(x/2)*cos(y)+3.0)
-    sage: maxima("expr_3: 5*(-sin(x/2)*cos(y) + cos(x/2)*sin(2*y))")
-    5*(cos(x/2)*sin(2*y)-sin(x/2)*cos(y))
+    sage: _ = maxima("expr_1: 5*cos(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0) - 10.0")
+    sage: _ = maxima("expr_2: -5*sin(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)+ 3.0)")
+    sage: _ = maxima("expr_3: 5*(-sin(x/2)*cos(y) + cos(x/2)*sin(2*y))")
     sage: maxima.plot3d ("[expr_1, expr_2, expr_3]", "[x, -%pi, %pi]", # not tested
     ....:     "[y, -%pi, %pi]", "['grid, 40, 40]",
     ....:     '[plot_format, openmath]')

src/doc/ru/tutorial/tour_algebra.rst

@@ -199,8 +199,8 @@ Sage может использоваться для решения диффер
 ::
 
     sage: de1 = maxima("2*diff(x(t),t, 2) + 6*x(t) - 2*y(t)")
-    sage: lde1 = de1.laplace("t","s"); lde1
-    2*((-%at('diff(x(t),t,1),t = 0))+s^2*'laplace(x(t),t,s)-x(0)*s) -2*'laplace(y(t),t,s)+6*'laplace(x(t),t,s)
+    sage: lde1 = de1.laplace("t","s"); lde1.sage()
+    2*s^2*laplace(x(t), t, s) - 2*s*x(0) + 6*laplace(x(t), t, s) - 2*laplace(y(t), t, s) - 2*D[0](x)(0)
 
 Данный результат тяжело читаем, однако должен быть понят как
 
@@ -210,9 +210,12 @@ Sage может использоваться для решения диффер
 
 ::
 
-    sage: de2 = maxima("diff(y(t),t, 2) + 2*y(t) - 2*x(t)")
-    sage: lde2 = de2.laplace("t","s"); lde2
-    (-%at('diff(y(t),t,1),t = 0))+s^2*'laplace(y(t),t,s) +2*'laplace(y(t),t,s)-2*'laplace(x(t),t,s) -y(0)*s
+    sage: t,s = SR.var('t,s')
+    sage: x = function('x')
+    sage: y = function('y')
+    sage: f = 2*x(t).diff(t,2) + 6*x(t) - 2*y(t)
+    sage: f.laplace(t,s)
+    2*s^2*laplace(x(t), t, s) - 2*s*x(0) + 6*laplace(x(t), t, s) - 2*laplace(y(t), t, s) - 2*D[0](x)(0)
 
 Результат: