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void-packages/srcpkgs/sagemath/patches/35707-maxima_5.47.0.patch
Gonzalo Tornaría 2e2ae571d3 sagemath: patch and rebuild for maxima 5.47.0 
Also:
 - patch for singular 4.3.2p2
 - patch for numpy 1.25.0
 - patch for setuptools 68.0.0
2023-06-26 12:04:24 -04:00

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diff --git a/src/doc/de/tutorial/interfaces.rst b/src/doc/de/tutorial/interfaces.rst
index edb4f383363..d83225b5315 100644
--- a/src/doc/de/tutorial/interfaces.rst
+++ b/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]')
diff --git a/src/doc/de/tutorial/tour_algebra.rst b/src/doc/de/tutorial/tour_algebra.rst
index baba2553a25..59eed8f1888 100644
--- a/src/doc/de/tutorial/tour_algebra.rst
+++ b/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
diff --git a/src/doc/en/constructions/linear_algebra.rst b/src/doc/en/constructions/linear_algebra.rst
index 8894de9a5fd..4e76c65ad0a 100644
--- a/src/doc/en/constructions/linear_algebra.rst
+++ b/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
diff --git a/src/doc/en/tutorial/interfaces.rst b/src/doc/en/tutorial/interfaces.rst
index b0e55345669..19c28f636d4 100644
--- a/src/doc/en/tutorial/interfaces.rst
+++ b/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
diff --git a/src/doc/en/tutorial/tour_algebra.rst b/src/doc/en/tutorial/tour_algebra.rst
index 2e872cc9059..225606a729f 100644
--- a/src/doc/en/tutorial/tour_algebra.rst
+++ b/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
diff --git a/src/doc/es/tutorial/tour_algebra.rst b/src/doc/es/tutorial/tour_algebra.rst
index dc1a7a96719..42c818fe8d7 100644
--- a/src/doc/es/tutorial/tour_algebra.rst
+++ b/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
diff --git a/src/doc/fr/tutorial/interfaces.rst b/src/doc/fr/tutorial/interfaces.rst
index 1cd662f3083..2cb14e772eb 100644
--- a/src/doc/fr/tutorial/interfaces.rst
+++ b/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]')
diff --git a/src/doc/fr/tutorial/tour_algebra.rst b/src/doc/fr/tutorial/tour_algebra.rst
index 658894b2e8b..267bd1dd4f9 100644
--- a/src/doc/fr/tutorial/tour_algebra.rst
+++ b/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
diff --git a/src/doc/it/tutorial/tour_algebra.rst b/src/doc/it/tutorial/tour_algebra.rst
index 5a5311e9b1c..cde427d3090 100644
--- a/src/doc/it/tutorial/tour_algebra.rst
+++ b/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
diff --git a/src/doc/ja/tutorial/interfaces.rst b/src/doc/ja/tutorial/interfaces.rst
index 9c16b2eba08..892fc6f852f 100644
--- a/src/doc/ja/tutorial/interfaces.rst
+++ b/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]')
diff --git a/src/doc/ja/tutorial/tour_algebra.rst b/src/doc/ja/tutorial/tour_algebra.rst
index 784fd0d5c40..746cbb4475c 100644
--- a/src/doc/ja/tutorial/tour_algebra.rst
+++ b/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
diff --git a/src/doc/pt/tutorial/interfaces.rst b/src/doc/pt/tutorial/interfaces.rst
index 386ef6456e5..5badb31ab35 100644
--- a/src/doc/pt/tutorial/interfaces.rst
+++ b/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]')
diff --git a/src/doc/pt/tutorial/tour_algebra.rst b/src/doc/pt/tutorial/tour_algebra.rst
index baeb37b1c71..170e0d8a367 100644
--- a/src/doc/pt/tutorial/tour_algebra.rst
+++ b/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
diff --git a/src/doc/ru/tutorial/interfaces.rst b/src/doc/ru/tutorial/interfaces.rst
index ea84527f478..061818ca4a5 100644
--- a/src/doc/ru/tutorial/interfaces.rst
+++ b/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]')
diff --git a/src/doc/ru/tutorial/tour_algebra.rst b/src/doc/ru/tutorial/tour_algebra.rst
index 9f08c41d118..bc0d4926f83 100644
--- a/src/doc/ru/tutorial/tour_algebra.rst
+++ b/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:
diff --git a/src/sage/calculus/calculus.py b/src/sage/calculus/calculus.py
index c707530b9f1..f7ce8b95727 100644
--- a/src/sage/calculus/calculus.py
+++ b/src/sage/calculus/calculus.py
@@ -783,7 +783,7 @@ def nintegral(ex, x, a, b,
Now numerically integrating, we see why the answer is wrong::
sage: f.nintegrate(x,0,1)
- (-480.0000000000001, 5.32907051820075...e-12, 21, 0)
+ (-480.000000000000..., 5.32907051820075...e-12, 21, 0)
It is just because every floating point evaluation of return -480.0
in floating point.
@@ -1336,7 +1336,7 @@ def limit(ex, dir=None, taylor=False, algorithm='maxima', **argv):
sage: limit(floor(x), x=0, dir='+')
0
sage: limit(floor(x), x=0)
- und
+ ...nd
Maxima gives the right answer here, too, showing
that :trac:`4142` is fixed::
diff --git a/src/sage/calculus/desolvers.py b/src/sage/calculus/desolvers.py
index e0c31925f44..6e91f7e2bb4 100644
--- a/src/sage/calculus/desolvers.py
+++ b/src/sage/calculus/desolvers.py
@@ -295,7 +295,7 @@ def desolve(de, dvar, ics=None, ivar=None, show_method=False, contrib_ode=False,
Clairaut equation: general and singular solutions::
sage: desolve(diff(y,x)^2+x*diff(y,x)-y==0,y,contrib_ode=True,show_method=True)
- [[y(x) == _C^2 + _C*x, y(x) == -1/4*x^2], 'clairault']
+ [[y(x) == _C^2 + _C*x, y(x) == -1/4*x^2], 'clairau...']
For equations involving more variables we specify an independent variable::
@@ -1325,7 +1325,7 @@ def desolve_rk4(de, dvar, ics=None, ivar=None, end_points=None, step=0.1, output
sage: x,y = var('x,y')
sage: desolve_rk4(x*y*(2-y),y,ics=[0,1],end_points=1,step=0.5)
- [[0, 1], [0.5, 1.12419127424558], [1.0, 1.461590162288825]]
+ [[0, 1], [0.5, 1.12419127424558], [1.0, 1.46159016228882...]]
Variant 1 for input - we can pass ODE in the form used by
desolve function In this example we integrate backwards, since
@@ -1333,7 +1333,7 @@ def desolve_rk4(de, dvar, ics=None, ivar=None, end_points=None, step=0.1, output
sage: y = function('y')(x)
sage: desolve_rk4(diff(y,x)+y*(y-1) == x-2,y,ics=[1,1],step=0.5, end_points=0)
- [[0.0, 8.904257108962112], [0.5, 1.909327945361535], [1, 1]]
+ [[0.0, 8.904257108962112], [0.5, 1.90932794536153...], [1, 1]]
Here we show how to plot simple pictures. For more advanced
applications use list_plot instead. To see the resulting picture
diff --git a/src/sage/functions/bessel.py b/src/sage/functions/bessel.py
index 95405c3d72f..48607c49f56 100644
--- a/src/sage/functions/bessel.py
+++ b/src/sage/functions/bessel.py
@@ -293,9 +293,6 @@ class Function_Bessel_J(BuiltinFunction):
sage: f = bessel_J(2, x)
sage: f.integrate(x)
1/24*x^3*hypergeometric((3/2,), (5/2, 3), -1/4*x^2)
- sage: m = maxima(bessel_J(2, x))
- sage: m.integrate(x)
- (hypergeometric([3/2],[5/2,3],-_SAGE_VAR_x^2/4)*_SAGE_VAR_x^3)/24
Visualization (set plot_points to a higher value to get more detail)::
@@ -1118,11 +1115,11 @@ def Bessel(*args, **kwds):
Conversion to other systems::
sage: x,y = var('x,y')
- sage: f = maxima(Bessel(typ='K')(x,y))
- sage: f.derivative('_SAGE_VAR_x')
- (%pi*csc(%pi*_SAGE_VAR_x) *('diff(bessel_i(-_SAGE_VAR_x,_SAGE_VAR_y),_SAGE_VAR_x,1) -'diff(bessel_i(_SAGE_VAR_x,_SAGE_VAR_y),_SAGE_VAR_x,1))) /2 -%pi*bessel_k(_SAGE_VAR_x,_SAGE_VAR_y)*cot(%pi*_SAGE_VAR_x)
- sage: f.derivative('_SAGE_VAR_y')
- -(bessel_k(_SAGE_VAR_x+1,_SAGE_VAR_y)+bessel_k(_SAGE_VAR_x-1, _SAGE_VAR_y))/2
+ sage: f = Bessel(typ='K')(x,y)
+ sage: expected = f.derivative(y)
+ sage: actual = maxima(f).derivative('_SAGE_VAR_y').sage()
+ sage: bool(actual == expected)
+ True
Compute the particular solution to Bessel's Differential Equation that
satisfies `y(1) = 1` and `y'(1) = 1`, then verify the initial conditions
diff --git a/src/sage/functions/hypergeometric.py b/src/sage/functions/hypergeometric.py
index 752b8422fc6..fc2fb5875ce 100644
--- a/src/sage/functions/hypergeometric.py
+++ b/src/sage/functions/hypergeometric.py
@@ -19,8 +19,11 @@
sage: sum(((2*I)^x/(x^3 + 1)*(1/4)^x), x, 0, oo)
hypergeometric((1, 1, -1/2*I*sqrt(3) - 1/2, 1/2*I*sqrt(3) - 1/2),...
(2, -1/2*I*sqrt(3) + 1/2, 1/2*I*sqrt(3) + 1/2), 1/2*I)
- sage: sum((-1)^x/((2*x + 1)*factorial(2*x + 1)), x, 0, oo)
+ sage: res = sum((-1)^x/((2*x + 1)*factorial(2*x + 1)), x, 0, oo)
+ sage: res # not tested - depends on maxima version
hypergeometric((1/2,), (3/2, 3/2), -1/4)
+ sage: res in [hypergeometric((1/2,), (3/2, 3/2), -1/4), sin_integral(1)]
+ True
Simplification (note that ``simplify_full`` does not yet call
``simplify_hypergeometric``)::
diff --git a/src/sage/functions/orthogonal_polys.py b/src/sage/functions/orthogonal_polys.py
index 7398c763971..6127f5d9490 100644
--- a/src/sage/functions/orthogonal_polys.py
+++ b/src/sage/functions/orthogonal_polys.py
@@ -974,7 +974,7 @@ def __init__(self):
sage: chebyshev_U(x, x)._sympy_()
chebyshevu(x, x)
sage: maxima(chebyshev_U(2,x, hold=True))
- 3*((-(8*(1-_SAGE_VAR_x))/3)+(4*(1-_SAGE_VAR_x)^2)/3+1)
+ 3*(...-...(8*(1-_SAGE_VAR_x))/3)+(4*(1-_SAGE_VAR_x)^2)/3+1)
sage: maxima(chebyshev_U(n,x, hold=True))
chebyshev_u(_SAGE_VAR_n,_SAGE_VAR_x)
"""
diff --git a/src/sage/functions/other.py b/src/sage/functions/other.py
index 3e2570e889e..5a0f06a27f8 100644
--- a/src/sage/functions/other.py
+++ b/src/sage/functions/other.py
@@ -498,10 +498,10 @@ def __init__(self):
<class 'sage.rings.integer.Integer'>
sage: var('x')
x
- sage: a = floor(5.4 + x); a
- floor(x + 5.40000000000000)
+ sage: a = floor(5.25 + x); a
+ floor(x + 5.25000000000000)
sage: a.simplify()
- floor(x + 0.4000000000000004) + 5
+ floor(x + 0.25) + 5
sage: a(x=2)
7
diff --git a/src/sage/functions/special.py b/src/sage/functions/special.py
index faa6a73cc7e..d72e780836a 100644
--- a/src/sage/functions/special.py
+++ b/src/sage/functions/special.py
@@ -455,9 +455,8 @@ class EllipticE(BuiltinFunction):
sage: z = var("z")
sage: elliptic_e(z, 1)
elliptic_e(z, 1)
- sage: # this is still wrong: must be abs(sin(z)) + 2*round(z/pi)
- sage: elliptic_e(z, 1).simplify()
- 2*round(z/pi) + sin(z)
+ sage: elliptic_e(z, 1).simplify() # not tested - gives wrong answer with maxima < 5.47
+ 2*round(z/pi) - sin(pi*round(z/pi) - z)
sage: elliptic_e(z, 0)
z
sage: elliptic_e(0.5, 0.1) # abs tol 2e-15
diff --git a/src/sage/interfaces/interface.py b/src/sage/interfaces/interface.py
index 6baa4eb597c..f8237d3ad94 100644
--- a/src/sage/interfaces/interface.py
+++ b/src/sage/interfaces/interface.py
@@ -1579,20 +1579,20 @@ def _mul_(self, right):
::
sage: f = maxima.function('x','sin(x)')
- sage: g = maxima('-cos(x)') # not a function!
+ sage: g = maxima('cos(x)') # not a function!
sage: f*g
- -cos(x)*sin(x)
+ cos(x)*sin(x)
sage: _(2)
- -cos(2)*sin(2)
+ cos(2)*sin(2)
::
sage: f = maxima.function('x','sin(x)')
- sage: g = maxima('-cos(x)')
+ sage: g = maxima('cos(x)')
sage: g*f
- -cos(x)*sin(x)
+ cos(x)*sin(x)
sage: _(2)
- -cos(2)*sin(2)
+ cos(2)*sin(2)
sage: 2*f
2*sin(x)
"""
@@ -1612,20 +1612,20 @@ def _div_(self, right):
::
sage: f = maxima.function('x','sin(x)')
- sage: g = maxima('-cos(x)')
+ sage: g = maxima('cos(x)')
sage: f/g
- -sin(x)/cos(x)
+ sin(x)/cos(x)
sage: _(2)
- -sin(2)/cos(2)
+ sin(2)/cos(2)
::
sage: f = maxima.function('x','sin(x)')
- sage: g = maxima('-cos(x)')
+ sage: g = maxima('cos(x)')
sage: g/f
- -cos(x)/sin(x)
+ cos(x)/sin(x)
sage: _(2)
- -cos(2)/sin(2)
+ cos(2)/sin(2)
sage: 2/f
2/sin(x)
"""
diff --git a/src/sage/interfaces/maxima.py b/src/sage/interfaces/maxima.py
index 4829560f98b..959e75459a2 100644
--- a/src/sage/interfaces/maxima.py
+++ b/src/sage/interfaces/maxima.py
@@ -49,9 +49,14 @@
::
+ sage: x,y = SR.var('x,y')
sage: F = maxima.factor('x^5 - y^5')
- sage: F
- -(y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4)
+ sage: F # not tested - depends on maxima version
+ -((y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4))
+ sage: actual = F.sage()
+ sage: expected = -(y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4)
+ sage: bool(actual == expected)
+ True
sage: type(F)
<class 'sage.interfaces.maxima.MaximaElement'>
@@ -71,18 +76,19 @@
::
+ sage: F = maxima('x * y')
sage: repr(F)
- '-(y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4)'
+ 'x*y'
sage: F.str()
- '-(y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4)'
+ 'x*y'
The ``maxima.eval`` command evaluates an expression in
maxima and returns the result as a *string* not a maxima object.
::
- sage: print(maxima.eval('factor(x^5 - y^5)'))
- -(y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4)
+ sage: print(maxima.eval('factor(x^5 - 1)'))
+ (x-1)*(x^4+x^3+x^2+x+1)
We can create the polynomial `f` as a Maxima polynomial,
then call the factor method on it. Notice that the notation
@@ -91,11 +97,11 @@
::
- sage: f = maxima('x^5 - y^5')
+ sage: f = maxima('x^5 + y^5')
sage: f^2
- (x^5-y^5)^2
+ (y^5+x^5)^2
sage: f.factor()
- -(y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4)
+ (y+x)*(y^4-x*y^3+x^2*y^2-x^3*y+x^4)
Control-C interruption works well with the maxima interface,
because of the excellent implementation of maxima. For example, try
@@ -161,20 +167,20 @@
sage: eqn = maxima(['a+b*c=1', 'b-a*c=0', 'a+b=5'])
sage: s = eqn.solve('[a,b,c]'); s
- [[a = -(sqrt(79)*%i-11)/4,b = (sqrt(79)*%i+9)/4, c = (sqrt(79)*%i+1)/10], [a = (sqrt(79)*%i+11)/4,b = -(sqrt(79)*%i-9)/4, c = -(sqrt(79)*%i-1)/10]]
+ [[a = -...(sqrt(79)*%i-11)/4...,b = (sqrt(79)*%i+9)/4, c = (sqrt(79)*%i+1)/10], [a = (sqrt(79)*%i+11)/4,b = -...(sqrt(79)*%i-9)/4..., c = -...(sqrt(79)*%i-1)/10...]]
Here is an example of solving an algebraic equation::
sage: maxima('x^2+y^2=1').solve('y')
[y = -sqrt(1-x^2),y = sqrt(1-x^2)]
sage: maxima('x^2 + y^2 = (x^2 - y^2)/sqrt(x^2 + y^2)').solve('y')
- [y = -sqrt(((-y^2)-x^2)*sqrt(y^2+x^2)+x^2), y = sqrt(((-y^2)-x^2)*sqrt(y^2+x^2)+x^2)]
+ [y = -sqrt((...-y^2...-x^2)*sqrt(y^2+x^2)+x^2), y = sqrt((...-y^2...-x^2)*sqrt(y^2+x^2)+x^2)]
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=-...{{\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]
To have the above appear onscreen via ``xdvi``, type
``view(s)``. (TODO: For OS X should create pdf output
@@ -200,7 +206,7 @@
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)
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)
+ (((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)
::
@@ -234,7 +240,7 @@
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]]]]
+ [[[0,4],[3,1]],[[[1,0,0,-4],[0,1,0,-2],[0,0,1,-...4/3...]],[[1,2,3,4]]]]
We can also compute the echelon form in Sage::
@@ -287,12 +293,12 @@
::
sage: maxima("laplace(diff(x(t),t,2),t,s)")
- (-%at('diff(x(t),t,1),t = 0))+s^2*'laplace(x(t),t,s)-x(0)*s
+ ...-...%at('diff(x(t),t,1),t = 0))+s^2*'laplace(x(t),t,s)-x(0)*s
It is difficult to read some of these without the 2d
representation::
- sage: print(maxima("laplace(diff(x(t),t,2),t,s)"))
+ sage: print(maxima("laplace(diff(x(t),t,2),t,s)")) # not tested - depends on maxima version
!
d ! 2
(- -- (x(t))! ) + s laplace(x(t), t, s) - x(0) s
@@ -396,7 +402,7 @@
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
+ -...{{i\,e^{3\,i\,x}}\over{6}}...-{{i\,e^{i\,x}}\over{2}}+c
Long Input
----------
@@ -684,7 +690,7 @@ def _expect_expr(self, expr=None, timeout=None):
sage: maxima.assume('a>0')
[a > 0]
sage: maxima('integrate(1/(x^3*(a+b*x)^(1/3)),x)')
- (-(b^2*log((b*x+a)^(2/3)+a^(1/3)*(b*x+a)^(1/3)+a^(2/3)))/(9*a^(7/3))) +(2*b^2*atan((2*(b*x+a)^(1/3)+a^(1/3))/(sqrt(3)*a^(1/3))))/(3^(3/2)*a^(7/3)) +(2*b^2*log((b*x+a)^(1/3)-a^(1/3)))/(9*a^(7/3)) +(4*b^2*(b*x+a)^(5/3)-7*a*b^2*(b*x+a)^(2/3)) /(6*a^2*(b*x+a)^2-12*a^3*(b*x+a)+6*a^4)
+ ...-...(b^2*log((b*x+a)^(2/3)+a^(1/3)*(b*x+a)^(1/3)+a^(2/3)))/(9*a^(7/3))) +(2*b^2*atan((2*(b*x+a)^(1/3)+a^(1/3))/(sqrt(3)*a^(1/3))))/(3^(3/2)*a^(7/3)) +(2*b^2*log((b*x+a)^(1/3)-a^(1/3)))/(9*a^(7/3)) +(4*b^2*(b*x+a)^(5/3)-7*a*b^2*(b*x+a)^(2/3)) /(6*a^2*(b*x+a)^2-12*a^3*(b*x+a)+6*a^4)
sage: maxima('integrate(x^n,x)')
Traceback (most recent call last):
...
diff --git a/src/sage/interfaces/maxima_abstract.py b/src/sage/interfaces/maxima_abstract.py
index 4f6306ba4fc..aecfcba5e23 100644
--- a/src/sage/interfaces/maxima_abstract.py
+++ b/src/sage/interfaces/maxima_abstract.py
@@ -856,9 +856,9 @@ def de_solve(self, de, vars, ics=None):
sage: maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'])
y = %k1*%e^x+%k2*%e^-x+3*x
sage: maxima.de_solve('diff(y,x) + 3*x = y', ['x','y'])
- y = (%c-3*((-x)-1)*%e^-x)*%e^x
+ y = (%c-3*(...-x...-1)*%e^-x)*%e^x
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*(5*%e^x-3*%e*x-3*%e)...
"""
if not isinstance(vars, str):
str_vars = '%s, %s'%(vars[1], vars[0])
@@ -1572,8 +1572,9 @@ def integral(self, var='x', min=None, max=None):
::
- sage: f = maxima('exp(x^2)').integral('x',0,1); f
- -(sqrt(%pi)*%i*erf(%i))/2
+ sage: f = maxima('exp(x^2)').integral('x',0,1)
+ sage: f.sage()
+ -1/2*I*sqrt(pi)*erf(I)
sage: f.numer()
1.46265174590718...
"""
diff --git a/src/sage/interfaces/maxima_lib.py b/src/sage/interfaces/maxima_lib.py
index bba8504aa92..cd1be891872 100644
--- a/src/sage/interfaces/maxima_lib.py
+++ b/src/sage/interfaces/maxima_lib.py
@@ -134,10 +134,11 @@
else:
ecl_eval("(require 'maxima)")
ecl_eval("(in-package :maxima)")
-ecl_eval("(setq $nolabels t))")
-ecl_eval("(defvar *MAXIMA-LANG-SUBDIR* NIL)")
ecl_eval("(set-locale-subdir)")
+# This workaround has to happen before any call to (set-pathnames).
+# To be safe please do not call anything other than
+# (set-locale-subdir) before this block.
try:
ecl_eval("(set-pathnames)")
except RuntimeError:
@@ -154,6 +155,8 @@
# Call `(set-pathnames)` again to complete its job.
ecl_eval("(set-pathnames)")
+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)
diff --git a/src/sage/matrix/matrix1.pyx b/src/sage/matrix/matrix1.pyx
index f38c429d994..47df9fc80a5 100644
--- a/src/sage/matrix/matrix1.pyx
+++ b/src/sage/matrix/matrix1.pyx
@@ -248,7 +248,7 @@ cdef class Matrix(Matrix0):
sage: a = maxima(m); a
matrix([0,1,2],[3,4,5],[6,7,8])
sage: a.charpoly('x').expand()
- (-x^3)+12*x^2+18*x
+ ...-x^3...+12*x^2+18*x
sage: m.charpoly()
x^3 - 12*x^2 - 18*x
"""
diff --git a/src/sage/modules/free_module_element.pyx b/src/sage/modules/free_module_element.pyx
index 0532ea0c9bd..6ea2bd4473d 100644
--- a/src/sage/modules/free_module_element.pyx
+++ b/src/sage/modules/free_module_element.pyx
@@ -4053,7 +4053,7 @@ cdef class FreeModuleElement(Vector): # abstract base class
sage: t=var('t')
sage: r=vector([t,t^2,sin(t)])
sage: vec,answers=r.nintegral(t,0,1)
- sage: vec
+ sage: vec # abs tol 1e-15
(0.5, 0.3333333333333334, 0.4596976941318602)
sage: type(vec)
<class 'sage.modules.vector_real_double_dense.Vector_real_double_dense'>
diff --git a/src/sage/symbolic/relation.py b/src/sage/symbolic/relation.py
index a72ab547c76..51dcaf8d847 100644
--- a/src/sage/symbolic/relation.py
+++ b/src/sage/symbolic/relation.py
@@ -657,7 +657,7 @@ def solve(f, *args, **kwds):
equations, at times approximations will be given by Maxima, due to the
underlying algorithm::
- sage: sols = solve([x^3==y,y^2==x], [x,y]); sols[-1], sols[0]
+ sage: sols = solve([x^3==y,y^2==x], [x,y]); sols[-1], sols[0] # abs tol 1e-15
([x == 0, y == 0],
[x == (0.3090169943749475 + 0.9510565162951535*I),
y == (-0.8090169943749475 - 0.5877852522924731*I)])
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