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last edited 2 years ago by test1 |
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Editor: test int
Time: 2018/06/10 12:51:40 GMT+0 |
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| Note: integrate(exp(x-x^2), x) | ||
added:
From testint Sun Jun 10 12:51:40 +0000 2018
From: test int
Date: Sun, 10 Jun 2018 12:51:40 +0000
Subject: integrate(exp(x-x^2), x)
Message-ID: <20180610125140+0000@axiom-wiki.newsynthesis.org>
\begin{axiom}
integrate((x+sin(x))^(1/2), x)
\end{axiom}
This page is set to execute \begin{axiom}... \end{axiom}
commands using FriCAS. See also FriCASIntegration.
fricas)version
Value = "FriCAS 1.3.3 compiled at Fri Mar 16 16:15:43 UTC 2018"
Any comments added here use this version of FriCAS?.
... --meliusja, Tue, 08 Apr 2008 10:38:33 -0700 replyfricassolve(s=v*t+a*t^2/2, t)
\begin{equation*}
\label{eq1}\left[{{{2 \ t \ v}+{a \ {{t}^{2}}}-{2 \ s}}= 0}\right]?\end{equation*}
Type: List(Equation(Fraction(Polynomial(Integer))))
fricasradicalSolve(s=v*t+a*t^2/2, t)
\begin{equation*}
\label{eq2}\left[{t ={{-{\sqrt{{4 \ {{v}^{2}}}+{8 \ a \ s}}}-{2 \ v}}\over{2 \ a}}}, \:{t ={{{\sqrt{{4 \ {{v}^{2}}}+{8 \ a \ s}}}-{2 \ v}}\over{2 \ a}}}\right]?\end{equation*}
Type: List(Equation(Expression(Integer)))
fricassolve(v*t+a*t^2/2-s=0, t)
\begin{equation*}
\label{eq3}\left[{{{2 \ t \ v}+{a \ {{t}^{2}}}-{2 \ s}}= 0}\right]?\end{equation*}
Type: List(Equation(Fraction(Polynomial(Integer))))
fricassolve(v*t+a*t/2-s=0, t)
\begin{equation*}
\label{eq4}\left[{t ={{2 \ s}\over{{2 \ v}+ a}}}\right]?\end{equation*}
Type: List(Equation(Fraction(Polynomial(Integer))))
fricassolve(v*t+a*t^2/2-s=0, t)
\begin{equation*}
\label{eq5}\left[{{{2 \ t \ v}+{a \ {{t}^{2}}}-{2 \ s}}= 0}\right]?\end{equation*}
Type: List(Equation(Fraction(Polynomial(Integer))))
fricasradicalSolve(p^3 - p + 1/10=0, p)
\begin{equation*}
\label{eq6}\begin{array}{@{}l}
\displaystyle
\left[{p ={{{{\left(-{3 \ {\sqrt{- 3}}}+ 3 \right)}\ {{\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{373}}}}\over{{60}\ {\sqrt{3}}}}}^{2}}}- 2}\over{{\left({3 \ {\sqrt{- 3}}}+ 3 \right)}\ {\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{373}}}}\over{{60}\ {\sqrt{3}}}}}}}}, \: \right.
\
\
\displaystyle
\left.{p ={{{{\left(-{3 \ {\sqrt{- 3}}}- 3 \right)}\ {{\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{373}}}}\over{{60}\ {\sqrt{3}}}}}^{2}}}+ 2}\over{{\left({3 \ {\sqrt{- 3}}}- 3 \right)}\ {\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{373}}}}\over{{60}\ {\sqrt{3}}}}}}}}, \: \right.
\
\
\displaystyle
\left.{p ={{{3 \ {{\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{37
3}}}}\over{{60}\ {\sqrt{3}}}}}^{2}}}+ 1}\over{3 \ {\root{3}\of{{-{3 \ {\sqrt{3}}}+{\sqrt{-{373}}}}\over{{60}\ {\sqrt{3}}}}}}}}\right] \end{array}
\end{equation*}
Type: List(Equation(Expression(Integer)))
fricasR1 ==> Record(foo1: String, remLexs: List Integer)
Type: Void
fricasR2 ==> Record(foo2: String, remLexs: List Integer)
Type: Void
fricasr1: R1 := ["a", [1, 2, 3]]
\begin{equation*}
\label{eq7}\left[{foo 1 = \verb#"a"#}, \:{remLexs ={\left[ 1, \: 2, \: 3 \right]?}}\right]\end{equation*}
Type: Record(foo1: String, remLexs: List(Integer))
fricasr2: R2 := ["b", [5]]
\begin{equation*}
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Type: Record(foo2: String, remLexs: List(Integer))
fricasr1.remLexs
\begin{equation*}
\label{eq9}\left[ 1, \: 2, \: 3 \right]?\end{equation*}
Type: List(Integer)
fricasr2.remLexs
\begin{equation*}
\label{eq10}\left[ 5 \right]?\end{equation*}
Type: List(Integer)
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fricas)set output algebra on
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(13)
[
[
f(n):
2 2
(- n - 17 n - 72)f(n + 3) + (4 n + 30 n + 44)f(n + 2)
+
2 2
(19 n + 113 n + 150)f(n + 1) + (14 n + 42 n + 28)f(n)
=
0
,
f(0) = 1, f(1) = 0, f(2) = 1]
]
Type: List(Expression(Integer))
fricasguessRec([1, 1, 0, 1, - 1, 2, - 1, 5, - 4, 29, - 13, 854, - 685])
2
(14) [[f(n): f(n + 2) + f(n + 1) - f(n) = 0, f(0) = 1, f(1) = 1]]
Type: List(Expression(Integer))
fricasintegrate(exp(x-x^2), x)
1
-
4 2 x - 1 +---+
%e erf(-------)\|%pi
2
(15) ---------------------
2
Type: Union(Expression(Integer), ...)
fricas1+1
(16) 2
Type: PositiveInteger?
2^3-2**3
2^3
fricas2^3
(17) 8
Type: PositiveInteger?
fricas2**3
There are no library operations named **
Use HyperDoc Browse or issue
)what op **
to learn if there is any operation containing " ** " in its name.
Cannot find a definition or applicable library operation named **
with argument type(s)
PositiveInteger
PositiveInteger
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
fricassqrt(2)^2-2
(18) 0
Type: AlgebraicNumber?
fricasa:=sqrt(2)
+-+
(19) \|2
Type: AlgebraicNumber?
fricasb:=sqrt(a)
+----+
| +-+
(20) \|\|2
Type: AlgebraicNumber?
fricasb^2-a
(21) 0
Type: AlgebraicNumber?
fricasf(a) == { local b=sqrt(a); b^2-a}
Line 1: f(a) == { local b=sqrt(a); b^2-a}
........A........B
Error A: Missing mate.
Error B: syntax error at top level
Error B: Possibly missing a }
3 error(s) parsing
fricasf(a) == { local b:=sqrt(a); b^2-a}
Line 1: f(a) == { local b:=sqrt(a); b^2-a}
..........A
Error A: syntax error at top level
Error A: Improper syntax.
2 error(s) parsing
fricas[q, r]
(22) [q, r]
Type: List(OrderedVariableList?([q, r]))
fricasf(a) == ( local b; b:=sqrt(a); b^2-a)
Type: Void
fricasf(2)
fricasCompiling function f with type PositiveInteger -> AlgebraicNumber
(24) 0
Type: AlgebraicNumber?
fricasf(sqrt(2))
fricasCompiling function f with type AlgebraicNumber -> AlgebraicNumber
(25) 0
Type: AlgebraicNumber?
fricasf(a) == ( local b; b:=sqrt(a); b^2-a)
Compiled code for f has been cleared.
1 old definition(s) deleted for function or rule f
Type: Void
fricasf(2)
fricasCompiling function f with type PositiveInteger -> AlgebraicNumber
(27) 0
Type: AlgebraicNumber?
fricasf(sqrt(2))
fricasCompiling function f with type AlgebraicNumber -> AlgebraicNumber
(28) 0
Type: AlgebraicNumber?
fricasf(z)
fricasCompiling function f with type Variable(z) -> Expression(Integer)
(29) 0
Type: Expression(Integer)
fricasf(%i)
fricasCompiling function f with type Complex(Integer) -> Expression(
Complex(Integer))
(30) 0
Type: Expression(Complex(Integer))
fricasf(a) == ( local b; b:=sqrt(a); b^2-a)
Compiled code for f has been cleared.
1 old definition(s) deleted for function or rule f
Type: Void
fricasf(2)
fricasCompiling function f with type PositiveInteger -> AlgebraicNumber
(32) 0
Type: AlgebraicNumber?
fricasc:=f(sqrt(2))
fricasCompiling function f with type AlgebraicNumber -> AlgebraicNumber
(33) 0
Type: AlgebraicNumber?
fricas)display properties c
Properties of c :
Value (has type AlgebraicNumber): 0
fricasf(a) == ( local b; b:=sqrt(a); b^2 = a)
Compiled code for f has been cleared.
1 old definition(s) deleted for function or rule f
Type: Void
\begin{AxiomCode?}
f(a) == ( local b; b:=sqrt(a); b^2-a)
f(2)
\end{AxiomCode?}
fricasf(a) == ( local b; b:=sqrt(a); b^2 = a)
1 old definition(s) deleted for function or rule f
Type: Void
fricasf(2)
fricasCompiling function f with type PositiveInteger -> Equation(
AlgebraicNumber)
(36) 2 = 2
Type: Equation(AlgebraicNumber?)
fricasf(%i)
fricasCompiling function f with type Complex(Integer) -> Equation(
Expression(Complex(Integer)))
(37) %i = %i
Type: Equation(Expression(Complex(Integer)))
fricasf(sqrt(2))
fricasCompiling function f with type AlgebraicNumber -> Equation(
AlgebraicNumber)
+-+ +-+
(38) \|2 = \|2
Type: Equation(AlgebraicNumber?)
fricasf(2^(1/2))
+-+ +-+
(39) \|2 = \|2
Type: Equation(AlgebraicNumber?)
fricasf(2^(1/3))
3+-+ 3+-+
(40) \|2 = \|2
Type: Equation(AlgebraicNumber?)
fricasf(a) == ( local b; b:=sqrt(a); b^2-a)
Compiled code for f has been cleared.
1 old definition(s) deleted for function or rule f
Type: Void
fricasf(sqrt(2))
fricasCompiling function f with type AlgebraicNumber -> AlgebraicNumber
(42) 0
Type: AlgebraicNumber?
fricas)set output fortran
--------------------------- The fortran Option ----------------------------
Description: create output in FORTRAN format
)set output fortran is used to tell FriCAS to turn FORTRAN-style output
printing on and off, and where to place the output. By default, the
destination for the output is the screen but printing is turned off.
Also See: )set fortran
Syntax: )set output fortran <arg>
where arg can be one of
on turn FORTRAN printing on
off turn FORTRAN printing off (default state)
console send FORTRAN output to screen (default state)
fp<.fe> send FORTRAN output to file with file prefix fp and file
extension .fe. If not given, .fe defaults to .sfort.
If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
FORTRAN output to the file polymer.sfort, issue the two commands
)set output fortran on
)set output fortran polymer
The output is placed in the directory from which you invoked FriCAS or
the one you set with the )cd system command.
The current setting is: Off:CONSOLE
f(sqrt(2))
(43) 0
Type: AlgebraicNumber?
fricas)set output tex
----------------------------- The tex Option ------------------------------
Description: create output in TeX style
)set output tex is used to tell FriCAS to turn TeX-style output
printing on and off, and where to place the output. By default, the
destination for the output is the screen but printing is turned off.
Syntax: )set output tex <arg>
where arg can be one of
on turn TeX printing on
off turn TeX printing off (default state)
console send TeX output to screen (default state)
fp<.fe> send TeX output to file with file prefix fp and file
extension .fe. If not given, .fe defaults to .stex.
If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
TeX output to the file polymer.stex, issue the two commands
)set output tex on
)set output tex polymer
The output is placed in the directory from which you invoked FriCAS or
the one you set with the )cd system command.
The current setting is: Off:CONSOLE
f(sqrt(2))
(44) 0
Type: AlgebraicNumber?
fricas)set output script
---------------------------- The script Option ----------------------------
Description: display output in SCRIPT formula format
)set output script is used to tell FriCAS to turn IBM Script formula-style
output printing on and off, and where to place the output. By default, the
destination for the output is the screen but printing is turned off.
Syntax: )set output script <arg>
where arg can be one of
on turn IBM Script formula printing on
off turn IBM Script formula printing off (default state)
console send IBM Script formula output to screen (default state)
fp<.fe> send IBM Script formula output to file with file prefix fp
and file extension .fe. If not given, .fe defaults to .sform.
If you wish to send the output to a file, you must issue this command
twice: once with on and once with the file name. For example, to send
IBM Script formula output to the file polymer.sform, issue the two commands
)set output script on
)set output script polymer
The output is placed in the directory from which you invoked FriCAS or
the one you set with the )cd system command.
The current setting is: Off:CONSOLE
f(sqrt(2))
(45) 0
Type: AlgebraicNumber?
fricasf(a) == ( local b; b:=sqrt(a); b^2-a)
Compiled code for f has been cleared.
1 old definition(s) deleted for function or rule f
Type: Void
fricasf(sqrt(2))
fricasCompiling function f with type AlgebraicNumber -> AlgebraicNumber
(47) 0
Type: AlgebraicNumber?
fricas)set output fortran on
f(sqrt(2))
R48=0
(48) 0
Type: AlgebraicNumber?
fricas)set output tex on
f(sqrt(2))
R49=0
(49) 0
\begin{equation}
\label{eq11}0\end{equation}
Type: AlgebraicNumber?
fricas)set output script on
f(sqrt(2))
.eq set blank @
:df.
0
:edf.
R50=0
(50) 0
\begin{equation}
\label{eq12}0\end{equation}
Type: AlgebraicNumber?
fricasf(a) == ( local b; b:=sqrt(a); b^2-a)
Compiled code for f has been cleared.
1 old definition(s) deleted for function or rule f
Type: Void
fricasf(sqrt(2))
fricasCompiling function f with type AlgebraicNumber -> AlgebraicNumber
.eq set blank @
:df.
0
:edf.
R52=0
(52) 0
\begin{equation}
\label{eq13}0\end{equation}
Type: AlgebraicNumber?
fricas)set output fortran console
f(sqrt(2))
.eq set blank @
:df.
0
:edf.
R53=0
(53) 0
\begin{equation}
\label{eq14}0\end{equation}
Type: AlgebraicNumber?
fricas)set output tex console
f(sqrt(2))
.eq set blank @
:df.
0
:edf.
R54=0
(54) 0
\begin{equation}
\label{eq15}0\end{equation}
Type: AlgebraicNumber?
fricas)set output script console
f(sqrt(2))
.eq set blank @
:df.
0
:edf.
R55=0
(55) 0
\begin{equation}
\label{eq16}0\end{equation}
Type: AlgebraicNumber?
fricasf(a) == ( local b; b:=sqrt(a); b^2-a)
Compiled code for f has been cleared.
1 old definition(s) deleted for function or rule f
Type: Void
fricasf(sqrt(2))
fricasCompiling function f with type AlgebraicNumber -> AlgebraicNumber
.eq set blank @
:df.
0
:edf.
R57=0
(57) 0
\begin{equation}
\label{eq17}0\end{equation}
Type: AlgebraicNumber?
fricas)set output fortran on
fricas)set output fortran console
f(sqrt(2))
.eq set blank @
:df.
0
:edf.
R58=0
(58) 0
\begin{equation}
\label{eq18}0\end{equation}
Type: AlgebraicNumber?
fricas)set output tex on
fricas)set output tex console
f(sqrt(2))
.eq set blank @
:df.
0
:edf.
R59=0
(59) 0
\begin{equation}
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Type: AlgebraicNumber?
fricas)set output script on
fricas)set output script console
f(sqrt(2))
.eq set blank @
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0
:edf.
R60=0
(60) 0
\begin{equation}
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Type: AlgebraicNumber?
fricasf(a) == ( local b; b:=sqrt(a); b^2-a)
Compiled code for f has been cleared.
1 old definition(s) deleted for function or rule f
Type: Void
fricasf(sqrt(2))
fricasCompiling function f with type AlgebraicNumber -> AlgebraicNumber
.eq set blank @
:df.
0
:edf.
R62=0
(62) 0
\begin{equation}
\label{eq21}0\end{equation}
Type: AlgebraicNumber?
fricas)set output fortran on
f(sqrt(2))
.eq set blank @
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0
:edf.
R63=0
(63) 0
\begin{equation}
\label{eq22}0\end{equation}
Type: AlgebraicNumber?
fricas)set output fortran off
fricas)set output tex on
f(sqrt(2))
.eq set blank @
:df.
0
:edf.
(64) 0
\begin{equation}
\label{eq23}0\end{equation}
Type: AlgebraicNumber?
fricas)set output tex off
fricas)set output script on
f(sqrt(2))
.eq set blank @
:df.
0
:edf.
(65) 0
Type: AlgebraicNumber?
fricas)set output script off
((1+2)/3)::SquareMatrix?(3,Integer)
fricas((1+2)/3)::SquareMatrix(3, Integer)
+1 0 0+
| |
(66) |0 1 0|
| |
+0 0 1+
Type: SquareMatrix?(3, Integer)
fricas((1+2)/3)::SquareMatrix(3, Integer)
+1 0 0+
| |
(67) |0 1 0|
| |
+0 0 1+
Type: SquareMatrix?(3, Integer)
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LaTeX Error: Environment AxiomCode undefined.
See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ...
l.153 \begin{AxiomCode}
Missing $ inserted. <inserted text> $ l.154 f(a) == ( local b; b:=sqrt(a); b^ 2-a)
LaTeX Error: \begin{document} ended by \end{AxiomCode}.
See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ...
l.156 \end{AxiomCode} \newpage Missing $ inserted. <inserted text> $ l.156 \end{AxiomCode} \newpage [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] (./4628360790889617791-16.0px.aux) ) (see the transcript file for additional information) Output written on 4628360790889617791-16.0px.dvi (24 pages, 7888 bytes). Transcript written on 4628360790889617791-16.0px.log.
integrate((x+sin(x))^(1/2),x)
>> Error detected within library code: integrate: implementation incomplete (constant residues)