login  home  contents  what's new  discussion  bug reports help  links  subscribe  changes  refresh  edit

# Edit detail for Symbolic Integration revision 3 of 12

 1 2 3 4 5 6 7 8 9 10 11 12 Editor: mcd Time: 2009/06/26 00:23:36 GMT-7 Note: teste

added:

From mcd Fri Jun 26 00:23:35 -0700 2009
From: mcd
Date: Fri, 26 Jun 2009 00:23:35 -0700
Subject: teste
Message-ID: <20090626002335-0700@axiom-wiki.newsynthesis.org>

\begin{axiom}
integrate(a*x,x);
\end{axiom}


## Errors in symbolic integration

AXIOM Examples

1)

axiom
integrate(sin(x)+sqrt(1-x^3),x) (1)
Type: Union(Expression(Integer),...)

 int(sin(x)+sqrt(1-x^3),x); reduce 2)

axiom
integrate(sqrt(1-log(sin(x)^2)),x)
>> Error detected within library code:
integrate: implementation incomplete (constant residues)

 int(sqrt(1-log(sin(x)^2)),x); reduce 3)

axiom
integrate(sqrt(sin(1/x)),x)
>> Error detected within library code:
integrate: implementation incomplete (constant residues)

That seems strange given the claims about the "completeness" of Axiom's integration algorithm! But to be fair, Maple also returns this integral unevaluated.

 int(sqrt(sin(1/x)),x); reduce 4)

axiom
integrate(sqrt(sin(x)),x) (2)
Type: Union(Expression(Integer),...)

 int(sqrt(sin(x)),x); reduce For this Maple 9 gives the following result: (3)

And Mathematica 4 gives: (4)

symbolic integration
Tue, 22 Mar 2005 11:48:00 -0600 reply
axiom
integrate(exp(-x^2),x) (5)
Type: Union(Expression(Integer),...)
Errorfunction
Wed, 23 Mar 2005 08:23:21 -0600 reply
axiom
integrate(exp(-x^2/2)/sqrt(%pi*2),x=%minusInfinity..%plusInfinity) (6)
Type: Union(f1: OrderedCompletion?(Expression(Integer)),...)

axiom
int(x,x)
There are no exposed library operations named int but there are 5
unexposed operations with that name. Use HyperDoc Browse or issue
)display op int
Cannot find a definition or applicable library operation named int
with argument type(s)
Variable(x)
Variable(x)
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need. axiom integrate(x,x) (7) Type: Polynomial(Fraction(Integer)) axiom axiomintegrate(x^6*exp(-x^2/2)/sqrt(%pi*2),x=%minusInfinity..%plusInfinity) There are no library operations named axiomintegrate Use HyperDoc Browse or issue )what op axiomintegrate to learn if there is any operation containing " axiomintegrate " in its name. Cannot find a definition or applicable library operation named axiomintegrate with argument type(s) Expression(Integer) SegmentBinding(OrderedCompletion(Integer)) Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.

axiom
integrate(x^6*exp(-x^2/2)/sqrt(%pi*2),x=%minusInfinity..%plusInfinity) (8)
Type: Union(fail: failed,...) (9)

integrate(exp(x)/x^2) --unknown, Thu, 25 Aug 2005 05:57:53 -0500 reply
Axiom does not perform the integration (while it perform the integration of exp(x)/x ), but the integration can be given in terms of Ei(x)

integrate(exp(x)/x^2,x) --> Ei(x)-exp(x)/x

int(sqrt(x), x)

int(sqrt(x), x);

axiom
integrate(a*x,x);
Type: Polynomial(Fraction(Integer))