Errors in symbolic integration
AXIOM Examples
1)
axiom
integrate(sin(x)+sqrt(1-x^3),x)
>> Error detected within library code:
failed - cannot handle that integrand
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)
Type: Union(Expression Integer,...)
int(sqrt(sin(x)),x); | reduce |
For this Maple 9 gives the following result:
And Mathematica 4 gives:
axiom
integrate(exp(-x^2),x)
Type: Union(Expression Integer,...)
axiom
integrate(exp(-x^2/2)/sqrt(%pi*2),x=%minusInfinity..%plusInfinity)
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
to learn more about the available operations.
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 "$" to specify which version of the function you need.
axiom
integrate(x,x)
Type: Polynomial Fraction Integer
axiom
axiomintegrate(x^6*exp(-x^2/2)/sqrt(%pi*2),x=%minusInfinity..%plusInfinity)
There are no library operations named axiomintegrate
Use HyperDoc Browse or issue
)what op axiomintegrate
to learn if there is any operation containing " axiomintegrate "
in its name.
Cannot find a definition or applicable library operation named
axiomintegrate with argument type(s)
Expression Integer
SegmentBinding OrderedCompletion Integer
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
axiom
integrate(x^6*exp(-x^2/2)/sqrt(%pi*2),x=%minusInfinity..%plusInfinity)
Type: Union(fail: failed,...)
The answer should be:
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)