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Submitted by : (unknown) at: 2007-11-17T22:24:25-08:00 (9 years ago)
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Following commands (being tested in SandBox) produce output looking as runtime error:

integrate(x^a*(x^b+1)^p, x)

x}{{\%F^a}\ {{\left({\%F^b}+ 1 \right)}^p}\ {d \%F}}(1)
Type: Union(Expression(Integer),...)
differentiate(%, x)

\label{eq2}{x^a}\ {{\left({x^b}+ 1 \right)}^p}(2)
Type: Expression(Integer)

if you replace p with, say, 2, it works. AFAIK, this binomial differential can be integrated in closed form only if a, b, and p satisfy certain constraints (aka "Chebyshev theorem"), so the failure itself is not surprising, but IMHO the produced output probably signals about some internal Axiom error or server misconfiguration. Version of the software reported: "Axiom (April 2006), Wednesday June 21, 2006 at 03:45:56".

The error returned by Axiom on linux is:

  Segmentation fault

and Axiom crashes. A similar abort occurs on the Windows version of Axiom.

Maple result --Bill Page, Thu, 03 Aug 2006 08:59:30 -0500 reply
In response to:
  integrate(x^a*(x^b+1)^p, x)

Maple 10 gives the result

{x}^{a+1}{\it hypergeom} \left( [-p,{\frac {a}{b}}+{b}^{-1}],[1+{
\frac {a}{b}}+{b}^{-1}],-{x}^{b} \right) {b}^{-1} \left( {\frac {a}{b}
}+{b}^{-1} \right) ^{-1}

with the derivative:

  differentiate(%, x)

{x}^{a+1} \left( a+1 \right) {\it hypergeom} \left( [-p,{\frac {a}{b}}
+{b}^{-1}],[1+{\frac {a}{b}}+{b}^{-1}],-{x}^{b} \right) {b}^{-1}
 \left( {\frac {a}{b}}+{b}^{-1} \right) ^{-1}{x}^{-1} +

{x}^{a+1}p{\it hypergeom} \left( [-p+1,1+{\frac {a}{b}}+{b}^{-1}],[2+{
\frac {a}{b}}+{b}^{-1}],-{x}^{b} \right) {x}^{b} \left( 1+{\frac {a}{b
}}+{b}^{-1} \right) ^{-1}{x}^{-1}

Status: open => fix proposed

Category: general => Axiom Library

Status: fix proposed => fixed somewhere

no patch available

From wh-sandbox --alfredo, Thu, 28 Aug 2008 18:44:23 -0700 reply

Status: fixed somewhere => fix proposed

  Subject:   Be Bold !!
  ( 13 subscribers )  
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