Robert,
>> <http://axiom.axiom-developer.org/axiom-website/CATS/>
>> view the pdf file for "Schaums 14.120-14.124" (schaum5.input.pdf)
>> See the result on page 3 of the pdf.
>>
>> The first integral result returned by Axiom is a list of answers.
>
>Hmm. I don't see any indication of the domain in which each
>result is applicable. Did I miss something?
>
>It appears that the ascii art display shows something different
>from the TeX display. Maybe they're equivalent, I can't tell.
Axiom does not use an assume facility. It computes all the answers
and returns a list if there is more than one.
The format of the file is one section per integral.
Within the section you see the Schaums input and expected answer in latex.
e.g.
\[ \int{sin(x)}dx \]
\[ -cos(x) \]
This is followed by an Axiom integrate command for the integral given.
(assigned to the aa variable)
e.g.
aa := integrate(sin(x),x)
The "ascii art" output (the things after the --R lines) are the Axiom output.
(Note: The -- is an Axiom comment. These are regression test files.) e.g.
-cos(x)
Following the integration call is an Axiom input of the answer given by
Schaums. (Assigned to the bb variable)
e.g
bb := -cos(x)
Next we difference the Axiom answer from the Schaums answer.
cc := aa - bb
They should only differ by a constant (hopefully zero). If they are
not immediately found to differ by a constant there are a series of
simplification steps applied to try to prove that the answers are
equivalent.
The final step in each section draws one of several possible
conclusions. See the comment on the last step in each section.
Axiom and Schaums agree means that we got a zero difference.
Axiom and Schaums differ by a constant of integration.
Axiom cannot do the integration ... which implies that there is no
closed form of the integral over the elementary functions. This
is a consequence of the Risch algorithm. If Axiom returns the
integral unevaluated then it is a proof that no closed form exists.
Axiom cannot simplify the result which means that we do not know if
Axiom and Schaums are equivalent. The most likely reason that the
simplification fails is that Axiom and Schaums are using different
branch cuts for trig functions.
Tim
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