Hi,
Latest Fricas can do the Shi and Chi integrals without
calling the pattern matcher:
(4) -> integrate(sinh(x)/x, x)
Ei(x) - Ei(- x)
(4) ---------------
2
Type: Union(Expression(Integer),...)
(5) -> integrate(cosh(x)/x, x)
Ei(x) + Ei(- x)
(5) ---------------
2
Type: Union(Expression(Integer),...)
That is nice to see :-)
Where do we need to add code such that Fricas can transform
these results into Shi and Chi respectively?
Even better to see how the new code handles more complicated
integrands like the following one:
(23) -> integrate(cosh(a*x^2+c)/x, x)
2 2 2 2
(Ei(a x ) - Ei(- a x ))sinh(c) + (Ei(a x ) + Ei(- a x ))cosh(c)
(23) ---------------------------------------------------------------
4
Type: Union(Expression(Integer),...)
(24) -> normalize(%)
2 c 2 2
Ei(a x )(%e ) + Ei(- a x )
(24) ---------------------------
c
4%e
Type: Expression(Integer)
(25) -> D(%, x)
2 2
c 2 a x - a x
(%e ) %e + %e
(25) -----------------------
c
2x %e
Type: Expression(Integer)
(26) -> normalize(%)
2 2
c 2 a x
(%e ) (%e ) + 1
(26) -------------------
2
c a x
2x %e %e
Type: Expression(Integer)
(27) -> normalize(cosh(a*x^2+c)/x)
2 2
a x + c
(%e ) + 1
(27) -----------------
2
a x + c
2x %e
Type: Expression(Integer)
I don't know why they do not normalize to the same form
but it's obvious the result is correct.
The other two are not possible at the moment and still use pattern matching.
(1) -> integrate(sin(x)/x, x)
(1) Si(x)
Type: Union(Expression(Integer),...)
(3) -> integrate(cos(x)/x, x)
(3) Ci(x)
Type: Union(Expression(Integer),...)
This is of course ok, but fails for more complicated arguments as we all know.
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