Some faulty integration:
integrate(a^(1/4)/(x^8-1),x)
-- following examples are from mapleok.input
in1867a:=integrate(1/(z^2-1)*(1-(I*z)^(1/2))^(1/2), z)
in1869a:=integrate(1/(z^2-1)*(1-1/(I*z)^(1/2))^(1/2), z)
in1870a:=integrate(1/(z^2-1)/(1+(I*z)^(1/2))^(1/2), z)
They are returning 0, which is obviously incorrect.
Also
in1724a:=integrate(-z^2/(z^2-1)*(1-(I*z)^(1/2))^(1/2), z)
is wrong, although its return value is not 0.
The problem happens in "pairsum" in irexpand.spad.
This "pairsum" function tries to avoid cases like both
x^(1/n) and (-x)^(1/n) (where n is even) appears in result.
Take "integrate(a^(1/4)/(x^8-1),x)" for example, in order to
solve "?^4+a/4096" appeared in
"split internalIntegrate(a^(1/4)/(x^8-1),x)",
"lg2func" uses "zeroOf" to introduce (-a)^(1/4) which causes
"pairsum" to return empty result.
I suggest:
1. Add a warning/error in "pairsum" when it tries to return empty.
2. We can handle cases like "?^4+a" "?^4+a*?^2+b" in "lg2func" better.
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