I think I have found a good enough solution:
by using "sign" from ElementaryFunctionSign,
it's already imported by IR2F.
I also find a new problem: IntegrationResult doesn't
even track the independent variable!
diff --git a/src/algebra/irexpand.spad b/src/algebra/irexpand.spad
index 3e1ca4f7..7ed8ea5a 100644
--- a/src/algebra/irexpand.spad
+++ b/src/algebra/irexpand.spad
@@ -104,6 +104,12 @@
-- they differ by a constant so it's ok to do it from an IR
tantrick(a, b) ==
retractIfCan(a)@Union(Q, "failed") case Q => 2 * atan(-b/a)
+ sa := sign a
+ sb := sign b
+ if sa case Z and sb case "failed" then return 2 * atan(-b/a)
+ if sb case Z and sa case "failed" then return 2 * atan(a/b)
+ -- if sa case "failed" and sb case "failed" then
+ -- print("potentially noncontinuous"::OutputForm)
2 * atan(a/b)
-- transforms i log((a + i b) / (a - i b)) into a sum of real
On Thu, Feb 2, 2017 at 6:24 PM, oldk1331 <[email protected]> wrote:
> A related problem with continuity:
>
> atan(A/B) and -atan(B/A), they differ by a constant, but
> their continuity is different, if A has no sign change
> (always positive), then it's better to be put in denominator.
> I think function "tantrick" can utilize that.
>
> This is a big source of discontinuity, and my solution
> mentioned in previous post will make many discontinous
> function continous and vice versa, I don't think this
> will be a problem?
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