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+--- Thread: HP PPL and Statistical distributions (/thread-16635.html)
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RE: HP PPL and Statistical distributions - robmio - 05-23-2021 01:43 PM
Undoubtedly your program is well done: fast and flexible. I use it for Tukey's post hoc analysis in randomized block-design ANOVA and for post hoc analysis in Fridman's ANOVA.
Thanks, you helped me a lot.
Best regards, Roberto.
RE: HP PPL and Statistical distributions - C.Ret - 05-23-2021 02:00 PM
(05-23-2021 01:32 PM)Albert Chan Wrote: CAS> inf > 3+4i → 1
CAS> -inf > 3+4i → 0
I am very surprised by reading this. I must have missed a step in the advancement of mathematics.
The last time I was told about the properties of complex numbers field, there were no order relation available for it.
Therefore, no one may attempt a comparison between any complex number nor between a complex number and a real !
What's the new under the sky that have ordered the complex numbers ? That is surely a Vander full invention or an epic monster !
In this CAS software environment , what would be the result of comparing 4 + 7i and 14 + 0.3i ?
RE: HP PPL and Statistical distributions - Albert Chan - 05-23-2021 03:36 PM
(05-23-2021 02:00 PM)C.Ret Wrote: The last time I was told about the properties of complex numbers field, there were no order relation available for it.
Therefore, no one may attempt a comparison between any complex number nor between a complex number and a real !
It was not about comparing 2 complex numbers, but against a "symbolic" infinity.
My guess symbolic infinity is defined bigger than any finite values, independent of type.
The issue is this line in quad:
< IF bool(a>b) == bool(mode==2) THEN d:=-d END
My patch to extend to complex numbers (which turned out not needed in PPL)
// If integration limits are [a, -inf] or [-inf, b], switch direction of integration.
> IF (mode==2 AND b<0) OR (mode==1 AND a<0) THEN d:=-d END
But, you do have a point.
Patch is more readable, and less reliance on PPL "feature" (which might changed in the future).
I am patching this to quad. Thanks, C.Ret
Update1: replace indirect (mode!=2) as (mode==1)
Update2: replace complicated test with simpler equivalent code
< IF mode == 2 THEN c:=a ELSE c:=b END
< IF (mode==2 AND b<0) OR (mode==1 AND a<0) THEN d:=-d END
< s := f(c+d)
> c, s := a, b; // c = finite edge
> IF mode == 1 THEN c, s := b, a END
> IF s < 0 THEN d:=-d END
> s := f(c+d)