Re: Motion P1788/M0043.01Div2Pair provisional NO
P1788
For the moment I vote NO.
Maybe I've missed some discussion, but it seems the motion doesn't handle the 3-argument form of mulRev, see draft 7.1§9.6.5, though Dmitry mentioned it (24 April 2013 02:48:07 GMT+01:00). An operation mulRevPair(bb,aa,xx) must give two intervals whose union encloses
X = { x ∈ xx | exist b in bb, a in aa such that b*x = a }
We know X = (xx intersect C) where
C = { x ∈ R | exist b in bb, a in aa such that b*x = a }
is as in Juergen's eqn (2), and C is *uniquely* the union of disjoint intervals C1,C2 where just one of these holds:
(a) C1, C2 both nonempty; C1 strictly less than C2
(in fact C1<0 and C2>0)
(b) C1 nonempty, C2 empty
(c) C1, C2 both empty
We have various options that I've not seen discussed:
OPT1. Don't give mulRevPair a 3-argument form, since by the above you can easily get it from the 2-argument form.
OPT2. Compute C1,C2 as above and return (C1',C2') = (C1 intersect xx, C2 intersect xx).
OPT3. Compute (C1',C2') as in (2) but then normalise them so that if just one of them is nonempty, it is put first. I.e. normalise like (a,b,c) above.
Example:
2-argument mulrev([-1,1], [2,2]) returns ([-oo,-2], [2,oo]) according to the motion.
Consider 3-argument mulrev([-1,1], [2,2], xx) for various xx:
xx=[-3,4]: returns [-3,-2], [2,4] in some order.
xx=[-3,1]: returns [-3,-2], Empty in some order.
xx=[-1,4]: returns Empty, [2,4] in some order.
xx=[-1,1]: returns Empty, Empty in some order.
I will vote YES as soon as we agree on one of these options; no need to interrupt the vote. Personally I am OK with OPT1, but prefer OPT2 because it's simple to implement the intersection within the function instead of making the user do it.
OPT3 looks mathematically nice, but I think would be *less* convenient in applications than OPT2. (In the case xx=[-1,4] above it would swap the outputs to give [2,4], Empty.)
Regards
John Pryce
On 30 Apr 2013, at 11:31, Ralph Baker Kearfott wrote:
> P-1788,
>
> The version of the div2pair motion Juergen posted on
> April 26 (attached) is the latest corrected version.
>
> The voting period herewith begins.