Question: Product of intervals

Here Maple treats the intervals as independent, as I think it should:

INTERVAL(1 .. 2)+INTERVAL(1 .. 2);
              INTERVAL(1 .. 2) + INTERVAL(1 .. 2)

INTERVAL(1 .. 2)-INTERVAL(1 .. 2);
              INTERVAL(1 .. 2) - INTERVAL(1 .. 2)

(even though for the first one an autosimplification to 2*INTERVAL(1..2) wouldn't matter). But as soon as there are non-linear terms, Maple ignores that rule:

INTERVAL(1 .. 2)^2-INTERVAL(1 .. 2)^2;
                               0

INTERVAL(1 .. 2)/INTERVAL(1 .. 2);
                               1

INTERVAL(-1 .. 1)*INTERVAL(-1 .. 1);
                                        2
                       INTERVAL(-1 .. 1) 

That means I cannot substitute intervals for variables in a formula. In fact, I don't know how INTERVAL(-1 .. 1)*INTERVAL(-1 .. 1) can be computed as a product of two independent intervals at all, there doesn't seem to be any way to pass it to evalr.

 

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