# Assumptions

var("a b")
assume(b > 0, b < 1, a > 0, a < 1)
bool(a*b < 1)


returns false, why?

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In Maxima (which handles our assumptions):

(%i1) assume(b>0);
(%o1)                               [b > 0]
(%i2) assume(b<1);
(%o2)                               [b < 1]
(%i3) assume(a>0);
(%o3)                               [a > 0]
(%i4) assume(a<1);
(%o4)                               [a < 1]
(%i5) is (a*b > 0);
(%o5)                                true
(%i6) is (a*b < 1);
(%o6)                               unknown


And Sage returns false for booleans if it doesn't know for sure that it's true.

I'm not sure whether they would consider this a bug; their assumptions framework is self-described as "weak", though of course it's better than having no assumptions at all!

more

bool(a*a < 1) works, its kind of strange.

( 2012-11-14 20:28:29 +0200 )edit

I got same when preparing materials for highschool students. Shouldn't bool in such case return a warning in addition to False? Current way of assuming False for Unknown makes things that are unknown impossible to distinguish from things that are truly false (and this can instead lead to confusion for younger users)

( 2012-11-23 02:12:18 +0200 )edit

@giniu: This is true, but then we would need to be adding this warning for bool nearly all the time. There isn't any perfect pedagogical solution to this kind of issue, unfortunately.

( 2012-11-23 10:43:28 +0200 )edit