Assumption bug of positive symbolic variable

[mathzeta]

There is an easily reproducible bug with assumptions:

sage: var("p", domain="positive")
p
sage: assume(p<1)
sage: bool(p<1)
True
sage: bool(p^2<1)
True
sage: bool(p^6<1) # Should be True
False

The same happens for var("p") and then assuming assume(p>0). The following list should be [0..999], but we see something different:

sage: [i for i in range(1000) if bool(p^i < 1)]
[1, 2, 3, 4, 5, 7, 8, 9, 11, 16, 25, 27, 32, 64, 81]

CC: @rwst

Component: symbolics

Keywords: days79

Issue created by migration from https://trac.sagemath.org/ticket/21923

[mathzeta]

Changed keywords from none to days79

[mo271]

comment:2

double floating problem?

sage: [bool(p^(i)<=1+1e-15) for i in range(20)]
[True, True, True, True, True, True, False, True, True, True, False, True, False, False, False, False, True, False, False, False]
sage: [bool(p^(i)<=1+1e-14) for i in range(20)]
[True, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False]

[mo271]

comment:3

sage: var("p", domain="positive")
sage: assume(p<1/1000000)
sage: bool(p^6<5)
False

[rwst]

comment:5

It is well known that there is no reasoning capability in Sage. See for example this thread: https://groups.google.com/d/msg/sage-support/AiPtd0x52kQ/WeOmvlFCEAAJ

The assume command mainly sets Maxima assumptions for use in DEs and integrals. Everything else is experimental.

[rwst]

comment:6

See also #19162.

[mathzeta]

comment:7

Yes, this is already in Maxima:

(%i1) assume(p>0);
(%o1)                               [p > 0]
(%i2) assume(p<1);        
(%o2)                               [p < 1]
(%i3) is(p^2<1); 
(%o3)                                true
(%i4) is(p^6<1);        
(%o4)                               unknown

Now I see that http://maxima.sourceforge.net/docs/manual/maxima_11.html#assume mentions
Maxima's deduction mechanism is not very strong; there are many obvious consequences which cannot be determined by is. This is a known weakness.
But Maxima does have a tristate, as can be seen above. See #17700 for more.

Should the milestone of this ticket be changed to sage-duplicate or to sage-wishlist?

[rwst]

comment:8

I think it's a duplicate of the enhancement ticket #19162.

[rwst]

comment:9

BTW for an overview of existing symbolic tickets please see https://trac.sagemath.org/wiki/symbolics

[sagetrac-tmonteil]

comment:10

I am not sure such tickets should be closed like that. Indeed, compared to #19162, there is a concrete use case (a bug), so it is important to keep track of it in the doctests, even if the fix comes from another ticket. At least, we have to copy the doctest on the other ticket, in order not to lose it.

[dimpase]

comment:11

still reproducible in 9.5.beta7