Hi there, I have entered the following,
a = var('a', domain='real')
b = var('b', domain='real')
assume(a > 0)
assume(b > 0)
stmt = log(a / b) == log(a) - log(b)
but when I do bool(stmt) it says False. Why is this? Did I miss some condition?
WorksForMe(TM) on Sage 9.8.beta1:
sage: var("a, b")
(a, b)
sage: log(a/b).log_expand()
log(a) - log(b)
sage: log(a/b).log_expand().log_simplify()
log(a/b)
HTH,
You have to keep in mind that when checking for an identity, Sage returns True if it has been capable to prove the identity and False if either (i) Sage has been capable to disprove it or (ii) Sage has not been capable to prove or disprove it. So, a False output means either "false" or "unknown". For instance, on your example, we have
sage: bool(log(a / b) == log(a) - log(b))
False
sage: bool(log(a / b) != log(a) - log(b))
False
These two results seem contradictory, but here the two False actually mean "unknown". This state of affairs is due to bool implementing a bivalent logic, not a ternary one (which would have permit Unknown as a possible output).
As @Emmanuel_Charpentier explains in his answer, you have to help Sage by invoking log_expand:
sage: stmt = log(a / b) == log(a) - log(b)
sage: bool(stmt.log_expand())
True
Asked: 2022-10-10 03:04:16 +0200
Seen: 103 times
Last updated: Oct 14 '22
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