id summary reporter owner description type status priority milestone component resolution keywords cc merged author reviewer upstream work_issues branch commit dependencies stopgaps
15395 Maxima fails to recognize some expressions as equal aginiewicz "Maxima fails to regard some expressions as equal:
{{{
sage: value_1 = 1-golden_ratio
sage: value_2 = -golden_ratio^(-1)
sage: bool(value_1 == value_2)
True
sage: bool(value_1^x != value_2^x)
True
}}}
while
{{{
sage: bool(((x+1)^2)^y == (x^2+2*x+1)^y)
True
sage: sin(0,hold=True)^x == 0^x
sin(0)^x == 0^x
sage: bool(sin(0,hold=True)^x == 0^x)
True
}}}
Previous description:
I tried to define Fibonacci sequence using golden ratio in two ways, using values:
{{{
sage: value_1 = 1-golden_ratio
sage: value_2 = -golden_ratio^(-1)
sage: bool(value_1 == value_2)
true
}}}
(gives true, so two definitions, F1 and F2 below should be equal, even though they are not according to Sage)
{{{
sage: F1(k) = (golden_ratio^k-(value_1)^(k))/sqrt(5)
sage: F2(k) = (golden_ratio^k-(value_2)^(k))/sqrt(5)
sage: bool(F1(k) != F2(k))
true
}}}
When simplified everything seems to be equal at least for first 10 or 1000 elements:
{{{
sage: [(F1(j)-F2(j)).full_simplify() for j in range(10)]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
}}}
Anyway, now to the error: limit for F1 gives wrong result:
{{{
sage: limit(F1(k+1)/F1(k), k=oo)
0
}}}
and for F2 works OK:
{{{
sage: limit(F2(k+1)/F2(k), k=oo)
1/2*sqrt(5) + 1/2
}}}
I've tested it with Sage 5.12 and 5.11, with same result. This can be as simple as some thing with how golden ratio is handled, or something far more involved maybe?" defect new major sage-9.3 calculus limit,golden_ratio kcrisman jakobkroeker N/A wrongAnswerMarker