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-9.4,calculus,,"limit,golden_ratio",kcrisman jakobkroeker,,,,N/A,,,,,wrongAnswerMarker