#15395: Maxima fails to recognize some expressions as equal
--------------------------------------+------------------------
Reporter: aginiewicz | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.4
Component: calculus | Resolution:
Keywords: limit,golden_ratio | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
--------------------------------------+------------------------
Description changed by rws:
Old 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?
New description:
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?
--
--
Ticket URL: <http://trac.sagemath.org/ticket/15395#comment:6>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
