Opened 6 years ago
Last modified 3 years ago
#15395 new defect
Maxima fails to recognize some expressions as equal
Reported by: | aginiewicz | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-6.4 |
Component: | calculus | Keywords: | limit, golden_ratio |
Cc: | kcrisman, jakobkroeker | Merged in: | |
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: | wrongAnswerMarker |
Description (last modified by )
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?
Change History (7)
comment:1 Changed 6 years ago by
- Cc kcrisman added
comment:2 Changed 6 years ago by
- Milestone changed from sage-6.1 to sage-6.2
comment:3 Changed 6 years ago by
- Milestone changed from sage-6.2 to sage-6.3
comment:4 Changed 5 years ago by
- Milestone changed from sage-6.3 to sage-6.4
comment:5 Changed 5 years ago by
comment:6 Changed 5 years ago by
- Description modified (diff)
- Summary changed from Wrong limit for squence involving Fibonacci sequence, 0 instead of golden ratio to Maxima fails to recognize some expressions as equal
comment:7 Changed 3 years ago by
- Cc jakobkroeker added
- Stopgaps set to wrongAnswerMarker
I don't know when it happened, but in 6.4.1 the limit works:
but the comparison
is still wrong. Slightly minified example: