Around usage results Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern) Announcing the arrival of Valued Associate #679: Cesar Manara Unicorn Meta Zoo #1: Why another podcast?SlotSequence (##) form analogous to #[[ ;; n]]How can I avoid getting the error message Goto::nolabel in my code?Association of pure functionsDictionaryLoopkup - pattern specificationWhat is the relationship between Thread and MapThreadWhat are the requirements for a well behaved indexed variable? Subscript, ToExpression, Downvalue?Understanding Part and Span operating on expressions with heads that are not ListWhy does using replacement rules give a different result than setting the variable?Problem storing $x_j$ terms in variable xUnexpected behavior from Apply
Why are the trig functions versine, haversine, exsecant, etc, rarely used in modern mathematics?
Around usage results
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Quick way to create a symlink?
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Closed form of recurrent arithmetic series summation
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Circuit to "zoom in" on mV fluctuations of a DC signal?
Around usage results
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)
Announcing the arrival of Valued Associate #679: Cesar Manara
Unicorn Meta Zoo #1: Why another podcast?SlotSequence (##) form analogous to #[[ ;; n]]How can I avoid getting the error message Goto::nolabel in my code?Association of pure functionsDictionaryLoopkup - pattern specificationWhat is the relationship between Thread and MapThreadWhat are the requirements for a well behaved indexed variable? Subscript, ToExpression, Downvalue?Understanding Part and Span operating on expressions with heads that are not ListWhy does using replacement rules give a different result than setting the variable?Problem storing $x_j$ terms in variable xUnexpected behavior from Apply
$begingroup$
Why is
Around[10, 1]^2
- +- 20
and
Around[10, 1] Around[10, 1]
giving 100 +- 14 ?
Just curious I would suspect them to be the same but I'm not an expert on this for sure.
core-language
asked 7 hours ago
LouLou
1,6581323
$endgroup$
add a comment |
$begingroup$
Why is
Around[10, 1]^2
- +- 20
and
Around[10, 1] Around[10, 1]
giving 100 +- 14 ?
Just curious I would suspect them to be the same but I'm not an expert on this for sure.
core-language
asked 7 hours ago
LouLou
1,6581323
$endgroup$
$begingroup$
If the intent forAroundin Mathematica is for propagating errors, then this is almost certainly a bug. Interestingly enough, I think the second one is correct, whereas the first is not.
$endgroup$
– march
7 hours ago
add a comment |
$begingroup$
Why is
Around[10, 1]^2
- +- 20
and
Around[10, 1] Around[10, 1]
giving 100 +- 14 ?
Just curious I would suspect them to be the same but I'm not an expert on this for sure.
core-language
asked 7 hours ago
LouLou
1,6581323
$endgroup$
Why is
Around[10, 1]^2
- +- 20
and
Around[10, 1] Around[10, 1]
giving 100 +- 14 ?
Just curious I would suspect them to be the same but I'm not an expert on this for sure.
core-language
core-language
asked 7 hours ago
LouLou
1,6581323
asked 7 hours ago
LouLou
1,6581323
asked 7 hours ago
LouLou
1,6581323
asked 7 hours ago
LouLou
1,6581323
asked 7 hours ago
LouLou
1,6581323
1,6581323
$begingroup$
If the intent forAroundin Mathematica is for propagating errors, then this is almost certainly a bug. Interestingly enough, I think the second one is correct, whereas the first is not.
$endgroup$
– march
7 hours ago
add a comment |
$begingroup$
If the intent forAroundin Mathematica is for propagating errors, then this is almost certainly a bug. Interestingly enough, I think the second one is correct, whereas the first is not.
$endgroup$
– march
7 hours ago
$begingroup$
If the intent for
Around in Mathematica is for propagating errors, then this is almost certainly a bug. Interestingly enough, I think the second one is correct, whereas the first is not.$endgroup$
– march
7 hours ago
$begingroup$
If the intent for
Around in Mathematica is for propagating errors, then this is almost certainly a bug. Interestingly enough, I think the second one is correct, whereas the first is not.$endgroup$
– march
7 hours ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
There's a subtlety here.
When operating together multiple Arounds, the two uncertainties will be considered separate and independent (in the statistical sense). Thus the result will be different from squaring a single one.
Consider
N@StandardDeviation@
TransformedDistribution[
x y,
x [Distributed] NormalDistribution[10, 1],
y [Distributed] NormalDistribution[10, 1]]
(* 14.1774 *)
versus
N@StandardDeviation@TransformedDistribution[x^2, x [Distributed] NormalDistribution[10, 1]]
(* 20.0499 *)
The same can also be observed with addition:
Around[10, 1] + Around[10, 1]
(* Around[20., 1.4142135623730951`] *)
2 Around[10, 1]
(* Around[20., 2.] *)
To specify that all occurrences of an Around expression are the same, use AroundReplace.
For example, compare
x^2 + x /. x -> Around[1, .1]
(* Around[2., 0.223606797749979] *)
with
AroundReplace[x^2 + x, x -> Around[1, .1]]
(* Around[2., 0.30000000000000004`] *)
edited 5 hours ago
Carl Lange
5,36411242
answered 7 hours ago
SzabolcsSzabolcs
164k14449953
$endgroup$
$begingroup$
Also,AroundReplace[ x1 x2, x1, x2 -> VectorAround[10., 10., 1., 1., 1.]]vsAroundReplace[ x1 x2, x1, x2 -> VectorAround[10., 10., 1., 1., 0.]].
$endgroup$
– b.gatessucks
7 hours ago
add a comment |
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
There's a subtlety here.
When operating together multiple Arounds, the two uncertainties will be considered separate and independent (in the statistical sense). Thus the result will be different from squaring a single one.
Consider
N@StandardDeviation@
TransformedDistribution[
x y,
x [Distributed] NormalDistribution[10, 1],
y [Distributed] NormalDistribution[10, 1]]
(* 14.1774 *)
versus
N@StandardDeviation@TransformedDistribution[x^2, x [Distributed] NormalDistribution[10, 1]]
(* 20.0499 *)
The same can also be observed with addition:
Around[10, 1] + Around[10, 1]
(* Around[20., 1.4142135623730951`] *)
2 Around[10, 1]
(* Around[20., 2.] *)
To specify that all occurrences of an Around expression are the same, use AroundReplace.
For example, compare
x^2 + x /. x -> Around[1, .1]
(* Around[2., 0.223606797749979] *)
with
AroundReplace[x^2 + x, x -> Around[1, .1]]
(* Around[2., 0.30000000000000004`] *)
edited 5 hours ago
Carl Lange
5,36411242
answered 7 hours ago
SzabolcsSzabolcs
164k14449953
$endgroup$
$begingroup$
Also,AroundReplace[ x1 x2, x1, x2 -> VectorAround[10., 10., 1., 1., 1.]]vsAroundReplace[ x1 x2, x1, x2 -> VectorAround[10., 10., 1., 1., 0.]].
$endgroup$
– b.gatessucks
7 hours ago
add a comment |
$begingroup$
There's a subtlety here.
When operating together multiple Arounds, the two uncertainties will be considered separate and independent (in the statistical sense). Thus the result will be different from squaring a single one.
Consider
N@StandardDeviation@
TransformedDistribution[
x y,
x [Distributed] NormalDistribution[10, 1],
y [Distributed] NormalDistribution[10, 1]]
(* 14.1774 *)
versus
N@StandardDeviation@TransformedDistribution[x^2, x [Distributed] NormalDistribution[10, 1]]
(* 20.0499 *)
The same can also be observed with addition:
Around[10, 1] + Around[10, 1]
(* Around[20., 1.4142135623730951`] *)
2 Around[10, 1]
(* Around[20., 2.] *)
To specify that all occurrences of an Around expression are the same, use AroundReplace.
For example, compare
x^2 + x /. x -> Around[1, .1]
(* Around[2., 0.223606797749979] *)
with
AroundReplace[x^2 + x, x -> Around[1, .1]]
(* Around[2., 0.30000000000000004`] *)
edited 5 hours ago
Carl Lange
5,36411242
answered 7 hours ago
SzabolcsSzabolcs
164k14449953
$endgroup$
$begingroup$
Also,AroundReplace[ x1 x2, x1, x2 -> VectorAround[10., 10., 1., 1., 1.]]vsAroundReplace[ x1 x2, x1, x2 -> VectorAround[10., 10., 1., 1., 0.]].
$endgroup$
– b.gatessucks
7 hours ago
add a comment |
$begingroup$
There's a subtlety here.
When operating together multiple Arounds, the two uncertainties will be considered separate and independent (in the statistical sense). Thus the result will be different from squaring a single one.
Consider
N@StandardDeviation@
TransformedDistribution[
x y,
x [Distributed] NormalDistribution[10, 1],
y [Distributed] NormalDistribution[10, 1]]
(* 14.1774 *)
versus
N@StandardDeviation@TransformedDistribution[x^2, x [Distributed] NormalDistribution[10, 1]]
(* 20.0499 *)
The same can also be observed with addition:
Around[10, 1] + Around[10, 1]
(* Around[20., 1.4142135623730951`] *)
2 Around[10, 1]
(* Around[20., 2.] *)
To specify that all occurrences of an Around expression are the same, use AroundReplace.
For example, compare
x^2 + x /. x -> Around[1, .1]
(* Around[2., 0.223606797749979] *)
with
AroundReplace[x^2 + x, x -> Around[1, .1]]
(* Around[2., 0.30000000000000004`] *)
edited 5 hours ago
Carl Lange
5,36411242
answered 7 hours ago
SzabolcsSzabolcs
164k14449953
$endgroup$
There's a subtlety here.
When operating together multiple Arounds, the two uncertainties will be considered separate and independent (in the statistical sense). Thus the result will be different from squaring a single one.
Consider
N@StandardDeviation@
TransformedDistribution[
x y,
x [Distributed] NormalDistribution[10, 1],
y [Distributed] NormalDistribution[10, 1]]
(* 14.1774 *)
versus
N@StandardDeviation@TransformedDistribution[x^2, x [Distributed] NormalDistribution[10, 1]]
(* 20.0499 *)
The same can also be observed with addition:
Around[10, 1] + Around[10, 1]
(* Around[20., 1.4142135623730951`] *)
2 Around[10, 1]
(* Around[20., 2.] *)
To specify that all occurrences of an Around expression are the same, use AroundReplace.
For example, compare
x^2 + x /. x -> Around[1, .1]
(* Around[2., 0.223606797749979] *)
with
AroundReplace[x^2 + x, x -> Around[1, .1]]
(* Around[2., 0.30000000000000004`] *)
edited 5 hours ago
Carl Lange
5,36411242
answered 7 hours ago
SzabolcsSzabolcs
164k14449953
edited 5 hours ago
Carl Lange
5,36411242
edited 5 hours ago
Carl Lange
5,36411242
edited 5 hours ago
Carl Lange
5,36411242
5,36411242
answered 7 hours ago
SzabolcsSzabolcs
164k14449953
answered 7 hours ago
SzabolcsSzabolcs
164k14449953
answered 7 hours ago
SzabolcsSzabolcs
164k14449953
164k14449953
$begingroup$
Also,AroundReplace[ x1 x2, x1, x2 -> VectorAround[10., 10., 1., 1., 1.]]vsAroundReplace[ x1 x2, x1, x2 -> VectorAround[10., 10., 1., 1., 0.]].
$endgroup$
– b.gatessucks
7 hours ago
add a comment |
$begingroup$
Also,AroundReplace[ x1 x2, x1, x2 -> VectorAround[10., 10., 1., 1., 1.]]vsAroundReplace[ x1 x2, x1, x2 -> VectorAround[10., 10., 1., 1., 0.]].
$endgroup$
– b.gatessucks
7 hours ago
$begingroup$
Also,
AroundReplace[ x1 x2, x1, x2 -> VectorAround[10., 10., 1., 1., 1.]] vs AroundReplace[ x1 x2, x1, x2 -> VectorAround[10., 10., 1., 1., 0.]].$endgroup$
– b.gatessucks
7 hours ago
$begingroup$
Also,
AroundReplace[ x1 x2, x1, x2 -> VectorAround[10., 10., 1., 1., 1.]] vs AroundReplace[ x1 x2, x1, x2 -> VectorAround[10., 10., 1., 1., 0.]].$endgroup$
– b.gatessucks
7 hours ago
add a comment |
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$begingroup$
If the intent for
Aroundin Mathematica is for propagating errors, then this is almost certainly a bug. Interestingly enough, I think the second one is correct, whereas the first is not.$endgroup$
– march
7 hours ago