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Results tagged with assumptions
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user 12
Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[].
2
votes
Accepted
Re[x] vs. x ∈ Reals in the context of Assuming
No. Re[x] > 0 means that the real part of x is positive, but it does not mean that the imaginary part is zero. Re[1+I] > 0 but 1+I is not real.
However, x > 0 is sufficient and (in Mathematica) imp …
- 236k
5
votes
Accepted
Hidden limitation of Assumptions (Is $x^2 < 0$ contradictory)?
A shorter example is
$Assumptions = x^2 < 0
During evaluation of $Assumptions::cas: Warning: contradictory assumption(s) x^2<0 encountered.
(* x^2 < 0 *)
Other functions, such as Reduce, also make … similar automatic assumptions. …
- 236k
2
votes
Assumptions about list elements
It is not Assuming that supports general patterns, but Element. This explains why
Assuming[x > 0, Refine@Sign[x]]
gives 1, while
Assuming[x[_] > 0, Refine@Sign[ x[1] ]]
does not.
- 236k
1
vote
Accepted
One more question about Assumptions and Integrate
For definite integrals this won't be a problem though as that complex constant is cancelled:
Integrate[1/x, {x, a, -1}, Assumptions -> a < -1]
(* ==> -Log[-a] *) …
11
votes
Accepted
Defining the domain of positive real numbers
There's a misunderstanding here. The third "dom" argument is not simply a set over which we solve the equation. There are only a few choices that can be used for the domain argument, and they have v …
- 236k
2
votes
Accepted
How to submit assumptions defined in master kernel to subkernels
$Assumptions cannot be distributed because it is in the System` context and because it is a symbol with special behaviour.
The correct way to handle this is to set it explicitly on all subkernels. … ParallelEvaluate[$Assumptions = m > 0 && m \[Element] Integers] …
- 236k
3
votes
Accepted
How to properly input limit of real function of real variable?
(* Limit[Log[x]^x, x -> 0, Assumptions -> Log[x]^x ∈ Reals] *)
More examples
From below:
Limit[Sqrt[x], x -> 0, Direction -> 1, Assumptions -> Sqrt[x] ∈ Reals]
During evaluation of Limit::cas: Warning … Assumptions -> Sqrt[x] ∈ Reals]
(* 0 *) …
- 236k
18
votes
Accepted
29
votes
Accepted
How to assume all variables in my code are reals
You can do something like this:
Simplify[Sqrt[x^2]]
(* Sqrt[x^2] *)
$Assumptions = _ ∈ Reals
(* _ ∈ Reals *)
Simplify[Sqrt[x^2]]
(* Abs[x] *)
This tells those functions that have an Assumptions option … There are other functions which do not have an Assumptions option but can still work with reals only. These will have a "domain" option, which can be set to real. …
- 236k