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Questions tagged [assumptions]

Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[].

Assumptions are used to indicate membership of domains (Integers, Reals) or other relationships that hold for certain variables.

546 questions
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Is it possible to add some pattern to $Assumptions

I apologize if it is a too elementary question but I could not find the appropriate documentation so far. My goal is simple. I would like to add some assumptions that are defined in terms of patterns rather than symbols. For example, I would like…
Sungmin
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Unknown function with arbitrary arguments assumption

Is it possible to define an assumption like this: $Assumptions=f[__]>0 So that: Simplify[f[x]+3==0] (*False*) Simplify[f[a,b,c]+4==0] (*False*) Etc... The way above doesn't work, but is intended to show what I want to do. I have this function…
Giovanni F.
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How to best add assumption that many variables are positive?

I often need to check whether integrals are solvable in closed form and use a notebook with 5–10 variables that need to be assumed positive. Is there a better way of doing this than adding the clunky line: $Assumptions=a>0&&b>0&&c>0&&d>0&&f>0; ? I…
WillG
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Problem with general assumptions

I hope I am not to redundant with my questions. As part of solving a physical problem, I want to assume once and for all that all my variables and parameters are real, positive and finite. Is it possible make such assumptions for all Mathematica…
Peter
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How can I specify the assumption 'a' is much greater than 'b' (a>>b) in Mathematica?

I want to evaluate an expression of type 1/(r-2 m), assuming r >> 2 m. This is regarding black hole physics and r = 2 m is the Schwarzschild radius. But I am working on something where I need to evaluate a similar type of expression assuming r >> 2…
apk
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How do I apply assumptions to a module (or any CompoundExpression)?

Edit: I am looking for a way to apply assumptions to all expressions contained in a compound expression. For example, f[x_] := CompoundExpression[Clear[n], If[x > 0, n = 1, n = 2], Array[#1 &, n]]; Output of this function is supposed to be an…
Arturs C.
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Assuming monotonicity and concavity

I have an expression that I would like to evaluate: 2 phi''[1 + a (-1 + u[10])] phi'[q]^3 > phi''[q] phi'[q] phi'[1 + a (-1 + u[10])]^2 Is there any way of telling Mathematica that the function phi is strictly increasing and convex?
RoyalTS
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How to check the assumptions attached to a given symbol?

Suppose there are a number of assumptions attached to a certain symbol. How do we query Mathematica to see if a given assumption holds? To be more precise, how can we define a function elementQ such that Block[{$Assumptions = Element[x, Reals]},…
glS
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Why does Assuming[...] work in one case but not in another?

Why does this work Assuming[α > 0 && ϵ > 0 && t > 0, FullSimplify @ Integrate[(z^2 Exp[-α t (z^2 + ϵ)])/(z^2 + 1), {z, 0, ∞}]] (E^(-t α ϵ) (Sqrt[π] - E^(t α) π Sqrt[t α] Erfc[Sqrt[t α]]))/(2 Sqrt[t α]) but not this? MyAssumptions := Assuming[α…
user6677
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simplify assuming a variable equals zero

How can one simplify an expression by assuming that one of the variables is equal to zero? For instance, while Simplify[%,a>0] gives the desired output, Simplify[%,a=0] produces the following error: $Assumptions::bass: 0 is not a well-formed…
user001
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Assuming a variable is imaginary

I am confused how to assume a variable is pure imaginary. As a test example, I used the code Assuming[{ x \[Element] I Reals}, Simplify[x + Conjugate[x]]] In the above, "I" means the imaginary unit. I find that it does not return me 0, but just x…
user34104
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List vs. && in Assumptions

When one gives values to the $Assumptions variable, it seems to not matter whether you separate the conditions with && or just give is a list of the conditions (see below). Is there any subtle difference I am not catching? Remove["Global`*"]…
ions me
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Making the assumption that variables are real

I have a problem with using Assumption. The question arises when I try generating matrix with rolling code: vect = {α, 1 - α, 0, 0, d, -Id }; prod0 = {vect}; prod1 = Transpose[prod0]; Assumptions -> {α > 0, α ∈ Integers, d > 0, d ∈ Integers}; matrix…
Unbelievable
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Restrict list to reals for statistics

I get conjugates in output when running this: Clear[X]; X:={x1,x2,x3}; Assuming[{Element[X, Reals]},StandardDeviation[X]] What is wrong with the code?
Student4K
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Limits with assumptions

I have an example where Mathematica is not able to compute limits in a function restricted to assume that the input parameter is Real. I don't understand why this is so. 1. Could someone explain why this is a problem? 2. Is there a way to get around…
Siva
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