Questions tagged [assumptions]

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

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Getting the same result from Integrate as Probability

I'm trying to solve a Baysian inference problem (although the details are not all that important for this question) I define two probability distributions P and <...
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2 answers
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`Assuming` combined with mathematical notation of `Integrate`

I am trying to write down the following expression Integrate[Exp[-a/2/x]/x/(x + 1), {x, 0, b}, Assumptions -> a > 0 && b > 0] using mathematical ...
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2 answers
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Assumptions in Integration for positive real values [closed]

I want to evaluate the following integral in Mathematica. $$ \int_0^\infty \frac{a^{-t}-b^{-t}}{t} dt = \ln \left(\frac{\ln b}{\ln a} \right)$$ I try to enter this, but Mathematica can't figure it out....
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How to declare at the beginning of the notebook that a variable belongs to a set?

In the notebook I am working on I have certain symbolic variables (e.g., c and r) which I would like to declare since the very first few lines to be non negative real numbers. Correct me if I am wrong ...
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1 answer
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How to use System`Private`AssumptionAccess and Assumptions`*?

I see this function is used by some symbols in Assumptions`*, and it HasDownCode and does not ...
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3 votes
1 answer
266 views

Mathematica tries to differentiate Abs[x] and this causes a problem? [duplicate]

I am trying to run the following code: ...
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0 answers
24 views

Global assumption non zero

I would like to define globally an assumption stating that I have a nonzero real vector $v$. For now, I put : $Assumptions = Element[v,Vectors[{100},Reals]] but $v$ ...
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  • 442
2 votes
1 answer
66 views

Simplifying an expression with complex conjugates

I have been unable to do the following. First I make an assumption $Assumptions = x \[Element] Reals; and define ...
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  • 79
1 vote
1 answer
51 views

Why does not ContourPlot consider the condition given in RegionFunction in the given code?

I have two functions $f(x,y)$ and $g(x,y)$. I am using RegionFunction in ContourPlot to see those values of $(x,y)$ for which $...
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  • 463
2 votes
2 answers
91 views

Is it possible to exclude a condition, say, $f(x,y)=const.$, from a ContourPlot code?

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  • 463
4 votes
2 answers
331 views

How to get a manipulated plot of the intersection points of two curves without finding them numerically?

I have four 2-variables functions for $0<x<3$ and $1<y<3$ ...
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  • 463
2 votes
1 answer
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Identical integral evaluating differently

I am trying to compute an integral but am getting two different answers using two near-identical methods. I wish to know why they differ. ...
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1 answer
51 views

Adding Assumptions in double integral written in "math input" mode

I've the following double integral and I'd like to write Assumptions->Re[c]>0, but if I try to do it, I get a syntax error. How can I add the above condition but without changing the ...
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How to make assertions for subscripted variables?

I'm trying to write a formula using subscripted variables like x₁, x₂, x₃, ..., so that I can later retrieve their values programmatically. However, I'm struggling ...
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1 answer
206 views

The derivation and simplification of the functions HeavisideTheta and Dirac

I encounter some problems, can you help me? Thanks. Step (1) gives the expected result 3 DiracDelta[x], why (2) and (3) can not give expected result ...
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60 views

Can I use assumptions to declare a variable's type?

I'm trying to declare $P$ as a vector. I searched for a while, the closest way seems to be Assumptions: ...
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1 vote
2 answers
48 views

How to assume some variables to "not" be a function of other variables at the time of defining a function [closed]

I have a function with the following definition: F[x]=Exp[q*w*x]; I want to take total derivatives of F. How can I define that q and w are not dependent on x at the ...
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  • 340
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0 answers
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Simplify expression with assumption that all variables are real

I have an expression in which all variables are real. However when I simplify the expression with appropriate assumptions a 'Conjugate' still remains. How can I get rid of this? Here is my code ...
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2 votes
0 answers
98 views

Why does this ConditionalExpression appear? [closed]

I am new to Mathematica. Could anyone help explain why ws > 0 appears in the solution? How to define symbolic variables' range? Thanks! EDIT to include code <...
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2 answers
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How to solve system of equations with complex variables

I'm trying to obtain the solution to the following system of 3 equations and 4 variables: ...
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1 vote
1 answer
62 views

How to 'define' value in Assumptions but not let Simplify replace it? [closed]

I want to let Simplify know the exact value of a symbol, to resolve logical statements, but don't want it to actually replace it. For instance, I would like ...
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1 vote
0 answers
48 views

TensorExpand ignores assumptions?

Here's a minimal example to demonstrate my problem: ...
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0 votes
1 answer
72 views

Simplify an expression with assumptions connected with OR

Mathematica doesn't seem to have any problem with these commands: ...
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4 votes
1 answer
246 views

Why isn't this expression returning true to being positive when it is clearly positive?

Consider: ...
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  • 465
0 votes
0 answers
38 views

How to simplify the conditional expression?

I have an assumption for mulitple value, ...
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0 answers
35 views

Test domain assumption of a variable

Using $Assumptions to define the domain of variable is straightforward, i.e. $Assumptions = Element[x, Reals]. Nevertheless, it'...
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0 answers
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Difference between Assuming[] and Refine[]

I'm trying to find the limit of a root. I've found that the limit is undefined if I use Refine[] ...
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4 votes
1 answer
150 views

Representing number domain by a symbol [closed]

I'd like to represent the number domain by a symbol rather than text word. While Solve[n^2 - 19 n + 99 == k^2 \[And] {k, n} > 0, {k, n}, Integers] works fine, I'...
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4 votes
3 answers
1k views

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 ...
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  • 147
1 vote
0 answers
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Piecewise and Assumptions [closed]

Assumptions sometimes work as expected with Piecewise, for example Simplify[Piecewise[{{A, a + b >= c}, {B, True}}], Assumptions -> a + b > c] correctly ...
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  • 339
1 vote
1 answer
74 views

Solving generating conditional expression despite assumptions

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2 answers
74 views

Triple integral: How do I include assumptions and conditions?

I would like to solve the following integral: $$I=\int_{0}^{a} \int_{0}^{y} \int_{0}^{z} e^{(a-x)^{3}} d x d z d y$$ with the condition that: $$a>0$$ So I tried to input the equation like below ...
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5 votes
2 answers
200 views

Why Mathematica is not assuming real variable as real?

I am dealing with the situation where despite of specifying my variables b1 and c to be greater than zero, Mathematica still ...
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0 votes
1 answer
97 views

how can I modify this function to convert to polar form for any complex expression?

The function from another post is to convert a complex number to polar form. polarForm = Expand[# /. z_?NumericQ :> Abs[z] Exp[I Arg[z]]] & Now if I apply ...
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1 vote
1 answer
55 views

How to generate assumptions automatically for definite integrals?

In Mathematica, a trick to speed up the process of definite integrals is by adding assumptions. For example, the following codes run faster if we add such assumptions: ...
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3 votes
0 answers
76 views

$Assumptions causing problems in Mathematica 12.3 vs. 10.4 [duplicate]

I would like to use $Assumptions to add global restrictions to the parameters in my notebook (Mathematica 12.3). I tried exactly this in Mathematica 10.4 and it ...
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2 votes
1 answer
119 views

Symbolic Mean and Variance Calculations

I need a tutorial that gets me started on basic symbolic calculations with random variables. My naive attempts did not get me far. ...
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1 vote
1 answer
122 views

FullSimplify is giving a condition that is implied by the assumptions

I've been trying to understand why FullSimplify is giving a condition that is implied by the assumptions (otherwise the set is empty). However, I couldn't ...
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1 vote
0 answers
64 views

Why is this integrand not integrating to a Bessel function? [duplicate]

I know from the identities of Bessel functions that the following is true: $$ J_{m}\left( x \right) = \frac{ 1 }{ 2 \ \pi \ i^{m} } \int_{0}^{2 \pi} \ d\phi \ e^{i \left( x \cos{\phi} \ - \ m \ \phi \...
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1 vote
1 answer
98 views

Using Simplify and Reduce with Assumptions when the inequality is already one of the assumptions

I am using the Simplify and Reduce functions to reduce inequalities, but somehow the function Simplify does not consistently give "True" when the inequality happens to be one of the ...
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1 vote
2 answers
53 views

Assuming r0 ≈ r1 && r0 ≈ 0 && r1 ≈ 0, to discourage division by near-zero

I’m using Mathematica for some conceptually simple algebra, that will ultimately land in Excel or a compiled language. ...
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  • 499
0 votes
1 answer
61 views

Solving an equation, and verifying that it is correct

I want to solve the equation Solve[e == 1/2 (-2 ef + hvk - Sqrt[9 hvk^2 + 4 j^2]), hvk] I then obtain the solutions ...
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3 votes
1 answer
75 views

Solve yields complex Root even if the domain is Reals

I want to solve $x^3=a^2$ for $x$ where $a>0$ and $x$ is real. The answer I want is $$x=a^{2/3}.$$ On Wolfram Cloud, I tried ...
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5 votes
2 answers
175 views

Help solving this differential equation

I am trying to solve this differential equation $$ y^{''}(x) + \frac{6}{x} y^{'}(x) +14 y(x) = -4 y(x) \; \ln(y(x)),\; x > 0$$ subject to the boundary conditions $y(0) = 1,\;y^{'}(0) = 0$. The ...
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4 votes
2 answers
109 views

Specify range of variable in a equation

I have a simple integral, I get the answer in terms of (h-1) whereas I know h is smaller than 1 and greater than zero. How could I implement this is the fully simplify. ...
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0 votes
0 answers
33 views

Assume some expression is false

I need to Reduce a complicated function and I want to exclude some conditions A and B. How do I assume that the expression A is ...
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1 vote
1 answer
71 views

Simplify not working

I am trying to simplify the following expression code: ...
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1 vote
0 answers
61 views

Intervals v.s. Domains: when to use which and why?

or: How to use Interval correctly? Mathematica provides these constructs for various symbolic deductions tasks. Among those constructs are symbolic number sets ...
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1 vote
1 answer
92 views

Real part of complex exponential

How do you obtain the real part of a complex exponential? For example, Mathematica gives $Re[e^{ik}]$ instead of $\cos(k)$, see figure. ...
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  • 121
2 votes
1 answer
78 views

Display assumptions of a variable

If I restrict a variable x to x>0 via $Assumptions=x>0, is there a way I can get ...
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