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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[].

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Mathematica stuck at running symbolic multidimensional Fourier Transform

I'm trying to compute the analytical FT of a bidimensional exponential decay as follows: $f_E(\vec{x}) = \exp \left( - \sqrt{ (\vec{x} - \vec{\mu})^T \Sigma^{-1} (\vec{x} - \vec{\mu}) } \right)$ ...
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3answers
47 views

Simplifying polynomial Roots with assumptions

I have acquired the following root from a minimization problem: ...
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0answers
49 views

I assume that a parameter is real and positive, but Mathematica still assigns a phase to it

If I run this line of code Assuming[{Element[a, Reals], a > 0}, TrigToExp[ComplexExpand[Sqrt[a]]]] I get ...
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26 views

$Assumptions not taken in account

Consider the following code : ...
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1answer
50 views

Choose a branch cut using assumptions

I understand Sqrt function won't simplify expressions such as $\sqrt{x^2}$ unless there is an assumption that $x \in \mathbb{R}$. In my computation, I get an output containing an expression like this ...
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1answer
59 views

Why is the function assuming not taken in consideration?

In the following code, I assume that my variables are strictly positive. However, mathematica doesn't take this in consideration when it evaluates the If : the If is still in a non simplified form. ...
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1answer
74 views

Fullsimplify with two Diracdelta functions

I am having a problem with the FullSimplify and DiracDelta functions. When I run the following line in mathmatica: ...
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1answer
51 views

Hidden limitation of Assumptions (Is $x^2 < 0$ contradictory)?

Is there a limitation of Assuming that I am not aware of? I would like to assume that the square of a number is negative: ...
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1answer
32 views

Sums of binomial expressions returns different and sometimes indeterminate expressions

A problem that I encountered multiple times when taking sums over expressions involving binomials, factorials, etc. is that Mathematica (version 11.2) returns indeterminate expressions when it should ...
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0answers
50 views

Positive integers instead of integers ($\mathbb{Z}$) in assumption

I can use Integers to represent integers. How to represent positive integers? I can define ...
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0answers
38 views

Different integral results within equivalent conditions

I input 3 functions as following, ...
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0answers
49 views

ConditionalExpression still resulting from Assuming a Module's local variables

I have a memoizing, recursive function whose MWE looks like this (the two fake inputs/ICs are from 'K' and 'Bfun2', the latter just a quick way to check the results coming out of the Residue.: ...
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0answers
41 views

Global assumptions

in the following code I evaluate a determinant of a matrix and then solve for one variable (kx). I get three solutions, but the solution kx=0 is in my opinion wrong. This one can see when one plugs kx=...
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3answers
41 views

Solving for positive square root of an equation, using assumptions

Is there a way to get the positive square root, while solving an equation. So far, this is what I am doing : ...
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0answers
87 views

Integrate under assumptions

I am trying to solve the following integral: $$\int_0^\infty u^{\sigma-1} \exp\left[-c u^\sigma\right] \mathrm{d}u$$ under the assumptions $\sigma \in (0,1)$ and $c>0$. I know the result is $$\...
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1answer
108 views

Can this integral be calculated using Mathematica?

I have the following integral: $$ \int_{-\infty}^{\infty} \frac{\mathrm d\tau}{2\pi \mathrm i} \int_{-\infty}^{\infty} \frac{\mathrm d\tau'}{2\pi \mathrm i} \frac{\mathrm e^{-c^2(\tau - \tau')^2}}{(\...
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1answer
61 views

Assume a variable is a Matrix

Is it possible to tell Mathematica to assume a variable is a matrix, analogous to assuming a variable is real with the Assuming command?
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1answer
36 views

How to assume lexicographical ordering

Suppose I have functions which depends on the symbols $c[I]$, where $I$ is some subset of $\{1,2,...,n\}$. For example, $$f = c[1] + c[1,2,3] + c[1,2],$$ $$g = c[2] + c[2,1],$$ Code: ...
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24 views

Using Assumptions Implied by other Assumptions

Is it possible to have assumptions about the smoothness of functions? As an example, suppose that I would like to simplify $u_{tt} - a^2 u_{xx}$ under the assumption that $u_t+au_x=0$. Under some ...
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2answers
90 views

How to apply assumptions to parameters for FindDistributionParameters?

Say I have data that I want to fit to a distribution while applying assumptions on one or more of the parameters. For example, for ParetoDistribution[k, α, μ] <...
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2answers
78 views

Integration using assumption in Mathematica

I want to reproduce the solution of the following integral, using Mathematica: $$\int_0^1duu(1-u)^2\frac{1}{(1-u)(1-v)}\left(\frac{1-u}{u}(1+\frac{1}{1-v})\theta(u-v)+\frac{1-v}{v}(1+\frac{1}{1-u})\...
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4answers
68 views

Problem with particular simplification of complex function under assumptions

I have proven that $expr=(1 - i)(\dfrac{1+z}{1-z})^{1/4}\dfrac{\sqrt{ 1-z^2+i z\sqrt{1 - z^2}}}{1+z-i\sqrt{1 - z^2}}=1$ when it is assumed that $z\in R$ and $|z|<1$ and when I also plot the real ...
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1answer
28 views

Taking residues with integer assumptions?

In some cases, Mathematica successfully produces a general result for residues with assumptions, such as: ...
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0answers
39 views

How to define a variable $x$ such that $Abs[x]<1$ and use this globally without having to re-write it again and again?

I am writing a code or a calculation of a very complicated function and my main variable is $x$ such that $-1<x<1$. This assumption has to simplify my final answer a lot, but since the final ...
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2answers
64 views

Combinations of variables that satisfy my inequality

This question is a continuation to one answered by kglr here. In the following situation, I find that given my assumptions, it is indeed possible for $g$ to be negative. ...
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3answers
190 views

Using Assuming with Reduce

I have the following code that includes Assuming to cut through irrelevant detail, or so I had hoped. ...
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1answer
116 views

Building a function that uses $Assumptions and works like Simplify, FunctionExpand, etc

I want to write a function MySimplify (like built-in Simplify) that takes a second argument to specify additional ...
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1answer
46 views
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38 views

How to test consistency of two assertions without hacking

Suppose I have a set of assumptions assum = x ∈ Reals && y ∈ Reals and I want to test an assertion like ...
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2answers
69 views

Getting around symbol favoritism of Simplify and FullSimplify [duplicate]

Simplify may or may not simplify depending on the symbols you use for its assumptions are good. For example, here is a case where ...
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1answer
188 views

Is there a way to automatically find the limits of integration given a set of constraints?

I have a complicated function $F(x,y,z)$ which I want to integrate subject to these constraints: $y\geq z\geq-y, y \geq 0, y \leq \frac{x+z}{3}$. It's only a 3D problem, so it's possible to draw a ...
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2answers
70 views

Using Assuming for conditional expression in Solve

When I solve the following equation I obtain a solution with a conditional expression Solve[{0 == k Sin[x - y] - Sin[x], 0 == k Sin[y - x] - Sin[y]}, {x,y}] How ...
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1answer
122 views

Is (x|y|…)∈set the same as x∈set&&y∈set&&…?

I've sometimes seen that this operator is used to specify that each of given variables is in some set, e.g. Reals. Like ...
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0answers
39 views

How to express continuity assumption for Integrate?

I am wondering if it is possible, and how if so, to express function continuity in the assumptions for the definite form of Integrate. First of all, while ...
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2answers
174 views

How to Integrate the Derivative of a function with Assumptions on the function?

I have a monotonic increasing function g and constant αsuch that ...
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1answer
29 views

Trigonometric simplification with assumptions fails

Consider the following input Assuming[Element[y, Integers], (-1 + E^(I \[Pi] (x + y)))/(-1 + E^(I \[Pi] (x - y)))//FullSimplify] ...
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0answers
95 views

Trigonometric integral with assumptions fails

Consider the following integral Assuming[Element[{n, m}, Integers] && n >= 0, Integrate[Cos[ϕ]^n Exp[I ϕ m], {ϕ, 0, 2 π}]] ...
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2answers
81 views

Using an implicit assumption to simplify

How can I simplify below expression knowing that r12>>z? Is there any way to expand below expression? ...
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1answer
52 views

Complex Conjugate with Refine

I am trying to do symbolic manipulations in MMA and I need it to take a complex conjugate of functions with real arguments, like: ...
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1answer
48 views

Constrain variables when using NSolve

I'm working with a system of n-equations andNsolve takes too long to get the results. I'm trying to speed things up by adding a restriction to the solutions, but I'...
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0answers
46 views

how can I solve this sum?

how can I solve this sum? Sum[1/(x[p]-x[q]),{p,1,l},p\[NotEqual]q] I tried these codes but not workin' ...
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0answers
93 views

Mathematica ignores my assumption when solving a qudratic equation

I try to solve the inequality $r-3t_0-2\sqrt{2 rt_0}<0$ with assumption that $0\leq r\leq 2t_0$. First, by observation, we can clearly see that if $r=0$, then clearly, this inequality holds. Then I ...
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1answer
86 views

Using the Squeezing Theorem of Limits in Mathematica

I wanted to compute the following limit Limit[ρ, {α -> 0}, Direction -> "FromAbove", Assumptions -> 1 <= ρ <= 1 + α] clearly this has the answer $\...
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1answer
82 views

How to force assumptions for solving a system of equations?

I am trying to solve a system of equations for the panel method using complex functions. Mathematica would not even attempt to produce a solution for the bcs term ...
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1answer
65 views

Using Assumption with LaplaceInverseTransform

I want to compute the the Laplace inverse transform of the following $$\bar f(s)=\frac{1}{s^2+a s+b}$$ which clearly depends on $a^2-4b$. When I use Mathematica, it just gives the answer for the ...
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1answer
57 views

How to have different $Assumptions for each notebook?

Sometimes I keep two or more notebooks side by side. I noticed that changing $Assumptions in one notebook affects the others, although I have changed Notebook's default context to "Unique to this ...
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1answer
87 views

Problem with Assuming [duplicate]

I have some involved complex expressions, relying upon constants and the variables t, C[i],$i=1,2,3$. Using Refine, I try to ...
2
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1answer
52 views

Sum using variables then evaluated with values gives different result than sum with values

I'm trying to do a sum symbolically. However, Mathematica is giving me a different result if I do the sum with numbers or symbols. What's causing this error? ...
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0answers
77 views

Fourier Cos coefficient vs Integrate vs common sense

I was trying to find out what the (discrete) Fourier transformation of the following function is $$ f(\nu, u) = \frac{\sinh \nu}{\cosh \nu - \cos u} $$ So at first, I tried to evaluate a fancy MMA ...
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1answer
57 views

Solving a trig equation in a specific range

I want to define a function as such g[n_] := Assuming[1<=x<=2, NSolve[n==-2 Cos[Pi x], x]] However the result comes out as a conditional expression, for ...