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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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2answers
103 views

Can pattern assumptions be made reliable?

It is possible to use patterns in assumptions such as f[_]>0. This does not seem to be explained in the documentation but is for instance pointed out in Is it ...
7
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2answers
521 views

Forcing Mathematica's Integrate to give more general answers

I have a simple gaussian integral: $\int^{\infty}_{-\infty}dx\:e^{i\alpha x^2}$. If $\alpha \in \mathbb{R}$, then: $$ \int^\infty_{-\infty} dx\; e^{i \, \alpha x^2} = \sqrt{\frac \pi {-i \alpha}} \...
2
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1answer
37 views

Using Series with Refine or Assuming to restrict the power

I have a system of differential equations which contain a singular point. To avoid the singular point, I am expanding the coefficients and solutions in a power series around that point. Due to the ...
3
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2answers
98 views

Can the Assuming function be used with ContourPlot or DensityPlot?

I'm new to Mathematica, and for most purposes the program has served me well and been straightforward. However, I'm hitting a snag while trying to create a contour plot for the distribution function ...
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1answer
241 views

Linearity Assumption [duplicate]

I'd like to define a set of variables of this sort: {K1[t],K2[t],...} Adding a general assumption: all such variables are linear. I'd like to do this to avoid ...
3
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0answers
58 views

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 ...
2
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1answer
30 views

Reevaluating an expression when Assumptions have changed

Is there a way to make this work? THM = TensorDimensions[M]; Assuming[ Element[M, Vectors[n]], THM ] Which gives: ...
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0answers
41 views

Not getting a solution to my maximization problem

I want to solve the following problem: For $0.5<q<1$, $q<r<1$, $0\leq n$, $0\leq n_1<=\lfloor{n/2}\rfloor$, and $n_1,n\in\mathbb{N}$ calculate $\arg max_{n_1} S(q,r,n,n_1) $ as a ...
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1answer
52 views

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
52 views

Simplifying polynomial Roots with assumptions

I have acquired the following root from a minimization problem: ...
0
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0answers
50 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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0answers
28 views

$Assumptions not taken in account

Consider the following code : ...
2
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1answer
52 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 ...
1
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1answer
65 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. ...
2
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1answer
79 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: ...
1
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1answer
53 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: ...
0
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1answer
33 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
55 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
40 views

Different integral results within equivalent conditions

I input 3 functions as following, ...
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0answers
50 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
56 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
50 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 : ...
4
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0answers
101 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 $$\...
1
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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
107 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
39 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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0answers
30 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
105 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})\...
1
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4answers
70 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 ...
1
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1answer
36 views

Taking residues with integer assumptions?

In some cases, Mathematica successfully produces a general result for residues with assumptions, such as: ...
1
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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 ...
4
votes
2answers
65 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. ...
4
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3answers
209 views

Using Assuming with Reduce

I have the following code that includes Assuming to cut through irrelevant detail, or so I had hoped. ...
3
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1answer
122 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
55 views
0
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0answers
39 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 ...
3
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2answers
70 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 ...
3
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1answer
193 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 ...
0
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2answers
97 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
124 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 ...
2
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0answers
40 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 ...
2
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2answers
175 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 ...
1
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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] ...
4
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0answers
96 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}]] ...
0
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2answers
88 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? ...
3
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1answer
58 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: ...
1
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1answer
49 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'...
0
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0answers
47 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' ...
0
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0answers
94 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 ...