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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1answer
39 views
Mathematica stuck at running symbolic multidimensional Fourier Transform
I'm trying to compute the analytical FT of a bidimensional exponential decay as follows:
$f_E(\vec{x}) = \exp \left( - \sqrt{ (\vec{x} - \vec{\mu})^T \Sigma^{-1} (\vec{x} - \vec{\mu}) } \right)$
...
0
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3answers
47 views
Simplifying polynomial Roots with assumptions
I have acquired the following root from a minimization problem:
...
0
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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
...
0
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0answers
26 views
2
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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 ...
1
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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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2
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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:
...
1
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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:
...
0
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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 ...
0
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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
1
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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.:
...
0
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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=...
1
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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 :
...
4
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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
$$\...
1
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1answer
108 views
Can this integral be calculated using Mathematica?
I have the following integral:
$$
\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}}{(\...
1
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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?
0
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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:
...
0
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0answers
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 ...
3
votes
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]
<...
1
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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
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 ...
1
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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:
...
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
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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4
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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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3
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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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0answers
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
...
3
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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 ...
3
votes
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 ...
0
votes
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 ...
6
votes
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 ...
2
votes
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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2
votes
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
...
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]
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4
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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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0
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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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3
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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:
...
1
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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'...
0
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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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0
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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 ...
1
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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 $\...
3
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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 ...
2
votes
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 ...
1
vote
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 $Assumptions in one notebook affects the others, although I have changed Notebook's default context to "Unique to this ...
0
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1answer
87 views
Problem with Assuming [duplicate]
I have some involved complex expressions, relying upon constants and the variables t, C[i],$i=1,2,3$.
Using Refine, I try to ...
2
votes
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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2
votes
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 ...
0
votes
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 ...
