Questions tagged [assumptions]
Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[].
1
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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
votes
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
votes
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
votes
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
...
10
votes
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
votes
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
votes
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:
...
0
votes
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 ...
1
vote
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)$
...
0
votes
3answers
52 views
Simplifying polynomial Roots with assumptions
I have acquired the following root from a minimization problem:
...
0
votes
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
...
0
votes
0answers
28 views
2
votes
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
vote
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
votes
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
vote
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
votes
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 ...
0
votes
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 ...
1
vote
0answers
40 views
1
vote
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.:
...
0
votes
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=...
1
vote
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
votes
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
vote
1answer
108 views
Can this integral be calculated using Mathematica?
I have the following integral:
$$
\int_{-\infty}^{\infty} \frac{\mathrm d\tau}{2\pi \mathrm i} \int_{-\infty}^{\infty} \frac{\mathrm d\tau'}{2\pi \mathrm i} \frac{\mathrm e^{-c^2(\tau - \tau')^2}}{(\...
1
vote
1answer
107 views
Assume a variable is a Matrix
Is it possible to tell Mathematica to assume a variable is a matrix, analogous to assuming a variable is real with the Assuming command?
0
votes
1answer
39 views
How to assume lexicographical ordering
Suppose I have functions which depends on the symbols $c[I]$, where $I$ is some subset of $\{1,2,...,n\}$.
For example, $$f = c[1] + c[1,2,3] + c[1,2],$$ $$g = c[2] + c[2,1],$$
Code:
...
0
votes
0answers
30 views
Using Assumptions Implied by other Assumptions
Is it possible to have assumptions about the smoothness of functions?
As an example, suppose that I would like to simplify $u_{tt} - a^2 u_{xx}$ under the assumption that $u_t+au_x=0$.
Under some ...
3
votes
2answers
105 views
How to apply assumptions to parameters for FindDistributionParameters?
Say I have data that I want to fit to a distribution while applying assumptions on one or more of the parameters. For example, for ParetoDistribution[k, α, μ]
<...
1
vote
2answers
78 views
Integration using assumption in Mathematica
I want to reproduce the solution of the following integral, using Mathematica: $$\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
vote
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
vote
1answer
36 views
Taking residues with integer assumptions?
In some cases, Mathematica successfully produces a general result for residues with assumptions, such as:
...
1
vote
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
votes
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 ...
0
votes
1answer
55 views
0
votes
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
votes
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
votes
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
votes
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 ...
6
votes
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
votes
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
votes
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
vote
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
votes
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
votes
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
votes
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
vote
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
votes
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
votes
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 ...
