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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56 views

Assuming that only the 2nd order terms are zero

I am dealing with first-order perturbative theory, that is, any variable may be decomposed as $a = a + \delta a$ and the same would occur with several different variables, let's say, $b$ and $c$. ...
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1answer
56 views

Analytical integration of a composite Dirac delta

From the well-known properties of the Dirac delta function $ \delta(f(x)) = \sum_k \frac{\delta(x-x_k)}{|f'(x_k)|} \qquad x_k = \text{zeros of }f(x) $, $ \delta(f(x))=0 \qquad \qquad\qquad \text{if ...
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1answer
33 views

Assuming x real, simplifying or refining Im[1/(x+i)] doesn't yield anything

I think it is straightforward from the title, Simplify[Im[1/(x+I)], x > 0] spits out, Im[1/(x+I)] while I would have ...
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0answers
30 views

Simplifying a sum

The expression I'm trying to do something with is Sum[1/(a!(s-a)!)b^(-(2a+1)/2) Sqrt[\[Pi]](2a)!/(4^a (a)!)Pochhammer[-a,k],{a,k,s}] where ...
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1answer
38 views

Implementing global Assumptions [closed]

Why do the following commands $Assumptions = {Element[x, Reals], x > 0}; Solve[{x^2 == 1}, {x}] Solve[{x^2 == -1}, {x}] give ...
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2answers
37 views

Correctly restricting domain of parameters within Solve

I have seen a few posts about this (such as this one), but none solved my problem. As a silly example, suppose I want to solve (1-x)^n = 0, knowing that n > 1. I ...
5
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1answer
78 views

Make assumption for function with variable argument

I would like to assume that a>t[b_] for any b, such that e.g. Simplify[a>t[c]]==True. ...
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1answer
53 views

Many global assumptions

I will do some calculations with probability distribution p[t] - which is a vector and each term corresponds to a probability of some event. Accordingly the sum over the terms in p[t] has to be one, ...
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58 views

Simplify with my own assumption to a^2+b^2=C^2

I am trying to use an assumption to simplify as a^2+b^2=C: ...
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2answers
57 views

Simplify the cubic root of cube assuming real and positive variable

I know this is very simple but I couldn't find a reasonable solution for it in the archive. It seems that my Mathematica does not take into account the assumptions when it wants to simplify the ...
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1answer
91 views

Why are some of my assumptions ignored?

In my opinion Mathematica should be able to further calculate and simplify the output of G1[...]. ...
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1answer
39 views

Integrate ignores Assumptions [closed]

I'm asking Mathematica to compute: ...
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1answer
77 views

Calculating Limit with option Analytic->True and $Assumptions yields Series::cas

Overview I am using Limit with the option Analytic->True to check the finiteness of some expressions with generic functions ...
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0answers
33 views

FullSimplify does not simplify at all

I have some problems simplifying things with FullSimplify. Suppose a matrix ...
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4answers
11k views

Defining the domain of positive real numbers

I am trying to solve an equation by assuming that all the variables are real and strictly positive. I can use the keyword Reals for the argument ...
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1answer
45 views

How to work properly with assumptions?

I'm trying to find an analytical solution which depends only of $i,j$ and $a$ variables, for a serie considering some initial assumptions. The series is $$s_{i0}=s_{0j} = 1,\\ s_{11} = 1-a,\\ s_{12} ...
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0answers
23 views

Problem with integrating special function under assumption

i found different results when integrating a special function (see below), depending where i place my assumption (x > 0, x0 > 0). The problem is that the two solutions are not compatible. In fact, if ...
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1answer
85 views

Taking real and imaginary parts after reciprocal

I noticed the following strange scenario. When I defined a variable to be real, Mathematica does not only recognize that it is real after taking an inverse. How can I resolve this so that it will ...
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1answer
40 views

I am asserting a variable in Mathematica as Real yet it is not implementing it!

Element[\[Theta], Reals]; Ga = g; Gb = g*Exp[I*\[Theta]]; {{Conjugate[Gb], Ga}, {Ga, Gb}} I have a code as such for a matrix as given above. as ...
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1answer
62 views

FullSimplify does not work well (require answer in terms of a particular variable)

(new to Mathematica) I am trying to simplify the Schwarzian derivative of f w.r.t. u.(In[10]). Here f is prime of Weierstrass function (In[8]) which has some constraints (In[9]) ...
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1answer
575 views

How to plot the eigenvalues of a parametric matrix efficiently?

I was wondering how can I set the variable type of matrix elements to be real. The problem is, I creat a variable-dependent matrix as follows and I get the eigenvalues now I want to plot the ...
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1answer
63 views

Multiple Assumptions for Symbolic Matrices

new to the forum and here's the question I'm pondering on: I'm trying to use FindInstance in Mathematica to solve a symbolic matrix equation with quite a few assumptions. For example, quite ...
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0answers
25 views

`Minimize` not working for general case

I'm trying to perform a minimization for an arbitrary natural number. If I enter a specific number, Mathematica performs the correct minimization. Am I specifying k ...
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1answer
41 views

Simplifying an expression involving a matrix and functions of it

I have implemented the following two matrices in Mathematica in order to compute s, but I don't know how I can further simplify the resulting expressions, e.g., ...
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0answers
93 views

Bug in Integrate with Assumptions?

I encountered behaviour I wasn't expecting with Integrate and thought I'd ask here before reporting a bug in case I'm just missing something obvious. A simple example is the following: Computing <...
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2answers
124 views

FullSimplify a trigonometric expression doesn't work as expected

I know this kind of question is frequent asked, yet each case has its own particularities. I will show my problem. I define the following: ...
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2answers
80 views

Result with assumptions contradicts previous result

Without assuming anything on the argument of the complex number inside the Gamma function ...
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2answers
130 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 ...
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1answer
59 views

Simplify with Semi-Infinite Interval

I'd like to Simplify an expression using an Interval constraint. This question shows that you need to put the variable in a <...
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1answer
39 views

Handling Errors in Slowly Converging Dirichlet Beta Infinite Sum

I have tried to calculate the following slowly converging double sum in Mathematica 11.3 $$\sum _{k=1}^{\infty } \left(\frac{ 1}{(2 k-1) (2 k+1)} \left(\sum _{n=1}^{\infty } \frac{(-1)^{n-1}}{(2 n-1)...
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1answer
90 views

How to define a complex function with assumptions?

I'm trying to define a complex function to be able to do analytic calculations. Specifically, I want to define a function $A(x,t)$ in the complex plane with argument $\theta(x,t)$ and modulus $R(x,t)&...
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2answers
34 views

Clarity of assumptions in PowerExpand

I am trying to simplify a complicated expression which involves $\log$ of sum of $e^{i x_{i}}$ terms, and I found out that using PowerExpand it gets greatly simplified. But I know that PowerExpand ...
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2answers
88 views

How to define an antisymmetric symbol?

I want to work with linear expressions involving the formal symbol $w[a_1,...,a_n]$, and I would like Mathematica to know that expressions such as ...
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2answers
129 views

How to add a vector variable to a vector value?

If we have a three dimensional vector variable: $Assumptions = a ∈ Vectors[3]; and a three dimensional vector value for example: ...
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0answers
121 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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2answers
548 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}} \...
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1answer
44 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 ...
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2answers
119 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 ...
4
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1answer
270 views

How to use Assuming and If together?

I would like to compare variables t and u and print either Yes or ...
10
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1answer
249 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 ...
1
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1answer
63 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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0answers
72 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
34 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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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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3answers
64 views

Simplifying polynomial Roots with assumptions

I have acquired the following root from a minimization problem: ...
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0answers
61 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
31 views

$Assumptions not taken in account

Consider the following code : ...
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1answer
65 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
72 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
92 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: ...