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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Exits and beeps on Integration

Evaluating ...
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Why does Mathematica miss some solutions for my integral?

When computing the integral of two orthogonal sine functions $\qquad \sin(n\,\pi\,x)\,\sin(m\,\pi\,x)$, where $n,\,m$ are integers > 0 Mathematica seems to miss the solution where $n=m$. I don't ...
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Using assumptions in DSolve

I want to solve the following differential equation DSolve[u'[\[Xi]] == a u[\[Xi]]^(2 - m) + b u[\[Xi]] + c u[\[Xi]]^m, u[\[Xi]], \[Xi]] with the assumpetion ...
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Simplify makes Mathematica forget that a matrix is Hermitian

Using Simplify with certain trivial assumptions makes Mathematica forget that a given matrix is Hermitian. See the minimal example below: ...
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Dealing with positive power variables in Taylor expansion and assumptions

I would like to compute the Taylor expansion of monomials whose powers are nonnegative rational variables. First, here is a function which encodes the multivariate Taylor expansion at the points <...
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1answer
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Using Assumptions [closed]

I’m trying to use Assumptions for the set of variables in a form: $Assumptions = {(k, z) ∈ Reals, (k, z) > 0}; But as a result a receive an errors. What is ...
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Definite Integration with Exponental Heaviside Step Funtions

As part of an equation of state calculator that I am working on, I have to handle a virial expansion for the equation of state. As such I have to solve for the virial coefficent, $B(T)$, which is ...
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36 views

How to use assumptions without Simplify[]?

According to this simple example program, the assumptions evaluated only with the Simplify[] function call. However, I wouldn't like to use Simplify[] because it can be very slow with longer ...
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34 views

Solving an integral using assumptions

I am trying to solve the integral Integrate[(Sin(theta))/sqrt((r^2) + (s^2) - 2 rs(cos(theta))), {theta, 0, pi}] with assumptions that ...
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66 views

Domain specifications for InverseFunction

I have difficulty implementing on how to specify the domain that I want for ry which is the inverse function of rho. The necessary condition is that, $\textbf{ry}$ must remain $\textbf{positive}$ for ...
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Vanishing with the derivative terms in perturbation theory

Following the question in here, now I would like to make the terms with derivatives to vanish. To shortly explain, given a variable decomposed as follows: $a(t,r) = a(r) + \delta a(t,r)$ in my long ...
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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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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
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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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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
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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
44 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 ...
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81 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
63 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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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
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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
95 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
41 views

Integrate ignores Assumptions [closed]

I'm asking Mathematica to compute: ...
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FullSimplify does not simplify at all

I have some problems simplifying things with FullSimplify. Suppose a matrix ...
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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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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
89 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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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
63 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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578 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
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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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28 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
52 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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2answers
131 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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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
88 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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1answer
62 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
40 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
116 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
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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
97 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
183 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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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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556 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
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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
143 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
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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 ...
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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 ...
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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: ...