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
995 views

How Simplify and Assume can be combined on matrix products?

What I am trying to do is to simplify some expressions involving matrices! The problem is that Simplify[] considers the simplifications based on alphabetical order and everything is Commutative. For ...
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1answer
86 views

Is it possible to use an assumption that a parameter is an odd or even number?

I am trying to integrate: Integrate[(Exp[x]*(x^m)/((Exp[x] + 1)^2)), {x, -Infinity, Infinity}] I know that for odd m the result is zero. How can I tell ...
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1answer
89 views

How to apply assumptions to pattern matching?

I'm trying to remove terms whose exponents are positive in a polynomial. I tried this one; Assuming[t > 0, x^t /. {x^a_ /; Positive@a -> 0}] but the result ...
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1answer
44 views

Assuming a variable is imaginary

I am confused how to assume a variable is pure imaginary. As a test example, I used the code Assuming[{ x \[Element] I Reals}, Simplify[x + Conjugate[x]]] In ...
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1answer
43 views

Using assumptions, weird output [closed]

I have a Piecewise function, of the type: $Assumptions = b > a > 0 fun[k_] := Piecewise[{{3k, 0<=k<a}, {k^2, a<=k<=b}}] fun[a] When evaluating ...
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1answer
49 views

Is there a global parameter that limits the number of variables handled by Simplify?

It seems that Simplify is unable to handle (at least some) expressions involving 22 or more variables. Consider the code snippet below: ...
4
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1answer
126 views

Simplify is not simplifying a compound inequality as expected

The Simplify command is having trouble verifying a compound inequality, even while it correctly handles the two corresponding single inequalities. I'm starting ...
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2answers
54 views

how to get rid of the denominator in the squareroot, that appears in the denominator?

Here is an example: $\frac{\nu y_0}{\left(x_0+\frac{1}{2}\right) \sqrt{\nu ^2+\frac{\left(4 x_0^2+4 y_0^2-1\right){}^2}{16 y_0^2}}}$ ...
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2answers
90 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
43 views

Exits and beeps on Integration

Evaluating ...
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0answers
40 views

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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241 views

What is a “generic case”?

Introduction With this question I am coming back to a long-standing issue I have with Mma's concept of a "generically correct" result. The basic idea seems to be, vaguely, that if a result is true in ...
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0answers
28 views

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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1answer
67 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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4answers
310 views

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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0answers
51 views

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 <...
0
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1answer
50 views

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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2answers
79 views

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 ...
0
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1answer
42 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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0answers
36 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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0answers
29 views

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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1answer
89 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 $c$. ...
2
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1answer
64 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
39 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
35 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
50 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
49 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
88 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
72 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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0answers
67 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: ...
3
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2answers
63 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 ...
0
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1answer
100 views

Why are some of my assumptions ignored?

In my opinion Mathematica should be able to further calculate and simplify the output of G1[...]. ...
0
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1answer
42 views

Integrate ignores Assumptions [closed]

I'm asking Mathematica to compute: ...
2
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1answer
90 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
37 views

FullSimplify does not simplify at all

I have some problems simplifying things with FullSimplify. Suppose a matrix ...
14
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4answers
12k 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 ...
0
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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} ...
0
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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 ...
2
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1answer
90 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 ...
0
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1answer
43 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
65 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]) ...
5
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1answer
582 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 ...
0
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1answer
100 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
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 ...
0
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1answer
55 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., ...
0
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0answers
95 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 <...
2
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2answers
132 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: ...
3
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2answers
139 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 ...
3
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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 <...
0
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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)...