Questions tagged [assumptions]
Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[].
366
questions
0
votes
0answers
32 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 ...
0
votes
1answer
60 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 ...
0
votes
0answers
25 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 ...
1
vote
1answer
80 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
votes
1answer
59 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 ...
1
vote
1answer
36 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 ...
0
votes
0answers
32 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 ...
1
vote
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
...
1
vote
2answers
40 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
votes
1answer
79 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. ...
1
vote
1answer
58 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, ...
0
votes
0answers
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:
...
3
votes
2answers
59 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
votes
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[...].
...
0
votes
1answer
40 views
0
votes
0answers
35 views
FullSimplify does not simplify at all
I have some problems simplifying things with FullSimplify. Suppose a matrix ...
0
votes
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
votes
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
votes
1answer
86 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
votes
1answer
41 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 ...
1
vote
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])
...
5
votes
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 ...
0
votes
1answer
70 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 ...
0
votes
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
votes
1answer
46 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., ...
2
votes
2answers
127 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:
...
0
votes
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
<...
0
votes
2answers
81 views
Result with assumptions contradicts previous result
Without assuming anything on the argument of the complex number inside the Gamma function
...
3
votes
1answer
60 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
votes
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
$$\sum _{k=1}^{\infty } \left(\frac{ 1}{(2 k-1) (2 k+1)} \left(\sum _{n=1}^{\infty } \frac{(-1)^{n-1}}{(2 n-1)...
1
vote
1answer
99 views
How to define a complex function with assumptions?
I'm trying to define a complex function to be able to do analytic calculations. Specifically, I want to define a function $A(x,t)$ in the complex plane with argument $\theta(x,t)$ and modulus $R(x,t)&...
1
vote
2answers
35 views
Clarity of assumptions in PowerExpand
I am trying to simplify a complicated expression which involves $\log$ of sum of $e^{i x_{i}}$ terms, and I found out that using PowerExpand it gets greatly simplified. But I know that PowerExpand ...
2
votes
2answers
91 views
How to define an antisymmetric symbol?
I want to work with linear expressions involving the formal symbol $w[a_1,...,a_n]$, and I would like Mathematica to know that expressions such as
...
1
vote
2answers
148 views
How to add a vector variable to a vector value?
If we have a three dimensional vector variable:
$Assumptions = a ∈ Vectors[3];
and a three dimensional vector value for example:
...
3
votes
2answers
132 views
Can pattern assumptions be made reliable?
It is possible to use patterns in assumptions such as f[_]>0. This does not seem to be explained in the documentation but is for instance pointed out in Is it ...
7
votes
2answers
551 views
Forcing Mathematica's Integrate to give more general answers
I have a simple gaussian integral: $\int^{\infty}_{-\infty}dx\:e^{i\alpha x^2}$.
If $\alpha \in \mathbb{R}$, then:
$$
\int^\infty_{-\infty} dx\; e^{i \, \alpha x^2} = \sqrt{\frac \pi {-i \alpha}} \...
2
votes
1answer
45 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
124 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
251 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
73 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
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:
...
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
65 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
66 views
Simplifying polynomial Roots with assumptions
I have acquired the following root from a minimization problem:
...
0
votes
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
...
0
votes
0answers
31 views
2
votes
1answer
67 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
73 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
93 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
55 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:
...
