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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3 votes
1 answer
74 views

Assume asymptotic value in a limit?

Is it possible to give Mathematica a limit about's function at infinity? For example I would like to ...
  • 438
2 votes
2 answers
43 views

Subtituting kronecker deltas for products in simplification

I have a problem where I have some vector, $a = (a_1, a_2, \ldots, a_n)^T$ that I want to have a Kronecker delta multiplication rule, $a[i]a[j] = \delta_{ij}$ (these are basically basis vectors, but ...
1 vote
0 answers
25 views

Making an "unsafe" simplify that ignores the validity conditions of simplifications

Mathematica will never make assumptions you don't tell it to make, and will state all conditions under which the answers it gives are valid. While this is overall a good thing, this often leads to ...
1 vote
0 answers
50 views

Compute symbolic identities for FourierTransform

Mathematica computes some of the identities for Fourier transforms for an arbitrary function f[t] directly, for example: FourierTransform[f'[t], t, w] ...
0 votes
0 answers
58 views

Refine not able to simplify for PositiveReals

If I type in Mathematica Refine[d^2 == a^2, {a ∈ PositiveReals, d ∈ PositiveReals}] I get d^2 == a^2 Why don't I get ...
0 votes
1 answer
53 views

How to tell Mathematica to solve an equation assuming all solutions are non-negative reals? [closed]

The title. I have a system of 6 equations that I want to solve. The system is non-linear. I want to solve it, but I just want Mathematica to give me solutions that are non-negative reals (so no ...
1 vote
1 answer
114 views

How can I force Mathematica to calculate this integral?

I have the following expression. I realize Mathematica has a little bit of trouble with Abs[] as it assumes variables to be complex and etc., but I am trying to compute an integral and it just keeps ...
1 vote
0 answers
47 views

Finding the (symbolic) eigenvalues of a matrix with some assumption

I have the following 3$\times$3 symmetric matrix with symbolic entries. Meff = \begin{array}{ccc} 2 \beta \text{c12}^2 \text{c13}^2 \text{$\eta $11} \text{m1}+\alpha \text{c13}^2 \text{D31} \text{...
1 vote
0 answers
42 views

Enforcing the continuity of solutions throughout the whole range of variable in NDSolve, when there are multiple solutions

I am solving differential equations numerically by using NDSolve. Let's say that the function that I want to obtain is f[t]. Then, it turns out that my differential equation is a sextic polynomial of ...
0 votes
0 answers
63 views

Why do I get different results for this complex line integral?

I want to compute line integral of $f(z) = \frac{1}{z(z-1)^{n+1}}$ over a closed curve $\gamma: t \mapsto 1 + \frac{1}{2} e^{i t}, t \in [0,2\pi]$ in the complex plane in two different ways but the ...
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4 votes
2 answers
181 views

How can I make assumptions in NDSolve?

Suppose I try to solve the following differential equation numerically. (My example is much more complicated, but for simplicity, let's consider this example.) ...
1 vote
0 answers
34 views

Is there a nice way to deal with sets in an abstract/symbolic way?

For instance, if I wanted to declare $A$ to be the set of all finite subsets of $\mathbb{Z}$, and declare $B$ to be a set comprising all finite subsets of $\mathbb{Z^{-}}$, and then declare $C$ to be ...
  • 753
0 votes
0 answers
32 views

Double variable integration unable to prove that integration limits are real

I have simple question regarding double integrating a function. J*Integrate[Integrate[Cos[ArcTan[Sqrt[(x - a)^2 + (y - b)^2]/L]], {b, -b, b}], {a, -a,a}] The error ...
4 votes
1 answer
84 views

Simplify and Assumptions

Am I missing something here? Thanks for any help! SN
1 vote
0 answers
35 views

Limitations of Assumptions

Why don't Simplify[x[2, 1] < x[1, 3], Assumptions -> {x[a_, b_] > x[c_, d_] /; a > b && c < d}] or ...
  • 593
0 votes
1 answer
61 views

Integral behaviour?

I'm trying to find a standard integral, which shows itself up in general relativity (proper distance in Schwarzschild metric). For example in this video. The integral is shown as where $r_s< r$ ...
  • 438
2 votes
1 answer
110 views

Why does the assuming not work as expected?

Why does this not work? I expect the output would be something like 1/s*e^-(sT). ...
  • 273
0 votes
1 answer
66 views

What is the most efficient/optimal way to simplify the given function? Does the given code need more assumptions?

I have a very long function for $\{x,b\}\in\mathbb{R}$ and $n=\{1,2,3,4,5,6,7,8,9,10\}$; here, I have only mentioned a short part of that. The function is a sum of the complex exponentials (a picture ...
  • 1,159
0 votes
1 answer
52 views

How to use Assuming and With together

(I am sorry for the ASCII form, I use the free WolframEngine which works in text mode.) I have these assumptions ...
  • 137
0 votes
0 answers
30 views

Assuming a variable arbitrarily close to a value in Refine

In my assumptions, I want Mathematica to use the fact that Theta is arbitrarily close to $\pi$ from below. I made this assumption : ...
  • 496
3 votes
1 answer
61 views

Selecting the negative expression

Let Theta,t be real variables and Phi an expression of ...
  • 496
0 votes
0 answers
30 views

Mathematica FullSimplify becomes less simplified with more specific assumptions?

As far as I always understood, Mathematica always assumes an expression to represent the most general state. For example, a variable is usually assumed to be Complex...
  • 1,212
2 votes
2 answers
85 views

Pattern or ForAll statment in Assumptions

I would like to simplify an expression like $\sum _{i=1}^k \sqrt{a_i^2}$, with the condition $\forall _{i\in \mathbb{Z}_{>\, 0}}a_i\in \mathbb{R}_{>\, 0}$ and with $k$ being undefined, which ...
  • 471
0 votes
1 answer
47 views

Need help with Assumptions for an integral

I want to solve this Log, Integrate[2a Log[-a+((A0 + (y-y1)²)^½, {y1, 0,b}] But Mathematica only gives me long conditional expressions or imaginary numbers. I (my thinking which can be wrong) assume I ...
  • 1
5 votes
3 answers
162 views

$Assumptions = _ ∈ Reals results in incorrect simplification of ConjugateTranspose[..]

The linear combination $Q$ of two Hermitian matrices $A^\dagger = A, B^\dagger = B$ with real coefficients $m,n \in \mathbb{R}$, i.e. $Q = m A + n B$ is itself a Hermitian matrix $Q^\dagger = Q$. ...
  • 53
2 votes
1 answer
101 views

Struggling to get Solve to accept assumptions

I can't get Solve to solve the following two equations under the appropriate assumptions. When I enter ...
0 votes
1 answer
75 views

Assuming one variable is greater than another variable

I want to add the assumption that M>m, but I am not sure how to do that. I tried Assuming[M > m, M > m] But this ...
6 votes
2 answers
184 views

Making a substitution within a typeset integral

This question derives directly from this one, but concerns instead a different matter... one related to display format. This integral $$I = \int\limits_2^4 \frac{\sqrt{\log (9-x)}}{\sqrt{\log (9-x)}+\...
8 votes
1 answer
223 views

Why Mathematica is treating the product of (specified) real variable as complex?

For the given matrix ...
  • 539
4 votes
1 answer
52 views

Proper usage of Assuming statement

I want to evaluate a command under an assumption, and thought Assuming was the right way to go. Suppose we want to calculate a Matrix rank. Following the second ...
  • 251
0 votes
0 answers
30 views

Put an initial condition on some parameter

Good morning, I'm new in the world of Mathematica, so I'm sorry if my question isn't very relevant. I'm trying to solve a system of 5 equations withs many parameters. To be clear, I will hit the core ...
  • 101
5 votes
2 answers
122 views

Simplifying expressions with nested square roots

When I run FullSimplify[Sqrt[(1 - Sqrt[1 - 2 x^2 y^2])^2], {1 > 2 x^2 y^2 > 0}] I obtain 1 - Sqrt[1 - 2 x^2 y^2]. However,...
  • 395
2 votes
2 answers
135 views

Why is my integral with the error function not being evaluated?

I'm new to Wolfram Mathematica and I was trying to evaluate this integral in particular: $$\int_{0}^{x}\frac{e^t \operatorname{erf}(\sqrt{t})\sqrt{\pi t}+1}{\sqrt{\pi t x -\pi t^2}}\mathrm dt$$ The ...
2 votes
1 answer
109 views

Integrate ignoring assumptions

I want to evaluate an integral with all variables real and positive. Specifically, ...
  • 339
1 vote
2 answers
150 views

Argument of a complex number with assumptions

I am trying to calculate the argument of a complex number: Arg[Cos[y]*Exp[I x]] where both x and y are real. The solution is clearly x, but I can't get it with ...
4 votes
2 answers
113 views

Simplify with False assumptions gives wrong answers

Simplify is very gullible: if it gets a False assumption, it'll believe anything is True: <...
  • 19k
6 votes
3 answers
141 views

Extracting a logarithmic divergence of an expression using Series

Consider the following expression: ...
  • 1,317
1 vote
1 answer
33 views

Getting the same result from Integrate as Probability

I'm trying to solve a Baysian inference problem (although the details are not all that important for this question) I define two probability distributions P and <...
0 votes
2 answers
50 views

`Assuming` combined with mathematical notation of `Integrate`

I am trying to write down the following expression Integrate[Exp[-a/2/x]/x/(x + 1), {x, 0, b}, Assumptions -> a > 0 && b > 0] using mathematical ...
0 votes
0 answers
39 views

Integer parameter assumption gives incorrect result when integrating

There are some dangerous pitfalls that can happen when evaluating some integrals, assuming that some parameters are integers. For example, consider the following: ...
  • 1,317
0 votes
2 answers
134 views

Assumptions in Integration for positive real values [closed]

I want to evaluate the following integral in Mathematica. $$ \int_0^\infty \frac{a^{-t}-b^{-t}}{t} dt = \ln \left(\frac{\ln b}{\ln a} \right)$$ I try to enter this, but Mathematica can't figure it out....
1 vote
0 answers
39 views

How to declare at the beginning of the notebook that a variable belongs to a set?

In the notebook I am working on I have certain symbolic variables (e.g., c and r) which I would like to declare since the very first few lines to be non negative real numbers. Correct me if I am wrong ...
  • 53
2 votes
1 answer
61 views

How to use System`Private`AssumptionAccess and Assumptions`*?

I see this function is used by some symbols in Assumptions`*, and it HasDownCode and does not ...
  • 3,630
3 votes
1 answer
278 views

Mathematica tries to differentiate Abs[x] and this causes a problem? [duplicate]

I am trying to run the following code: ...
  • 5,061
0 votes
0 answers
72 views

Global assumption non zero

I would like to define globally an assumption stating that I have a nonzero real vector $v$. For now, I put : $Assumptions = Element[v,Vectors[{100},Reals]] but $v$ ...
  • 496
2 votes
1 answer
83 views

Simplifying an expression with complex conjugates

I have been unable to do the following. First I make an assumption $Assumptions = x \[Element] Reals; and define ...
  • 79
1 vote
1 answer
59 views

Why does not ContourPlot consider the condition given in RegionFunction in the given code?

I have two functions $f(x,y)$ and $g(x,y)$. I am using RegionFunction in ContourPlot to see those values of $(x,y)$ for which $...
  • 659
2 votes
2 answers
108 views

Is it possible to exclude a condition, say, $f(x,y)=const.$, from a ContourPlot code?

...
  • 659
4 votes
2 answers
409 views

How to get a manipulated plot of the intersection points of two curves without finding them numerically?

I have four 2-variables functions for $0<x<3$ and $1<y<3$ ...
  • 659
2 votes
1 answer
68 views

Identical integral evaluating differently

I am trying to compute an integral but am getting two different answers using two near-identical methods. I wish to know why they differ. ...

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