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
1answer
68 views

Restricting a plotted expression to reals in a Manipuate

I have an expression from which I'm trying to create a plot that I can manipulate. The expression contains Abs, and I only want to have it evaluated for reals. What ...
4
votes
1answer
2k views

Is it possible to impose “Assumptions” in DSolve or equivalent? (differential equation solving)

When DSolve tries to solve differential equations, it is sometimes not smart enough to generate conditions according to different possible value of parameters. ...
0
votes
1answer
155 views

Simplifying Complex Numbers that contain physical units

I am trying to evaluate the following: Simplify[Meter Nano Re[(a + I b)/(Meter Nano)], Assumptions -> Element[{a, b}, Reals]] However, Mathematica returns: ...
1
vote
4answers
3k views

How can I use assumptions with FindRoot?

I have something like FindRoot[f[x], {x, a}] Now I want FindRoot to constrain the solutions to 0 < x < 1. How can I ...
14
votes
2answers
1k views

Usage of Assuming for Integration

For some reason, when I enter the following integration in Mathematica Assuming[{k ∈ Integers}, Integrate[ Exp[ I k t], {t, -π, π}]] the result turns out to be ...
0
votes
2answers
410 views

Integrating hat functions

I am trying to integrate a hat function for a project that I am doing and have found a method to do so but I find it sloppy. Currently I have the basis function ...
3
votes
2answers
91 views

Detecting operator Set in Assumptions

Here is a typical issue: Simplify[x + y, x = y] produces 2 True. Is there a way to detect operator ...
2
votes
1answer
153 views

How to evaluate the sum over a hyperplane

I have difficulties in evaluating the following expression: $$\sum_{\small n_1+...+n_{k}=m-k}\; \prod_{i=1}^{k}\frac{1}{(n_i+1)(n_i+2)}$$ I have tried the function ...
4
votes
1answer
193 views

Why does Assuming for Integrate not work as expected?

I'm trying to perform the following integral with Mathematica 7: ...
21
votes
4answers
874 views

An apparently “simple” limit?

Let $c$ and $h$ be real values. I was using Mathematica to compute the limit $(h \rightarrow \infty)$ of the following expression: $$ \frac{\left(h^2 +c^2 h^2 + \sqrt{4 h^2+\left(h^2+c^2 ...
1
vote
1answer
138 views

Assumptions are not being applied to integral

I am trying to use assumptions to simplify an integral, but I can't seem to get the assumptions to apply themselves. Here is the code I am using: Note the expressions in the assumption can be found ...
2
votes
1answer
156 views

How to define a large number of assumptions?

Please consider the following simple and larger example: ...
5
votes
2answers
528 views

Replacements/Substitutions in Mathematica

I am a new user of Mathematica and have some questions about the simplifications of calculated expressions. I am unable to attach an image of the session, but my Mathematica commands are: ...
2
votes
1answer
608 views
3
votes
1answer
203 views

One Integral — Two Results

I compared Mathematica's default integral evaluation to what you get by computing the indefinite integral and then plugging in the limits. (I did this because the latter approach was much faster for ...
9
votes
1answer
180 views

What exactly does GenerateConditions do?

Consider for example this strange behavior: Integrate[1/x, {x, 0, Infinity}, GenerateConditions -> False] (*0*) I'd also like to know the difference between ...
10
votes
1answer
757 views

Is my expression too complicated for FullSimplify or am I doing something wrong?

I have a messily defined function $v(h, w)$ with $h, w \in \mathbb{R}$ and with a removable singularity at $h=1/2$, and I am trying to prove some of its properties using Mathematica. In particular I ...
14
votes
2answers
344 views

How to make use of NumericQ[x] = True (and use it safely)?

Basic Issue: I'm trying to understand the proper use of NumericQ's "magical" capabilities. Please consider the examples below. Actual question and some links are ...
7
votes
4answers
1k views

Mathematica gives wrong answer for an integral

When I execute the following, Integrate[ Exp[-w^2 + I w^3], {w, -∞, ∞}] I get (2 E^(2/27) BesselK[1/3, 2/27])/(3 Sqrt[3]) ...
2
votes
1answer
322 views

Assumptions with D

I want to give assumptions for the D function. Say I want to calculate $\frac{d|x|}{dx}$ for $x>0$, which is 1. I write ...
5
votes
0answers
131 views

Calculating a limit with a result that is discontinuous in the parameters

The following limit is left unevaluated (Edit: added the assumption that $\epsilon$ is real thanks to the comment below): ...
0
votes
1answer
319 views

Get Mathematica to simplify $\cosh(i x)$ [closed]

I want Mathematica to simplify Cosh[I x] to Cos[x] if I tell Mathematica that x is Real. I ...
19
votes
2answers
879 views

Optimization with assumptions

I have the following problem, when I am trying to optimize function with pre-defined assumptions. I am using Mathematica 8 and I wrote the following simple code ...
8
votes
1answer
2k views

Is it possible to set a variable as a positive one in the whole notebook?

I'm having issues during integration due to the fact that Mathematica doesn't know if an undefined variable is positive or not (it gives me complexes which bothers me in the end). For example I do ...
8
votes
1answer
1k views

Assumptions on unknown functions

I'm trying to do analytic calculations in a quantum mechanic harmonic oscillator basis. Specifically I want to be able to evaluate functions of the many particle density. I define the following ...
4
votes
1answer
224 views

Assumptions seem not to be considered

In the following a,b is a probability distribution, i.e. a+b==1 with ...
7
votes
4answers
462 views

Attaching persistent assumptions to symbol definition

Is it possible to attach assumptions to a symbol? This relates to this question. Most of my work involves physical equations, i.e. there are basic assumptions on variables that will always hold true ...
4
votes
1answer
678 views

Does the Im function work with symbolic arguments?

Does the Im function work with symbolic arguments? ...
11
votes
2answers
1k views

Maximizing a function with assumptions

Using f[s_] := Log[(s/r)^α ((α - 2) n0 r^α + 2 π Pmax ρ r^2) /((α - 2) n0 s^α + 2 π Pmax ρ s^2)]/s When I run the following line: ...
16
votes
2answers
872 views

Why doesn't FullSimplify drop the Re function from an expression known to be real?

For some reason Mathematica does not properly simplify this expression: ...
13
votes
5answers
774 views

Does $x>0$ imply that $x\in\mathbb{R}$?

Let’s assume I input Assuming[x > 0, expression] Is it assumed by Mathematica that $x$ is a real number? Or that the real part of $x$ is positive? Something ...
8
votes
5answers
546 views

simplifying $\frac{\log x^a}{a} = \log x$

If one makes the assumptions $x>0,a>0$, then $\frac{1}{a}\log x^a = \log x$. Thus, in Mathematica, Simplify[1/a*Log[x^a], {a > 0, x > 0}] returns ...
3
votes
2answers
929 views

simplify assuming a variable equals zero

How can one simplify an expression by assuming that one of the variables is equal to zero? For instance, while Simplify[%,a>0] gives the desired output, ...
12
votes
2answers
7k views

How to specify assumptions before evaluation?

If I request mathematica evaluate an integral for me, I'll often get a more general ConditionalExpression than I want. Example : ...