Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[].
15
votes
1answer
420 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
...
3
votes
1answer
181 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
85 views
How to tell Mathematica to make assumptions? [duplicate]
Say I want to integrate 1/(x^2+a^2) and I want Mathematica to know that $a>0$. What would be the command? Something like:
...
1
vote
0answers
93 views
I can't solve this set of equations
I am having trouble solving a set of equations in mathematica. I do not get any errors, but i don't get any answers as well.
I have some restrictions on my parameters and variables in the equations ...
4
votes
2answers
114 views
Strange behavior of Integrate
I'm trying to calculate the following integral using Mathematica 9.0.1.0
a11=Integrate[Abs[Sin[b+x]],{x,0,2*\[Pi]}]
This should be a simple problem; however, it ...
1
vote
1answer
104 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 ...
0
votes
1answer
89 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:
...
3
votes
0answers
72 views
Assuming monotonicity and concavity
I have an expression that I would like to evaluate:
2 phi''[1 + a (-1 + u[10])] phi'[q]^3 > phi''[q] phi'[q] phi'[1 + a (-1 + u[10])]^2
Is there any way of ...
2
votes
0answers
56 views
Simplify yelds an incorrect expression [closed]
I was trying to simplify an expression:
DSolve[d'@t == a + b Sin@d@t, d@t, t]
Simplify[%, Abs@a < -b < 0]
and I got
...
1
vote
2answers
91 views
How to take conjugate of a function?
Naïvely this is what happens and it obviously is not helpful!
...
0
votes
0answers
77 views
How to have Mathematica find asymptotics with correct asumptions
I'm tried to find a certain expansion of the Hypergeometric1F1 function using Mathematica:
...
2
votes
1answer
94 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 ...
0
votes
3answers
99 views
Assume function is real valued
I want to create a function returning subscripted symbols and I want these symbols to be assumed real. How do I do that?
...
6
votes
2answers
164 views
Why does Integrate declare a convergent integral divergent?
When I try this command
Integrate[1/Sqrt[(s^2 - u)^2 - 1], {s, m, Infinity}, Assumptions -> u > 2 && m > 10]
Mathematica declares that the ...
3
votes
1answer
54 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 ...
1
vote
0answers
68 views
Problem with using Assumptions in Simplify [closed]
I want to simplify
Log[E^(2 \[Pi] I m/n)]/(2 \[Pi] I)
To obtain m/n.
I have tried
...
0
votes
3answers
273 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 ...
4
votes
2answers
127 views
Usage of Assuming for Integration
For some reason, when I enter the following integration in Mathematica
Assuming[{k \[Element] Integers}, Integrate[Exp[I * k* t], {t, -Pi, Pi}]]
the result turns ...
0
votes
2answers
206 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
66 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 ...
20
votes
4answers
564 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 ...
3
votes
1answer
97 views
Why does Assuming for Integrate not work as expected?
I'm trying to perform the following integral with Mathematica 7:
...
7
votes
1answer
471 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
372 views
Does the Im function work with symbolic arguments?
Does the Im function work with symbolic arguments?
...
2
votes
1answer
83 views
How to define a large number of assumptions?
Please consider the following simple and larger example:
...
5
votes
2answers
264 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
215 views
3
votes
1answer
166 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 ...
6
votes
1answer
115 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
289 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 ...
13
votes
2answers
224 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 ...
10
votes
2answers
1k 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 :
...
4
votes
4answers
568 views
Mathematica gives wrong answer for integral
When I execute the following,
Integrate[Exp[-w^2 + I w^3], {w, -\[Infinity], \[Infinity]}]
I get
...
2
votes
1answer
109 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 ...
13
votes
5answers
630 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 ...
5
votes
0answers
88 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
197 views
Get Mathematica to simplify $\cosh(i x)$
I want Mathematica to simplify Cosh[I x] to Cos[x] if I tell Mathematica that x is Real.
I ...
8
votes
1answer
416 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 ...
4
votes
1answer
137 views
Assumptions seem not to be considered
In the following a,b is a probability distribution, i.e. a+b==1 with ...
6
votes
4answers
234 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 ...
10
votes
2answers
418 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
461 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:
...
8
votes
5answers
383 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
353 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, ...
