Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[].

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0
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1answer
64 views

One more question about Assumptions and Integrate

There are many questions about assumptions here. Many of them are problem specific. That is why I want to ask a question in the most general way. Why does Mathematica solves this ...
1
vote
1answer
67 views

How can we tell Series to treat the expansion parameter as an integer?

It is simple for Mathematica to find an asymptotic expansion for $\frac{1}{-1+p}$ as $p \rightarrow \infty$. However, if we want to restrict $p$ to be an integer and also include some terms that ...
0
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1answer
133 views

Re[x] vs. x ∈ Reals in the context of Assuming

Let's say that $x$ is some real valued number $>0$. Are the following commands interchangeable in the context of using Assuming? ...
1
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0answers
76 views

How does TensorReduce use assumptions?

I would like to use TensorReduce by assuming that certain patterns of functions are tensors. From documentation of TensorReduce: ...
2
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2answers
117 views

Simplification with assumptions

I'm trying to make Mathematica do some simplifications for me. I have the expression ((1 + s[1]) (-1 + s[2]) )/(-1 + s[1] s[2]) and want to simplify this with ...
1
vote
1answer
100 views

Simplifying using assumptions

Is there a way to simplify the following equation (-p(a-x)((a-b)P(b-x)+Q(b+x)(a-b+2x))+q(a+x)(-(a-b)Q(b+x)+P(b-x)(-a +b+2x)))/((b-x)(-a + x)(a+x)(b+x)) assuming ...
3
votes
2answers
208 views

RSolve with assumptions

I want to solve the following non-linear first order difference equation: $$ k_{t+1} = (1-a) k_t^{a} $$ with $0 < a < 1$, and $k_0 = \text{const.}$ . Of course, the solution is easily found, ...
9
votes
0answers
230 views

Simplify and Sqrt, inconsistent behavior?

I have encountered some problems when using Simplify with expressions containing a square root and isolated a following test case ...
10
votes
3answers
388 views

Reduce can't reduce an equation without appropriate assumptions

When there are three unknowns (x, y, z), Mathematica can solve it: ...
2
votes
2answers
146 views

FullSimplify used with Assuming giving unexpected results

Can someone shed some light on why Assuming[{x ∈ Reals}, x (Sign[x]^2 - 1)] // FullSimplify returns x (-1 + Sign[x]^2) ...
3
votes
2answers
104 views

Assumptions within Simplify

I am using the ratio between two error probabilities in various functions. I want Mathematica to display this ratio in the most simple manner. How do I let Mathematica know that, in this case, the ...
1
vote
1answer
130 views

Assumptions in mathematica when Symplify on Log[Exp[a/b]]

In mathematica 9.0: This: Assuming[b > 0 || b < 0, Simplify[Log[Exp[a/b]]]] yields: a/b However, this: ...
9
votes
1answer
225 views

Limit of sequence of functions behaving strange

I'm trying to determine the limit of the sequence of functions $$f_n(x)=\left(\frac{1}{\pi}\arctan(n x) + 1/2\right)^n. $$ I define ...
5
votes
1answer
299 views

Use Pattern with Vectors in Assumptions

I had a problem using Pattern with Vectors in Assumptions. Here's how I use ...
4
votes
2answers
165 views

Assumptions for RotationMatrix

I'm making C++ program, and in my program I need a rotation matrix around any vector. I wanted to extract RotationMatrix[fi,{x,y,z}] output and put it in my ...
1
vote
1answer
125 views

Assumptions about list elements

I am trying to simplify some expressions using assumptions and got an inconsistent behavior of Mathematica 9 when working with indexed variables. Consider ...
4
votes
1answer
193 views

Can't simplify Abs[a*Cos[x]]^2

Why doesn't FullSimplify[ Abs[a*Cos[x]]^2, Assumptions -> {{a, x} ∈ Reals}] simplify to (a*Cos[x])^2 but this query ...
0
votes
2answers
95 views

How to add a condition to a formula so that it will not appear at the result? [duplicate]

Sometimes I have very long and complicated equations, when I evaulate the equations for example taking derivative or integral there will be several conditions with the answer. My question is that; is ...
0
votes
0answers
134 views

Solve differential equation with undetermined constants making the assumption that the constants are positive

I want to solve: eqn = D[f[w], {w,2}] + (3/2 c^2 k Exp[c w] - 9/4 c^2 k^2 Exp[2 c w]) f[w] + m^2 f[w] sol = DSolve[eqn == 0, f[w], w] with the assumption ...
2
votes
1answer
242 views

How to select TransformationFunctions based on Assumptions made when using Simplify?

I am re-writing the question using a very simple example so not to confuse matters with the another question being asked where I used the example from there. In general, how to add logic to switch ...
4
votes
1answer
1k views

Use of $Assumptions [duplicate]

I don't really understand the behaviour and the usage of $Assumption. For instance, when I set $Assumptions = λ > 0, I expect ...
1
vote
2answers
1k views

Simplifying expressions with square roots

I would like Mathematica to simplify this expression: $4 \left(16 \sqrt{\left(-1+2 c^2\right)^2}-32 c^2 \sqrt{\left(-1+2 c^2\right)^2}+\sqrt{\left(1-8 c^2+8 c^4\right)^2}\right)^2$ ...
11
votes
1answer
180 views

Keeping Integrate from making unnecessary assumptions

I would like to evaluate the integral $\int_{-\infty}^\infty \mathrm{d}x \, \exp\left(- a x^2 - x^4\right)$ for any real value of $a$. Mathematica 8.0.4 gives the following result: ...
3
votes
1answer
140 views

Double Integral and Assumptions

I'm afraid this is going to be a really stupid question. Evaluating the following definite integral Integrate[Sqrt[1 - (x^2 + y^2)], {x, -1, 1}, {y, -1, 1}] ...
0
votes
1answer
126 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: ...
2
votes
0answers
468 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
138 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 ...
3
votes
0answers
121 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 ...
1
vote
3answers
1k views

How to take conjugate of a function?

Naïvely this is what happens and it obviously is not helpful! ...
0
votes
3answers
471 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? ...
10
votes
2answers
579 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
66 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
1k 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
151 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
3answers
2k 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 ...
13
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
361 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
87 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
148 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
186 views

Why does Assuming for Integrate not work as expected?

I'm trying to perform the following integral with Mathematica 7: ...
21
votes
4answers
839 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
134 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
143 views

How to define a large number of assumptions?

Please consider the following simple and larger example: ...
5
votes
2answers
489 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
559 views
3
votes
1answer
200 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 ...
7
votes
1answer
148 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
653 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
329 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]) ...