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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12
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0answers
364 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 ...
7
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0answers
254 views

What is a “generic case”?

Introduction With this question I am coming back to a long-standing issue I have with Mma's concept of a "generically correct" result. The basic idea seems to be, vaguely, that if a result is true in ...
7
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0answers
106 views

Need explanation on strange behavior of Simplify under given assumption

This is quite surprising to me. Simplify[a == b, {a == {1}, b == {1}}] a == b does not evaluate the equality, while ...
5
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0answers
135 views

Integrate under assumptions

I am trying to solve the following integral: $$\int_0^\infty u^{\sigma-1} \exp\left[-c u^\sigma\right] \mathrm{d}u$$ under the assumptions $\sigma \in (0,1)$ and $c>0$. I know the result is $$\...
5
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0answers
91 views

External and internal Assumptions on `PiecewiseExpand` and `Mod`

After this question I'm intrigued about the different behaviors depending where and how the assumptions are given. ...
5
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0answers
78 views

SumConvergence fails in version 10

SumConvergence[(-1)^(n + 1) ((Cos[n^2] + Sin[n + 2])/7^n), n] Mathematica fails to provide a result (true/false) but wolfram alpha works. What should I do ? It ...
5
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0answers
167 views

Why does setting $Assumptions make my Fourier transforms slow?

Consider these Fourier transforms ...
5
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0answers
206 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): ...
4
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0answers
102 views

Trigonometric integral with assumptions fails

Consider the following integral Assuming[Element[{n, m}, Integers] && n >= 0, Integrate[Cos[ϕ]^n Exp[I ϕ m], {ϕ, 0, 2 π}]] ...
4
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0answers
123 views

Why isn't Mathematica listening to my assumptions?

I'm trying to simplify the expression ωplus := 1/2 c (I f V + Sqrt[4 k^2 - f (f + 8 I k) V^2]) so that I can get it in the form $a+i b$. I am using the global ...
4
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0answers
212 views

Multiple Constrained Sum

I need to perform a multiple summation, that obeys some conditions. This arises in the study of a statistical physics model. q=Exp[-β]. I would like to ask if ...
4
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0answers
170 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 ...
4
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1answer
42 views

Is it better to use a single binary operator in each Assumption entry?

I am trying to understand why FullSimplify[x^a < 1, {0 < x^a < 1}] does not simplify but ...
3
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0answers
84 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 ...
3
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0answers
537 views

How to simplify exponentials into hyperbolic functions

I have a function of real exponentials and I'd like to simplify it using hyperbolic functions. How can I tell mathematica to use $e^x +e^{-x}=2\cosh(x)$ when simplifying? (and obviusly the $\sinh$ ...
3
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0answers
43 views

Evaluating inequality involving powers

I want to evaluate an inequality of the form $x^a > x$ under the assumptions $x > 1$ and $a > 1$. I expect this inequality to be true, but ...
2
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0answers
40 views

Summing with assumptions provides unexpected output

I am computing a closed form of a number of sums having generally the following form: $$ \sum_{i = 0}^{m/2}\sum_{\substack{0\leq k \leq i \\ 2k \equiv i + m \, \text{mod } 3}} k $$ It looks like ...
2
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0answers
84 views

Does Assumptions not work on Root objects?

Typically, one can restrict symbolic quantities using Assumptions. Suppose, for instance, that I want to solve $a=x^2$ for $x$, with $a>0$, restricting my answer to the positive root. ...
2
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0answers
59 views

How to express continuity assumption for Integrate?

I am wondering if it is possible, and how if so, to express function continuity in the assumptions for the definite form of Integrate. First of all, while ...
2
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0answers
91 views

Fourier Cos coefficient vs Integrate vs common sense

I was trying to find out what the (discrete) Fourier transformation of the following function is $$ f(\nu, u) = \frac{\sinh \nu}{\cosh \nu - \cos u} $$ So at first, I tried to evaluate a fancy MMA ...
2
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0answers
102 views

Error computing sum “Infinite expression 1/0 encountered”

I am trying to calculate a symbolic sum.The expression is defined as follows: ...
2
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0answers
363 views

Piecewise functions Integration with symbol

I want to integrate one piecewise functions as following, ...
2
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0answers
151 views

Getting long complex-valued integrals when simpler real-valued expressions exist

I have a long list of real-valued functions I'd like to integrate symbolically. For many of them, Mathematica gives me results with long complex-valued expressions involving weird functions such as <...
2
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0answers
550 views

Computing a sum

I'm trying to make Mathematica compute this sum: Sum[(-1)^k (n - k)^2 Binomial[2 n, k], {k, 0, n}] As is, I get an awful formula: ...
2
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0answers
855 views

I can't solve this set of equations

I am having trouble solving a set of equations using Mathematica 8. I do not get any errors, but I don't get any solutions either. My parameters and variables are real and non-negative. ...
1
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1answer
57 views

I need to create abstract vectors

$Assumptions = {q \[Element] Vectors[{15}, Reals]}; $Assumptions = {p1[q] \[Element] Vectors[{3}, Reals]}; So I have been using this code in order to define an ...
1
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0answers
42 views

Why does Mathematica miss some solutions for my integral?

When computing the integral of two orthogonal sine functions $\qquad \sin(n\,\pi\,x)\,\sin(m\,\pi\,x)$, where $n,\,m$ are integers > 0 Mathematica seems to miss the solution where $n=m$. I don't ...
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0answers
50 views

Different integral results within equivalent conditions

I input 3 functions as following, ...
1
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0answers
57 views

ConditionalExpression still resulting from Assuming a Module's local variables

I have a memoizing, recursive function whose MWE looks like this (the two fake inputs/ICs are from 'K' and 'Bfun2', the latter just a quick way to check the results coming out of the Residue.: ...
1
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0answers
41 views

How to define a variable $x$ such that $Abs[x]<1$ and use this globally without having to re-write it again and again?

I am writing a code or a calculation of a very complicated function and my main variable is $x$ such that $-1<x<1$. This assumption has to simplify my final answer a lot, but since the final ...
1
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0answers
103 views

Finding the limit of an expression correctly

I have an algebraic curve given by ...
1
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0answers
41 views

Assigning domains of variables automatically

I want to find a feasible solution for mixed integer linear program. The first $t$ variables in the system are integers and other are reals. The problem is that the no. of variables is more than ...
1
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0answers
453 views

Assumptions aren't working in this sum

I have a sum that should be real: FullSimplify@Sum[1/(α n^4 + β), {n, 1, ∞}, Assumptions -> α > 0 && β > 0] But the result have involved even ...
1
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0answers
278 views

Assumptions don't work as expected in FourierTransform

The 2D rectangular function and its Fourier Transform is $$ g_{in}(x,\,y) = rect(\frac{x}{x0}) \, rect(\frac{y}{y0}) \quad \xrightarrow{\mathscr{F}} \quad G_{in}(u,v) = x0 \, y0 \, sinc(\pi u x0) \, ...
1
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0answers
450 views

How can I force the assumption that a symbol is a vector of n zeros

Using $Assumptions = Element[n, Integers] && Element[a, Vectors[n, Reals]] I can assume that a is a n-dimensional vector of Reals. How can I assume that ...
1
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0answers
362 views

Using assumptions when calling Simplify from Collect

I am quite new to Mathematica, so please be patient ;) I have a very long equation that I have to sort for powers of a variable called e and that I want to ...
1
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0answers
122 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: ...
0
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0answers
39 views

Regarding “Assumptions” under “Integrate”

Sir, I tried to integrate the following in mathematica ...
0
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0answers
30 views

Truncate series with real powers that are not fully numerical

Take a function with the following expansion A3[z_]:=Sum[Subscript[a3x, jj]*z^jj, {jj, 0, 2}] + z^r Sum[Subscript[a3NAx, jj]*z^jj, {jj, 0, 1}]; where ...
0
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0answers
96 views

Rubi/Mathematica gives different values for the same integrand

Consider this integral: $$ \int_0^\pi d\theta \sin\theta\, {1 \over \gamma^q}\left((1-\gamma^2)^2\sqrt{1 \over 1-\left(1-(1-\gamma^2)^4\right)\cos^2\theta} - 1\right)^q $$ for $0\leq \gamma < 1$. ...
0
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0answers
31 views

Defining a function with certain regularity (e.g. smooth)

My goal is to understand how Mathematica computes limits that would require differentiability assumptions on functions (for, for instance, L'Hopital or Taylor Series). Consider, for instance, the ...
0
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0answers
41 views

Simplification of symbolic vector and matrices representation

I'm new to the Wolfram Language programming and I cannot manage to do the following. I wish to use Wolfram Cloud to simpilfy a heavy vector and matrix expression using symbolic complex vectors (...
0
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0answers
51 views

How do I apply assumptions to a table of functions

I have a table, really its a tensor but anyways I would like to apply an assumption to it, i.e. 1 - 2 phi[t,x,y,z] == 1 and have it print the tensor after it has ...
0
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0answers
35 views

Using assumptions in DSolve

I want to solve the following differential equation DSolve[u'[\[Xi]] == a u[\[Xi]]^(2 - m) + b u[\[Xi]] + c u[\[Xi]]^m, u[\[Xi]], \[Xi]] with the assumpetion ...
0
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0answers
53 views

Dealing with positive power variables in Taylor expansion and assumptions

I would like to compute the Taylor expansion of monomials whose powers are nonnegative rational variables. First, here is a function which encodes the multivariate Taylor expansion at the points <...
0
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0answers
38 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
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0answers
32 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 ...
0
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0answers
37 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 ...
0
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0answers
69 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: ...
0
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0answers
38 views

FullSimplify does not simplify at all

I have some problems simplifying things with FullSimplify. Suppose a matrix ...