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

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4
votes
2answers
163 views

Assumptions with patterns

I want that Mathematica assumes every symbol like Subscript[s,i] to be evaluate as a real and positive number. I have tried ...
3
votes
2answers
47 views

Simplify with assumption of unknown function [duplicate]

I have an unknown multivariate function entry[x,y,z], which is positive. Then how to get FALSE and entry[1,2,3] in the following evaluations? ...
4
votes
1answer
125 views

Mathematica does not help in this integral

I am trying to solve this integral with assumptions: ...
4
votes
2answers
118 views

Well-defined symbolic integral leading to ConditionalExpression

I would like to determine a closed-form expression for the following symbolic integral $$ \int_{-1/2}^{1/2} \!\!\!\! \mathrm{d} x \int_{-1/2}^{1/2} \!\!\!\! \mathrm{d} y \, \frac{1 + b x + c y}{1 + e ...
0
votes
2answers
55 views

Defining the domain of positive real numbers

I am trying to solve an equation by assuming that all the variables are real and strictly positive. I can use the keyword Reals for the argument ...
0
votes
1answer
57 views

Assumptions and Conditions in Integrate Function in Mathmatica

I was trying to Integrate the gravitational potential at r = x produced by a uniform sphere positioned at the origin. I wrote the following code: ...
1
vote
1answer
40 views

Simplify CubeRoot of meter cubes

Why Mathematica doesn't simplify CubeRoot of meter cubes to meters? r = Quantity[10, "Meters"]; v = 4/3 r^3 Pi; CubeRoot[% * 3/4 / Pi] returns ...
1
vote
2answers
57 views

Abs[Sin[4a]] not equal to 2Sin[2a]Abs[Cos[2a]] for a in [0,\pi/2]

I have a long expression which is not fully simplified because Abs[Sin[4a]] is considered different from 2Sin[2a]Abs[Cos[2a]] ...
2
votes
1answer
145 views

Is there a way to simplify a symbolic expression at assignment, once-for-all?

I have a series of symbolic function calls that could be greatly simplified using some assumptions. I think I would like for these assumptions to be used in the definition of the function so that they ...
2
votes
2answers
87 views

Simplifying expressions with Abs

I have a long expression which seems really complicated due to some Abs[] terms that should be simplified. However, even with the right assumptions, the expression ...
4
votes
1answer
66 views

Problem with Simplify, Sqrt, and Set: What's going on?

I am having some trouble getting Mathematica to simplify an expression of the form Sqrt[x]*Sqrt[1/x], where x>0. The problem is that x is assigned to some complicated form by the time Mathematica ...
1
vote
3answers
102 views

IntegerQ returning False despite setting Assumptions

Why does the following not return True? Assuming[z ∈ Integers, IntegerQ[z]] False I tried this on a fresh session of ...
1
vote
1answer
51 views

How to make strong assumptions?

Or put in another way, how to make a variable behave as it belongs to a specific domain, even outside the use of simplify or other commands alike? For example: ...
1
vote
1answer
61 views

Assuming variable is plus or minus 1

I have a long calculation that I am doing, which involves a particular variable h, which in the end, is either +1 or -1. (I would like a general result that is true for both cases.) Since h only ...
1
vote
1answer
56 views

Defining a matrix with the symmetry Transpose[A(q)]=A(-q)

I am trying to construct a symbolic matrix with the following property- $$ \left(D_{3\times3}(q)\right)^T = D_{3\times3}(-q) $$ Note that for $q\in \mathbb{R}$, $D(q)$ would be hermitian. So far i ...
5
votes
0answers
54 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 ...
2
votes
1answer
75 views

Simplifying conditional expressions using assumptions does not work

I have a conditional expression f[x_] := x /; x ∈ Reals This works fine for normal numbers and symbols, e.g. ...
0
votes
1answer
48 views

Assuming: what am I doing wrong? [duplicate]

Why doesn't this simple line work? Assuming[Element[#, Reals] & /@ {x}, Reduce[x^4 == 1]] (* x==-1||x==-I||x==I||x==1 *) I'm trying to do something a little ...
1
vote
2answers
72 views

VectorFieldPlot Assumptions - restricted domain

I would like to plot the 2-D vector field: VectorFieldPlot[{ x/Sqrt[x^2 + y^2], y/Sqrt[x^2 + y^2]}, {x, -5, 5}, {y, -5, 5} ] but I encounter zero division at ...
2
votes
0answers
58 views

How do I apply assumptions to a module (or any CompoundExpression)?

Edit: I am looking for a way to apply assumptions to all expressions contained in a compound expression. For example, ...
0
votes
0answers
45 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 ...
7
votes
1answer
77 views

Inconsistent results for Integrate depending on irrelevant assumptions

I stumbled across this amusing issue today when doing some definite integrals: ...
0
votes
0answers
54 views

Piecewise functions Integration with symbol

I want to integrate one piecewise functions as following, ...
7
votes
3answers
111 views

Unknown function with arbitrary arguments assumption

Is it possible to define an assumption like this: $Assumptions=f[__]>0 So that: ...
0
votes
1answer
106 views

How do I declare that a variable represents a real number?

How do I tell Mathematica that a variable is a real number. I searched for this question here and in Google and nothing that was suggested seems to work for me. I must be missing something. My code is ...
5
votes
0answers
191 views

Integrate wrong for absolute value of trig function

I was trying to get $\int_0^1 \lvert \cos(2 \pi k x) \rvert \,\mathrm{d}x$ for $k \in \mathbb{Z}$, and was surprised by the result (using Mathematica 10.0.1.0): ...
5
votes
3answers
156 views

Assuming reals of unknown variables in a Matrix valued function

I am trying to write a generic matrix valued function in a package, of the form: f[matrix_] := Module[...] My problem is that I want to accept any matrix, but ...
1
vote
1answer
53 views

How to use many global assumptions [closed]

I would like to use many global assumptions. Say I have two global assumptions. $Assumptions = 0 < a < 1 $Assumptions = 0 < b < 1 Then I would like ...
3
votes
1answer
106 views

How to use Assuming and If together?

I would like to compare variables t and u and print either Yes or ...
1
vote
1answer
63 views
5
votes
1answer
85 views

Problem with general assumptions

I hope I am not to redundant with my questions. As part of solving a physical problem, I want to assume once and for all that all my variables and parameters are real, positive and finite. Is it ...
4
votes
1answer
248 views

Can I check if an expression is positive using assumptions?

I have the following notebook: ...
1
vote
1answer
245 views

Appending to $Assumptions - Error “Nonatomic expression expected” [closed]

I need to use lots of assumptions in my code. Therefore I put them into the $Assumptions variable. When I do it like this, all is well: ...
0
votes
0answers
58 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 ...
14
votes
3answers
256 views

Why does Mathematica simplify $x/x\to1$?

If I enter x/x, I get 1. Such behavior leads to this: Simplify[D[Sqrt[x^2], x, x]] 0 ...
3
votes
2answers
75 views

Why does Assuming[…] work in one case but not in another?

Why does this work Assuming[α > 0 && ϵ > 0 && t > 0, FullSimplify @ Integrate[(z^2 Exp[-α t (z^2 + ϵ)])/(z^2 + 1), {z, 0, ∞}]] ...
1
vote
1answer
49 views

PiecewiseExpand doesn't take all kind of assumptions

Running PiecewiseExpand[expr, assum] does not work with all kind of assumptions. For example, the following line will not split the expression with absolute values in the chambers, considering m1=m2. ...
0
votes
0answers
32 views

Assumptions for simplifying a long equation

I'm having trouble combining assumptions with the execution of Simplify in a long equation. The idea is to separate imaginary and real parts of a complex equation. ...
0
votes
0answers
22 views

Assumption for all the notebook [duplicate]

I would like to know how to fix an assumption over a variable that will be fixed for all notebook. For example a>0 in all the notebook.
0
votes
0answers
63 views

Making sense of output of Assuming/Refine

I have a conditional statement as output: ...
0
votes
2answers
109 views

How to use Assumptions in a Series Expansion

I want to series expansion the expression $\frac{1}{2} \left(e_1+e_2-\sqrt{e_1^2-2e_1e_2+e_2^2+4V_{12}^2} \right)$ up to second order in $V_{12}$ using the assumption $e_1>e_2$. So I tried ...
0
votes
0answers
63 views

Inconsistent behavior of Assuming[] in combination with Simplify[] [duplicate]

The following integral gives the correct result ...
2
votes
0answers
141 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: ...
1
vote
3answers
92 views

FullSimplify assumptions for function body

I'd like to pass an assumption to FullSimplify so whenever it gets a function that is squared and square rooted would return me only the function body, without ...
2
votes
1answer
135 views

Taylor expansion of function of vectors—simplifying the output

I've got a real-valued function of several vectors $f(u,v,w)$ formed by taking scalar products of linear combinations of the vectors, I want to Taylor expand around small $v$ by writing $$f(u,\delta ...
0
votes
2answers
542 views

Evaluate conditional expression

I solved an integral and get a conditional expression as the result. The conditions are quite heavy but if I use Assumptions within my ...
2
votes
1answer
213 views

Prove (or check) an expression is positive given constraints on variables?

I'm trying to figure out whether an expression is always positive given positive parameters. When the expression is complicated, I can't do this by eye. Is there any way to make Mathematica prove ...
1
vote
1answer
97 views

How to study the sign of an expression including a function, with conditions on the function?

I'm trying to study the sign of an expression, having information on some of my parameters. I don't know how to code these conditions. For example, I want to know when this expression: ...
2
votes
3answers
511 views

DSolve will not apply assumption m ∈ Integers

I am trying to solve a linear second order ODE using DSolve which involves an arbitrary integer m. ...
0
votes
3answers
100 views

Evaluating an expression assuming a value for a variable only in the local context

Imagine we wish to evaluate some expression like NIntegrate[x^2*q,{x,0,100}] assuming some value for q like ...