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

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28 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 ...
6
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1answer
59 views

Inconsistent results for Integrate depending on irrelevant assumptions

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

Piecewise functions Integration with symbol

I want to integrate one piecewise functions as following, ...
5
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3answers
91 views

Unknown function with arbitrary arguments assumption

Is it possible to define an assumption like this: $Assumptions=f[__]>0 So that: ...
0
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1answer
65 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
152 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
140 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 ...
0
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1answer
40 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
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1answer
94 views

How to use Assuming and If together?

I would like to compare variables t and u and print either Yes or ...
1
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1answer
60 views
4
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1answer
65 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
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1answer
201 views
1
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1answer
140 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
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0answers
51 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
234 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
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2answers
71 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
45 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
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0answers
28 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
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0answers
20 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
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0answers
49 views

Making sense of output of Assuming/Refine

I have a conditional statement as output: ...
0
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2answers
104 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
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0answers
61 views

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

The following integral gives the correct result ...
2
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0answers
121 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
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3answers
86 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
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1answer
107 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
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2answers
309 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
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1answer
144 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
79 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
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3answers
410 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
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3answers
88 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 ...
1
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1answer
97 views

Mathematica does not respect tensor order?

I'm trying to verify an identity involving symmetric traceless tensors over the reals. What I tried was: ...
2
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4answers
125 views

Cancelling units in two-argument ArcTan

Consider ArcTan[3, -3] (* out: *) -Pi/4 ArcTan[3 a Sin[t/2], -3 a Sin[t/2]] (* out: *) ArcTan[3 a Sin[t/2], -3 a Sin[t/2]] However, we can fix the ...
0
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1answer
115 views

Impose an specific Trigonometric expansion with TrigExpand

Is there a way to impose in mathematica an specific trigonometric expansion with TrigExpand? I have various double-angle expressions for cosine and sine in my ...
2
votes
2answers
307 views

Why doesn't Abs simplify further?

Why does this: Simplify[Abs[x + I], Element[x, Reals]] give me Abs[x + i] Is there a way to force Mathematica to give me ...
0
votes
1answer
67 views

Simplifying complex expressions

I'm trying to work with complexes and I want Mathematica to know that all variables are real unless I explicitly assigned the variable with an I so I wrote: ...
20
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0answers
257 views

Are greek symbols causing different evaluation?

I've updated today to Mathematica 9.0.1.0 from version 8 and found something that absolutely confuses me. Let us define a piecewise function: ...
4
votes
2answers
118 views

Inconsistent results for equivalent converging symbolic integrals

I have looked at previous questions and I'm aware that this seems to be a known bug: Mathematica giving inconsistent results for symbolic integrals done in different ways. The origins for the bugs ...
6
votes
0answers
80 views

When and why are Assuming and Assumptions not equivalent? [duplicate]

In this question there's an example of an integral where using Assuming and Assumptions give different results: ...
3
votes
1answer
115 views

Problem with limit that requires L'Hôpital's rule to compute

Consider the following limit. Limit[(a - Sqrt[a^2 + x])/(a^2 - a*Sqrt[a^2 - x]), x -> 0, Assumptions -> {a > 0}] Mathematica 9.0.1.0 gives ...
0
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0answers
51 views

Using Assumptions with Solve [duplicate]

Suppose i have a function defined as follows - f[x_] := E^-x - E^(-2 x); I want to find the max/min hence need to find when f'[x]==0. So i tried the following - ...
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
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1answer
65 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
120 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
75 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
votes
2answers
114 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
94 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
200 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
218 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
374 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
142 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) ...