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

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5
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0answers
61 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 ...
4
votes
1answer
169 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
57 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
109 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
78 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
97 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
88 views

Inconsistent results for Integrate depending on irrelevant assumptions

I stumbled across this amusing issue today when doing some definite integrals: ...
1
vote
0answers
108 views

Piecewise functions Integration with symbol

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

Unknown function with arbitrary arguments assumption

Is it possible to define an assumption like this: $Assumptions=f[__]>0 So that: ...
0
votes
1answer
150 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
1answer
288 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
181 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 ...
3
votes
1answer
129 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
73 views
5
votes
1answer
120 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
417 views

Can I check if an expression is positive using assumptions?

I have the following notebook: ...
1
vote
0answers
73 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 ...
15
votes
3answers
313 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
77 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
55 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
36 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
2answers
129 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 ...
2
votes
0answers
191 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
101 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
218 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
1k 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
433 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
189 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
725 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
133 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
vote
1answer
133 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
votes
4answers
185 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
votes
1answer
212 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
335 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
172 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: ...
26
votes
1answer
461 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
128 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 ...
8
votes
0answers
93 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
336 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
votes
1answer
74 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
77 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
votes
1answer
213 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
vote
0answers
83 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
142 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
112 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
267 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, ...
11
votes
0answers
291 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
431 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
155 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
115 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 ...