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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1answer
49 views

Solving generating conditional expression despite assumptions

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2answers
62 views

Triple integral: How do I include assumptions and conditions?

I would like to solve the following integral: $$I=\int_{0}^{a} \int_{0}^{y} \int_{0}^{z} e^{(a-x)^{3}} d x d z d y$$ with the condition that: $$a>0$$ So I tried to input the equation like below ...
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2answers
181 views

Why Mathematica is not assuming real variable as real?

I am dealing with the situation where despite of specifying my variables b1 and c to be greater than zero, Mathematica still ...
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1answer
81 views

how can I modify this function to convert to polar form for any complex expression?

The function from another post is to convert a complex number to polar form. polarForm = Expand[# /. z_?NumericQ :> Abs[z] Exp[I Arg[z]]] & Now if I apply ...
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1answer
45 views

How to generate assumptions automatically for definite integrals?

In Mathematica, a trick to speed up the process of definite integrals is by adding assumptions. For example, the following codes run faster if we add such assumptions: ...
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0answers
75 views

$Assumptions causing problems in Mathematica 12.3 vs. 10.4 [duplicate]

I would like to use $Assumptions to add global restrictions to the parameters in my notebook (Mathematica 12.3). I tried exactly this in Mathematica 10.4 and it ...
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1answer
89 views

Symbolic Mean and Variance Calculations

I need a tutorial that gets me started on basic symbolic calculations with random variables. My naive attempts did not get me far. ...
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1answer
89 views

FullSimplify is giving a condition that is implied by the assumptions

I've been trying to understand why FullSimplify is giving a condition that is implied by the assumptions (otherwise the set is empty). However, I couldn't ...
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0answers
62 views

Why is this integrand not integrating to a Bessel function? [duplicate]

I know from the identities of Bessel functions that the following is true: $$ J_{m}\left( x \right) = \frac{ 1 }{ 2 \ \pi \ i^{m} } \int_{0}^{2 \pi} \ d\phi \ e^{i \left( x \cos{\phi} \ - \ m \ \phi \...
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1answer
76 views

Using Simplify and Reduce with Assumptions when the inequality is already one of the assumptions

I am using the Simplify and Reduce functions to reduce inequalities, but somehow the function Simplify does not consistently give "True" when the inequality happens to be one of the ...
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2answers
51 views

Assuming r0 ≈ r1 && r0 ≈ 0 && r1 ≈ 0, to discourage division by near-zero

I’m using Mathematica for some conceptually simple algebra, that will ultimately land in Excel or a compiled language. ...
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1answer
59 views

Solving an equation, and verifying that it is correct

I want to solve the equation Solve[e == 1/2 (-2 ef + hvk - Sqrt[9 hvk^2 + 4 j^2]), hvk] I then obtain the solutions ...
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1answer
65 views

Solve yields complex Root even if the domain is Reals

I want to solve $x^3=a^2$ for $x$ where $a>0$ and $x$ is real. The answer I want is $$x=a^{2/3}.$$ On Wolfram Cloud, I tried ...
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0answers
19 views

How to assume that an unknown function of many variables and all its derivatives is real?

I'm working on modified theories of gravity and I extensively use Mathematica to derive differential equations starting from the general covariant expressions of field equations of a theory. For ...
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2answers
169 views

Help solving this differential equation

I am trying to solve this differential equation $$ y^{''}(x) + \frac{6}{x} y^{'}(x) +14 y(x) = -4 y(x) \; \ln(y(x)),\; x > 0$$ subject to the boundary conditions $y(0) = 1,\;y^{'}(0) = 0$. The ...
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0answers
30 views

Assume some expression is false

I need to Reduce a complicated function and I want to exclude some conditions A and B. How do I assume that the expression A is ...
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1answer
66 views

Simplify not working

I am trying to simplify the following expression code: ...
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0answers
42 views

Intervals v.s. Domains: when to use which and why?

or: How to use Interval correctly? Mathematica provides these constructs for various symbolic deductions tasks. Among those constructs are symbolic number sets ...
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1answer
58 views

Real part of complex exponential

How do you obtain the real part of a complex exponential? For example, Mathematica gives $Re[e^{ik}]$ instead of $\cos(k)$, see figure. ...
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1answer
63 views

Display assumptions of a variable

If I restrict a variable x to x>0 via $Assumptions=x>0, is there a way I can get ...
2
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1answer
79 views

Can Limit take limits of unknown functions?

For example, when I input this f[0] = 0; Limit[f[x], x -> 0] , it does not output 0. Is there a way to get it to output <...
2
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0answers
67 views

Unexpected results with Integrate/AsymptoticIntegrate with assumptions

I am quite disturbed by the result provided by Mathematica, and I am not sure if I understand perfectly its behavior. What I want to do is to check the asymptotic form of the function $I(\tau)$ with $\...
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0answers
54 views

How to assume a number to be a half integer?

For integer x $\left(\cos 2\pi x\right) ^2=1$ and I can check this as follows ...
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2answers
100 views

Mathematica ruins domain after explicit summation?

I'm working with this function ...
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0answers
80 views

How reliable is AsymptoticIntegrate?

In new mathematica 12 there is a new function AsymptoticIntegrate. However, it seems that it gives me incorrect results in some cases. To be completely honest, it ...
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2answers
393 views

Behavior of Solve with $Assumptions changed in 12.2

Something changed with Solve between versions 12.1 and 12.2. 12.1: ...
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3answers
344 views

How can I write in Mathematica that 2*x is an integer? [closed]

I have to maximize $h/k^2$, where $h/k^2 < 0.1974$ and $k$ is an integer, and $2\cdot h$ is an integer, $h>0$, $k>0$. How can I write this problem in Mathematica?
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0answers
77 views

Issue with several replacements in a function under certain conditions

I am trying to define a function (reduce[x]) which does several substitutions, depending on the values of certain parameters. Concretely, consider an expression x, which contains an arbitrary number ...
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1answer
53 views

How do I give assumptions to Simplify or Solve? [closed]

I've have the expression: q2sol = (Sec[2*a1]*Tan[a1]^3*(-7 + 6*Cot[a1]^3*Sqrt[Tan[a1]^2]))/(6*Sqrt[Tan[a1]^2]) I know that a1...
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0answers
19 views

Assumptions with piecewise problem?

I am trying to apply the assumpion of 0<s<1 throughout the calculation however the piecewise condition does not accept it automatically. Is there any way to avoid the manual choice of x>0. ...
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0answers
64 views

Assuming a monotonic function

I'm trying to tell Mathematica that a function is increasing. More specifically, I would like at least one of the following statements to report 'true'. ...
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2answers
57 views

Expression simplification

I have this term Sqrt[(B Bc)/(A^2-B Bc)]Sqrt[B Bc+A(-A+Sqrt[A^2-B Bc])]Sqrt[-B Bc+A(A + Sqrt[A^2-B Bc])], which actually can be simplified to B*Bc. However, it ...
2
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1answer
73 views

Trouble evaluating this definite integral, either directly or with indefinite + limits

I have the function $$ \Sigma(x) = \frac{\sqrt{R^2-x^2}(\left| R\right| -1)}{\left(R^2-1\right) \left(x^2-1\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{R^2-x^2}}{\sqrt{R^2 \left(1-x^2\right)}}\right)-\...
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0answers
32 views

Simplify with Assumptions: Puzzle for 4 variables [duplicate]

I have a rather specific question about Simplify[] (hope this is not off-topic). The puzzle I have is that Simplify[] with ...
2
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2answers
62 views

Solving an Algebraic Equation with Constraints on Multiple Parameters

Suppose we have the following equation to solve (with respect to $x$): $$ \frac{m\omega^2x^2}{2} + \frac{m\alpha x^3}{3} = E,\quad\text{where }m,\omega,\alpha,E>0\text{ and } E < \frac{m\omega^6}...
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0answers
30 views

Why a complementary inequality for function values does not simplify to False?

I have a general assumption of a function to be positive. The direct inequality (f[x]>0) does simplify to True, but a complementary one (f[x] < 0) does not simplify at all despite the fact that ...
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1answer
66 views

How can I get rid of Abs?

In the following code, the functions WP[t] and WS[t] are real. Time also is a positive parameter. As you can see, MATHEMATICA enters Abs in the calculations. Including Abs only complicates the next ...
2
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1answer
94 views

Mathematica and its default assumptions

I am a bit surprised that evsluating Integrate[Exp[I n x],{x, 0, Pi}] gives $\qquad \frac{-i(e^{in\pi}-1)}{n}$. What if $n = 0$? I didn't assume anything about $n$ ...
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1answer
54 views

Use the fact that $u(t)\cdot u'(t)=0$ for $u\in\mathcal{S}^2$

If for all $t$, $u(t)$ is a point on the unit sphere $\mathcal{S}^2 \subset\mathbb{R}^3$, $u'(t)$ is orthogonal to $u(t)$, because $u'(t)$ is in the tangent plane of the sphere. I have large ...
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3answers
338 views

Problems with solutions involving Lambert W function of transcendental equation

Solve and Reduce fail here with rational parameter l, but succeed when I plug in a value <...
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1answer
111 views

Why does Simplify work diferently for (a+b)/e versus (a+b+c)/e?

I am playing around with Simplify amd assumptions. I noticed that: Simplify[x > (a + b)/e, x < (a + b)/e] ...
1
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1answer
62 views

How to evaluate a multidimensional NIntegral in a range where certain conditions must be satisfied by the variables

I have a function f which looks similar to this : f[a_, b_, c_] := NIntegrate[sigma[a, b, c], {a, -valueA, valueA}, {b, -valueB, valueB}, {c, -valueC, valueC}] and ...
2
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1answer
83 views

Getting two different results for the same computation

I have the following two codes: ...
0
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1answer
55 views

Specifying assumptions at the start of a piece of code

I am aware of the use of 'Assumptions' or 'Assuming' to attach to certain operations (e.g. integrals) to aid Mathematica. Is there a way of listing asssumptions at the beginning of a piece of code ...
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1answer
67 views

How do I introduce an assumption when defining a piecewise function?

Define m as an integer. I want to specify a Piecewise function f[x,n] that takes value ...
3
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1answer
65 views

NMinimize with assumptions gives result that does not satisfy assumptions

I am trying to determine if a function is always positive given a set of assumptions. I am using NMinimize following the advice of previous posts in this site. ...
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0answers
41 views

Regarding “Assumptions” under “Integrate”

Sir, I tried to integrate the following in mathematica ...
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1answer
36 views

Need help understanding the results of the unit function

I want to get Limit of the following function at $T\to 0$. $$ Eig=\frac{8 (\eta +J \sinh (2 \beta \eta ) \sinh (2 \beta J)+\eta \cosh (2 \beta \eta ) \cosh (2 \beta J))}{\eta Z^2} $$ where $Z=2 (...
3
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1answer
75 views

Solve an equation with real parameters

I am trying to solve $$ \left(\eta ^2-1\right) \cosh ^2(\beta \eta )+2 J^2=2 \eta (J \sinh (\beta \eta ) \sinh (\beta J)+\eta \cosh (\beta \eta ) \cosh (\beta J)) $$ for $\eta$. Where, $\beta, ...
0
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1answer
65 views

Problem with DiracDelta evaluating to zero

I am having an issue (in Mathematica 11.2.0.0) where the following integral evaluates to zero: ...

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