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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57 views

This expression isn't simplifying [closed]

Consider: expr = -(((s β - γ - ν) (s (β - γ) - i γ - ν))/(s β)); I tried: 1) ...
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1answer
51 views

How to 'define' value in Assumptions but not let Simplify replace it? [closed]

I want to let Simplify know the exact value of a symbol, to resolve logical statements, but don't want it to actually replace it. For instance, I would like ...
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63 views

Mathematica can FullSimplify general but not specific case of a square root

FullSimplify[ Sqrt[(M^2 + A^2 - B^2)^2], M^2 + A^2 - B^2 > 0 ] outputs the desired: A^2 - B^2 + M^2 I've followed the ...
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TensorExpand ignores assumptions?

Here's a minimal example to demonstrate my problem: ...
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1answer
50 views

Simplify an expression with assumptions connected with OR

Mathematica doesn't seem to have any problem with these commands: ...
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37 views

How to simplify the conditional expression?

I have an assumption for mulitple value, ...
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22 views

Test domain assumption of a variable

Using $Assumptions to define the domain of variable is straightforward, i.e. $Assumptions = Element[x, Reals]. Nevertheless, it'...
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40 views

Difference between Assuming[] and Refine[]

I'm trying to find the limit of a root. I've found that the limit is undefined if I use Refine[] ...
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3answers
742 views

How can I specify the assumption 'a' is much greater than 'b' (a>>b) in Mathematica?

I want to evaluate an expression of type 1/(r-2 m), assuming r >> 2 m. This is regarding black hole physics and r = 2 m is the Schwarzschild radius. But I am working on something where I need to ...
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42 views

Piecewise and Assumptions [closed]

Assumptions sometimes work as expected with Piecewise, for example Simplify[Piecewise[{{A, a + b >= c}, {B, True}}], Assumptions -> a + b > c] correctly ...
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62 views

Solving generating conditional expression despite assumptions

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2answers
67 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
185 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
83 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
47 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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$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
95 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
97 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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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
82 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
60 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
67 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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20 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
174 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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31 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
68 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
70 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
68 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 ...
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1answer
82 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 <...
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70 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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59 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
122 views

Mathematica ruins domain after explicit summation?

I'm working with this function ...
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82 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
426 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
347 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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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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26 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
66 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
58 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 ...
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1answer
74 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
33 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 ...
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2answers
66 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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31 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
80 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 ...
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1answer
100 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
57 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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