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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54 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
61 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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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
163 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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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
64 views

Simplify not working

I am trying to simplify the following expression code: ...
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38 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
48 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
61 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
78 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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0answers
59 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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48 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
84 views

Mathematica ruins domain after explicit summation?

I'm working with this function ...
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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
312 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
339 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
49 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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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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63 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
52 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
72 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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31 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
59 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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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
63 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
93 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
311 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
110 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] ...
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1answer
61 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 ...
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1answer
78 views

Getting two different results for the same computation

I have the following two codes: ...
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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
60 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 ...
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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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40 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 (...
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1answer
72 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, ...
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1answer
62 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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1answer
52 views

How can I add assumptions on the coefficients when using FindFit? [closed]

I have an equation of the following type: $$f(z) \overset{!}{=} a f_a(z) + \sum_{s=0}^\infty c(s) f_c(z,s)\tag{1}$$ where I know $f$ numerically and $f_a$ and $f_c$ analytically (they are long, ...
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37 views

Truncate series with real powers that are not fully numerical

Take a function with the following expansion A3[z_]:=Sum[Subscript[a3x, jj]*z^jj, {jj, 0, 2}] + z^r Sum[Subscript[a3NAx, jj]*z^jj, {jj, 0, 1}]; where ...
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102 views

Rubi/Mathematica gives different values for the same integrand

Consider this integral: $$ \int_0^\pi d\theta \sin\theta\, {1 \over \gamma^q}\left((1-\gamma^2)^2\sqrt{1 \over 1-\left(1-(1-\gamma^2)^4\right)\cos^2\theta} - 1\right)^q $$ for $0\leq \gamma < 1$. ...
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1answer
77 views

complex number from the integration of a real integrand

Consider this integral: $$ \int_0^\pi d\theta \sin\theta\, {1 \over \gamma^q}\left((1-\gamma^2)^2\sqrt{1 \over 1-\left(1-(1-\gamma^2)^4\right)\cos^2\theta} - 1\right)^q $$ for $0\leq \gamma < 1$. ...
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1answer
68 views

Two different Integration results for the same integrand in Mathematica

I want to calculate $$ \int_0^\pi d\theta\sin\theta\, \left(\sqrt{1 \over 1-\left(1-(1-\gamma^2)^4\right)\cos^2\theta} - 1\right)^q $$. For the simplest case of $q=1$ we have ...
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0answers
52 views

Summing with assumptions provides unexpected output

I am computing a closed form of a number of sums having generally the following form: $$ \sum_{i = 0}^{m/2}\sum_{\substack{0\leq k \leq i \\ 2k \equiv i + m \, \text{mod } 3}} k $$ It looks like ...
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33 views

Defining a function with certain regularity (e.g. smooth)

My goal is to understand how Mathematica computes limits that would require differentiability assumptions on functions (for, for instance, L'Hopital or Taylor Series). Consider, for instance, the ...
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1answer
67 views

Expanding Determinant as Multilinear Alternating Function

I am working with the expression $$\det\big{|}f(-kx), f(-(k-1)x),\cdots,f(0),\cdots, f((k-1)x), f(kx), g(x)\big{|},$$ where $f,g\colon\mathbb{R}\mapsto \mathbb{R}^{2k+2}$, and want to use the Taylor ...
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1answer
28 views

Assumptions in Integrate not working properly

I have the following code: ...
2
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1answer
46 views

How to state nontrivial tensor symmetry assumptions?

For example dddg, the third derivative of the metric tensor, in dimension $4$. I need to state that it is symmetric in the first two indices and symmetric in the ...
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0answers
37 views

Assumptions behavior in Refine[Sin[n Pi/2]] [duplicate]

I don't understand why this first expression returns a correct result: In> Refine[Sin[n Pi/2], Element[n, Integers] && Mod[n, 2] == 1] ...

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