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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2
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0answers
54 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 $\...
0
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0answers
42 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 ...
0
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2answers
71 views

Mathematica ruins domain after explicit summation?

I'm working with this function ...
1
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0answers
78 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 ...
11
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2answers
275 views

Behavior of Solve with $Assumptions changed in 12.2

Something changed with Solve between versions 12.1 and 12.2. 12.1: ...
2
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3answers
336 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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76 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 ...
0
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1answer
45 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...
0
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0answers
17 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. ...
1
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0answers
62 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'. ...
0
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2answers
47 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
63 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
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
57 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
27 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 ...
0
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1answer
60 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
90 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 $n$ ...
1
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1answer
51 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
277 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 <...
8
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1answer
109 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
56 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
75 views

Getting two different results for the same computation

I have the following two codes: ...
0
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1answer
52 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 ...
0
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1answer
51 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
40 views

Regarding “Assumptions” under “Integrate”

Sir, I tried to integrate the following in mathematica ...
0
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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
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, ...
0
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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: ...
0
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1answer
47 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, ...
0
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0answers
36 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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0answers
100 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
76 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 $0\leq \gamma < 1$. ...
1
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1answer
66 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 ...
2
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0answers
49 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 ...
0
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0answers
32 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 ...
2
votes
1answer
61 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 ...
1
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1answer
27 views

Assumptions in Integrate not working properly

I have the following code: ...
2
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1answer
33 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 ...
0
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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] ...
0
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1answer
44 views

Why does restricting the domain not eliminate this solution?

Beside this specific problem I'm wondering if there's a more explicit way that I can understand when Solve and Reduce will find solutions. I find myself repeatedly getting stuck where I'll get ...
7
votes
1answer
185 views

How to best add assumption that many variables are positive?

I often need to check whether integrals are solvable in closed form and use a notebook with 5–10 variables that need to be assumed positive. Is there a better way of doing this than adding the clunky ...
0
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0answers
45 views

Simplification of symbolic vector and matrices representation

I'm new to the Wolfram Language programming and I cannot manage to do the following. I wish to use Wolfram Cloud to simpilfy a heavy vector and matrix expression using symbolic complex vectors (...
2
votes
1answer
56 views

Count based hypothesis test for inhomogeneous Poisson process

I am intended to fit the following data using InhomogeneousPoissonProcess[] in v12.0. The original form of data tabulated given as below Such a table contains ...
0
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1answer
87 views

Mathematica assumptions [closed]

Mathematica produces the answer to integral((x + 5)/(x^2 + x − 2) dx). Find what is missing and explain what assumptions it seems that Mathematica is making.
2
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1answer
88 views

Why does this boolean computation get stuck?

I want to build a boolean function which takes three one-parametric functions. I really don't know how to write a function for this, but this seems to be working for me as long as the parameter is <...
3
votes
1answer
122 views

Does Assumptions not work on Root objects?

Typically, one can restrict symbolic quantities using Assumptions. Suppose, for instance, that I want to solve $a=x^2$ for $x$, with $a>0$, restricting my answer to the positive root. ...
0
votes
2answers
101 views

I need to create abstract vectors

$Assumptions = {q \[Element] Vectors[{15}, Reals]}; $Assumptions = {p1[q] \[Element] Vectors[{3}, Reals]}; So I have been using this code in order to define an ...
0
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0answers
58 views

How do I apply assumptions to a table of functions

I have a table, really its a tensor but anyways I would like to apply an assumption to it, i.e. 1 - 2 phi[t,x,y,z] == 1 and have it print the tensor after it has ...
3
votes
3answers
130 views

Simplifying square roots of squared reals

I am using Mathematica to check some long, tedious calculations and I am stumped by some mysterious behavior. If I simplify a long expression that clearly has square real factors under a radical, for ...

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