Questions tagged [complex]

Questions about using complex numbers in Mathematica. This includes basic arithmetic, functions of complex numbers, plotting complex functions, and dealing with branch cuts.

152 questions with no upvoted or accepted answers
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500 views

Expansion for Modified Bessel Function Around Infinity

I'm somewhat new to Mathematica, and I don't understand why I'm getting inconsistent series expansions for the modified Bessel Function of first kind near $x=\infty$. First problem: I get different ...
7
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0answers
90 views

Plot[Im[f[x]],…] incorrectly gives graph of identical zero function

Consider Plot[Im[(1 + (-1)^(2/3)*x)/((-1)^(2/3) + x)], {x, 0, 1}] At least in Mma 11 it gives the following picture: Meanwhile, ...
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72 views

Where is the mistake in computing the particular eigenvector of the following DFT Matrix?

I have the following matrix (the DFT Matrix for N = 3) $$W = \frac{1}{\sqrt{3}}\begin{pmatrix} 1 & 1 & 1 \\ 1 & e^{-\frac{i 2 \pi}{3} } & e^{\frac{i 2 \pi}{3} } \\ 1 & e^{\frac{...
5
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164 views

Find regions in which the roots of a third degree polynomial are real

I have to find the roots of a third degree polynomial in $\phi$ that depends from 3 parameters, namely $t,s,w\in \mathbb R$. In order to do that I've used the command ...
4
votes
1answer
128 views

Plotting a hexagonal histogram

For positive integers $D$, I have a function s[D_] which creates a list of complex numbers, all of the form $a+b\sqrt{-D}$, where $a$ and $b$ are integers. These ...
4
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0answers
109 views

Prime factorization over the Eisenstein integers $\mathbb{Z}[\zeta]$

I am trying to write a function f[a_,b_] which takes in two integers $a,b$ and returns the unique factorization of $a+be^{2\pi i/3}$ into the primes belonging to $\...
4
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0answers
72 views

Is `InverseMellinTransform` unaware of second Barnes lemma?

Consider evaluating ...
4
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0answers
129 views

Why isn't Mathematica listening to my assumptions?

I'm trying to simplify the expression ωplus := 1/2 c (I f V + Sqrt[4 k^2 - f (f + 8 I k) V^2]) so that I can get it in the form $a+i b$. I am using the global ...
4
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0answers
67 views

Why does FreeQ seem not to work with complex numbers?

I guess I do not understand how Mathematica evaluates this simple expression inside FreeQ ...
3
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1answer
73 views

Export ComplexPlot3D as Mesh with Material

If I generate a complexplot as follows: a1 = ComplexPlot3D[Log[z], {z, -5 - 5 I, 5 + 5 I}] I can export it to a 3D mesh (for use in external applications) with: <...
3
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0answers
115 views

Does anyone have a Mathematica implementation of the standard $\arg\zeta(s)$ function required to evaluate $S(T)$?

This question is related to my question Is there an elegant exact formula for the zeta zero counting function? on Math StackExchange. Question: Does anyone have a Mathematica implementation of the ...
3
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0answers
59 views

About what does FunctionSurjective think so long time?

Having tried a new in 12.2 command FunctionSerjective, I executed FunctionSurjective[z^(5/2), z, Complexes] // AbsoluteTiming ...
3
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3answers
669 views

Plot a specific branch of a multi-valued complex function

Let's say I want to plot a branch of the following function $f(z) = \sqrt{z(z-1)}$. Let $z = r_1 e^{i\theta_1}$ and $z-1 = r_2 e^{i\theta_2}$. How can I tell Mathematica to plot the branch for which $...
3
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0answers
118 views

Weird behavior of PolyLog

I have asked Mathematica (11.1.0.0) to calculate Sum[Log[n]/n (-9/10)^n, {n, 2, ∞}] This is the sum $\sum_{n=2}^{\infty}\limits\frac{\log n}{n}\left(-\frac{9}{10}...
3
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0answers
110 views

Solving a differential equation with a complex (independent) varible

I'm trying to plug in complex values in the numerical solutions of ODEs without success. For instance y[I] /. NDSolve[{y'[x] == 0, y[0] == 3}, y, {x, -10, 10}] ...
3
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0answers
1k views

Discrepancy in the series expansion of $\log(z/(z-1))$ in Mathematica 5

When I calculate the series expansion of $\log\frac{z}{z-1}$ around $0$ in Mathematica 5.2, I obtain: ...
3
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0answers
692 views

Taking real and imaginary parts of indexed functions and speeding up ComplexExpand

I am setting up a large system of ODEs and in order to use the IDA method (which is sig. faster for my system and thus attractive), I must split my equations into real and imaginary parts. I am ...
2
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0answers
50 views

Maximize a function over complexes

Assume that I have a bounded real valued function $h(a,b)$ such that $a\in \mathbb{C}$ and $b\in [0,1]$. Can Mathematica maximize such function over $\mathbb{C}\times [0,1]$? I tried some functions ...
2
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0answers
79 views

How to use _Complex types in CUDAFunctionLoad?

The documentation for CUDAFunctionLoad specifies various base datatypes you can use for your function's arguments, including ...
2
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0answers
45 views

How to numerically solve ODEs with a complex variable?

I want to solve the following ODEs: 3(a'[z])^2 == 1/2 a[z]^2 (p'[z])^2 - 1 ; a[z]p''[z] + 3a'[z]p'[z] + z^2 == 0 ; where z is ...
2
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0answers
82 views

How to convince Mathematica that $(-1)^{2/3} = e^{2\pi i /3}$

I have a list T which contains 3 + 4*E^(2*Pi*I/3). Yet MemberQ[ T , 3 + 4*(-1)^(2/3) ] ...
2
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0answers
123 views

Plotting from the celebrated Euler's formula

ContourPlot[ x^(I*y) == -1, { x, 1, 3}, {y, 1, 3}] A newbie's query..The most famous equation should ( methinks) yield a lot of points other than the real pair $(...
2
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0answers
47 views

How is a Lévy stabile process pdf normalized?

I'm interested in how to deal with α-stabile probability density functions, for example one with the Laplace image like: $ \phi(s) = s^{(\alpha-1)}*e^{-\nu s^{\alpha}} $ I can work with this ...
2
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0answers
140 views

Numerical estimates on asymptotic of given functional as $x\rightarrow \infty$

Consider the following functional : $$ I(x,s) =\int_0^\infty\mathrm dy \frac{F(x + \mathrm iy, s) − F(x −\mathrm iy, s)}{\mathrm e^{2πy}-1}, $$ where $ F(z, s) = \dfrac{\sin^2[π\Gamma(z)/(2z)]}{z^s} ...
2
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0answers
408 views

Speed up Mathematica's Simplify and ComplexExpand functions

I am trying to simplify an expression and taking the real part only. However Mathematica use ages to run the command (if it is able to do so in the end). The problem is that the expression I am ...
2
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0answers
143 views

Integral on unit disk of a function with two singularities

The goal is to prove, using Mathematica, that for $\mathbb{D}$ the unit disk and $u,v \in \mathbb{D}$, $u \neq v$, $$\frac{1}{\pi} \int_{\mathbb{D}} \frac{\mathrm{d}^2z}{(z-u)\overline{(z-v)}} = \ln(1-...
2
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0answers
46 views

Linearity of the Conjugate operator

The output of Grad[Conjugate[x + y + z], {x, y, z}] is ...
2
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0answers
68 views

How MandelbrotSetBoettcher function is computed?

Boettcher function is a solution of Boettcher's functional equation, so in case of complex quadratic map: $B(f(z)) = (B(z))^2$ where: B is Boettchers function f is complex quadratic map There is a ...
2
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0answers
31 views

`FunctionDomain` working with real part

Is there any reason why Mathematica evaluates the following FunctionDomain[Re[((I + 1) x)], x] (* False *) as False, where I'...
2
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0answers
95 views

Amplitude of a transfer function

I'm looking to calculate the amplitude of a transfer function which is defined in a symbolic way : T=(1 + 2 I r λ)/(1 - r^2 + 2 I r λ) I try this, i doesn't work ...
2
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0answers
108 views

How to ComplexExpand Jacobi elliptic functions?

It seems that Mathematica cannot expand Jacobi $\text{sn}, \text{cn}, \text{dn}$ functions. For example, A&S 16.20.1-3 say that for real $y$ $$ \operatorname{sn}(i y \mid m) = i\operatorname{sc}(y ...
2
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0answers
397 views

Padé approximation of a complex function

I have an interesting problem for the Mathematica. I have some function, let's call it $G$. This is function of discrete set of equidistant points on imaginary axis, $i \omega_n$, so the typical data ...
2
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0answers
351 views

Using Arnoldi Method with Multiple Options

I have a matrix with many complex eigenvalues, but I only need a few near a particular complex number. I am only looking at the imaginary parts, so I need the few closest on the imaginary scale to my ...
2
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0answers
362 views

Tricky inverse Laplace transform

I'm trying to compute the inverse Laplace transform of $f(s) = s^c/(N + s^{ir} )$ where $c,N \in \mathbb{C}$ and $r \in \mathbb{R}^+$ using the Bromwich integral $$ F(t) = \frac{1}{2 \pi i} \int_{- ...
2
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0answers
157 views

Constrain integration to be over real domain

I am trying to integrate the following: Integrate[(2*Cos[Sqrt[F]*z - G])/E^(D*(p + z)^2), {z, -(h/2), h/2}] I am getting solution in complex domain: ...
2
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0answers
88 views

The number of real values assumed by combinations of complex roots of a decic

Define complex conjugate as the pair of complex numbers $a+bi,a-bi$. Assume you have 5 such pairs and they are the 10 roots $x_i$ of a 10th-deg equation with integer coefficients. In general, how many ...
2
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0answers
422 views

Simple contour integral with a parameter gone wrong

Bug introduced in 7.0 and fixed in 7.0.1 I run into the following problem, I tried to evaluate a very simple integral: ...
1
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0answers
45 views

Specifying Contours in “CyclicReImLogAbs” for ComplexPlot/ComplexPlot3D

How can I specify where and/or how many contours appear in ComplexPlot and ComplexPlot3D when using the "CyclicReImLogAbs" color function? I'm referring specifically to the black and white ...
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0answers
56 views

Integrating real function gives a complex value

I want to integrate this quite complicated function Sin[2 Pi n x r0/L]*u[x, (m + 1/2) Pi - (nu I Pi/2), kappa I, nu] over x, where ...
1
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0answers
34 views

How to write a complex no linear term in loop of a differential equation system?

I have this system of equations $$ i \frac{d \psi_{m}}{dt} = k \psi_{m-1} + k \psi_{m+1} + \gamma \vert \psi_{m} \vert^{2} \psi_{m} $$ and this is my code ...
1
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0answers
50 views

numerical integration of an integral with singularity

I want to compute the following integral numerically in Mathematica, $$ \int_{-\infty}^{\infty} dw' \;\frac{\Gamma(\delta-4iw') 4^{4iw'}}{(i(w'-1)+\epsilon)^{1-4iw'}} $$ where $0<\epsilon, \delta≪1$...
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0answers
64 views

One more an incorrect result of FunctionAnalytic

Studying a new in 12.2 command FunctionAnalytic, I execute ...
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0answers
37 views

Integrate returning complex values

I am having trouble using mathematica to calculate some integrals Namely this : ...
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0answers
55 views

How do you define the domain and range of the variables for a plot?

How do I define the domain to be only reals and the range to be only complexes? Everytime I plot using ComplexPlot[], I get a C->C function so there are basically too many variables to plot and I ...
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0answers
56 views

Ordinary differential equation in the real domain

If I have the following equation (y - 1) ^5 == 32 I can select the real solution with Solve[(y - 1) ^5 == 32, x, Reals] Now, I ...
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0answers
43 views

What are “VariableReplacementDump” and “TranscendentalDump”?

I have run into a Mathematica object I've never seen before and Googling those reveals nothing. I'm talking about VariableReplacementDump and ...
1
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0answers
63 views

Simplification of expression with sum of absolute values

I try to simplify following expression 1/2*(Abs[a1] + Abs[b1] + Abs[c1] + Abs[d1]), where a1, b1, c1, d1 are quite long: ...
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0answers
50 views

Change the PolyLog branch cut in Wolfram Mathematica

The problem is to change the branch cut of PolyLog[2,z] function from the default half line z=1+x, x>0 to the new one ...
1
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0answers
42 views

Mathematica cannot evaluate the real part of a fraction?

I am encountering some confusing behaviour with Mathematica that maybe you can help me resolve: If I type: Im[1/a]~Refine~(a \[Element] Reals) I get the output: ...
1
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0answers
37 views

Solving ODEs in the Complex Plane for General z

I saw with the new 12.0 update, they have introduced expanded functionality for solving complex ODEs. In the given example, they solve for $y(t)$ and plot results using the new ...