Questions on exact, symmetric reversal of a definition or functional mapping (i.e. the original form is returned when applied twice). Use this tag for issues on inversion of Mathematica expressions, or general inversion of math constructs.

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6
votes
3answers
217 views

Why doesn't Lambert function (ProductLog) simplify?

I have Simplify[ProductLog[x*Exp[x]]] By the definition of the Lambert function, this should be simply x. But Mathematica outputs this: ...
1
vote
0answers
36 views

How to invert an Elliptic function where the elliptic nome is a function of an independent variable?

I have a Jacobian elliptic function as a function of two independent variables $x$ and $y$. The elliptic parameter $m=m(y)$, $0 \leq m \leq 1$, is also a function of the variable $y$, and thus the ...
1
vote
4answers
140 views

Implicitly inverting a function from numerical solution [closed]

I have the following piecewise continuous function: ...
4
votes
1answer
86 views

Function inversion [closed]

I have an expression of this kind ...
1
vote
1answer
67 views

A question on JordanDecomposition in Mathematica

How can I have Mathematica show me also the inverse matrix of the similarity matrix of JordanDecomposition of a matrix? Obviously I need to use here the ...
2
votes
0answers
68 views

How do I invert a function with two arguments? [closed]

I begin with a function defined by c[u_, mH_] I won't go into details because it comes from countless lines of partial differential equations, boundary ...
0
votes
1answer
63 views

InverseFourierTransform very slow

I determined a distribution dist = SmoothKernelDistribution[ListOfValues];. Then I determined the FT of the PDF, which is the ...
3
votes
2answers
665 views

How do I get the inverse of a homogeneous transformation matrix?

I want to get the inverse of this homogeneous transformation matrix: iab = { {1, 0, 0, 0}, {0, 0, -1, 0}, {0, 1, 0, 3}, {0, 0, 0, 1} } ...
5
votes
3answers
179 views

How to tell Mathematica to get the real-only inverse function?

The problem I have is that Mathematica seems to play better with complex numbers so that the result of N[InverseFunction[Function[x,x^3]][-1]] is ...
1
vote
1answer
46 views

How to find selected elements of inverse of a banded matrix without inverting it?

Is it possible to find some selected elements of the inverse of a large sparse matrix without inverting it? For example consider this Hermitian matrix (as a general case). ...
1
vote
2answers
117 views

Back from transfer function (s-domain) to differential equation (in t-domain)

I've got the following transfer function (in the s-domain): $$\text{H}(s)=\frac{\text{C}s}{\text{RC}s+1}$$ Is there a function in Mathematica 10 that I can go back to the differential equation (in ...
1
vote
1answer
49 views

Evaluation of InverseFunction at the boundaries of its domain

Folks, I want to numerically evaluate a InverseFunction h[x] close to the edges x5 and <...
0
votes
1answer
99 views

Replace variable with # and pass function body as an argument to a function

I have a very simple problem, which I would like to make a bit general, but none of my naive approaches have worked yet. This is what I want to do step by step: Define a parameter: ...
0
votes
0answers
42 views

Don't understand results from solving polynomial equation [duplicate]

I attempting to solve an equation for x so that I may then switch x & y to get the inverse function. This is the code I have for solving for x: ...
1
vote
1answer
53 views

find the inverse of a hyperbolic function

Hi everyone I am new in Mathematica and I am trying to find the inverse of a function which contains hyperbolic tangents and I hope someone can help me. The function is y=(a)tanh(d(x-g))+ (a/2)(...
0
votes
1answer
51 views

InverseFunction of [E, 1, 1][c/Sqrt[K[1]]] isn't it just Log[c/Sqrt[K[1]]? [closed]

The problem is DSolve[E[del x'[t]/x[t]] x[t]^.5 == c, x[t], t] the answer is ...
-1
votes
1answer
199 views

Inverse of a Digamma/ Polygamma Function

How one can find the inverse of a digamma/ Polygamma function in Mathematica 10?
2
votes
0answers
73 views

Approximate inverse of large sparse matrix with small diagonal element

I need to find inverse of a large sparse matrix with small diagonal element. I follow this question - Is there any way to obtain an approximate inverse for very large sparse matrices? and try to use ...
4
votes
0answers
103 views

Inverse of piecewise function with pieces invertible on specific domain

I have piecewise continuous function defined below: f=Piecewise[{ {15 + 1/6*(# - 3), # <= 27}, {# - 12 + 4 * Exp[-5/24*(#-27)], 27 < #} }]; This ...
0
votes
0answers
16 views

How to plot `y=y[x]` from `f[x_,y_]=f0` [duplicate]

Given a two-variable function f[x_,y_]:=(*complicated stuff in terms of x and y *) what I want is to do is Plot ...
0
votes
1answer
108 views

Creating Matrix,Inverted and Upper Triangulate inside Module

I was trying to fit this into a module but I didn't have any luck. And for some reason it won't Inverse the Matrix. Here's the code: Input: ...
0
votes
1answer
199 views

Symbolic matrix inversion

If I try to get an inverse of a matrix: a | b | c b | d | 0 c | 0 | 0 Inverse[{{a, b, c}, {b, d, 0}, {c, 0, 0}}] I get the answer: ...
0
votes
1answer
91 views

Interpreting Mathematica output or producing cleaner output [closed]

Could someone please explain what the following would look like in standard math notation (or explain to me what this means): ...
1
vote
0answers
69 views

Why are my 3D plots getting inverted? [closed]

For some reason, all 3D plots that I make in Mathematica 9 get inverted in both the image and the axes. For example, using the simple plot: ...
6
votes
2answers
262 views

How to reverse irreversible function in Mathematica?

How to reverse formula $y(x)=x (\frac{1}{sin \frac{\pi x}{2}})^\alpha$ i.e. express it as $x = x(y)$ in Mathematica? I did this way ...
0
votes
0answers
39 views

How to use FindFit to find the parameter in Laplace space(numerically inverting Laplace transforms)

I am trying to find the parameter in Laplace space, and a very simple example is shown below: I have known the solution $y_{laplace}$ in the laplace space is $a/s^2$, and I also have some discrete ...
5
votes
2answers
390 views

How can I get the inverse of my function?

The original function is $$f=\frac{1}{e^{\frac{\phi }{k t}}-1}-\frac{m+1}{e^{\frac{(m+1) \phi }{k t}}-1}$$ I want to express $e^{\frac{\phi }{k t}}$ about $m$ and $f$, so I tried: ...
0
votes
0answers
47 views

Having trouble reading this output (pure functions) [duplicate]

I'm after decoupling some odes and trying to solve them using mathematica but my output is in terms of Functions and InverseFuntions and I'm afraid I have no idea how to translate the output into ...
2
votes
1answer
126 views

Inverting matrix with assumptions

I want to invert a matrix that contains some variables, so I thought I should give some assumptions to Mathematica to speed up the process. How do I assume that $s0,...,s8$ are positive constants ...
1
vote
1answer
39 views

Inverse KroneckerProduct given other arguments

I'm having problems working out how to do the inverse of a two argument Kronecker Product, given one of the decomposed column vectors. For example, say I have used the Kronecker Product on two ...
5
votes
0answers
427 views

How to invert a matrix with 100 trillion elements?

I have a $10^{7}\times 10^{7}$ matrix with the following properties: it is sparse it is gamma-5 it is almost Hermitian. If $M$ is the matrix we are trying to invert, we know $M=A M^{\dagger} A$ ...
2
votes
2answers
566 views

Get inverse of a matrix step-by-step [duplicate]

How can I get the inverse of a matrix step by step? An example: Given the matrix `{{8, 2}, {3, 2}}´, the result is {{$\frac{1}{5}$, -$\frac{1}{5}$}, {-$\frac{3}{10}$, $\frac{4}{5}$}}. But how can I ...
4
votes
2answers
144 views

Inverse of LogIntegral

I wanted the inverse logarithmic intgral, so I typed InverseFunction[LogIntegral] and received the expected symbolic answer. But when I try to integrate it or ...
0
votes
2answers
200 views

Block matrix definition and inversion

I would like to define the following block matrix $$ A=\begin{bmatrix} H-G_1 & -G_1 & \ldots & -G_1 \\ -G_2 & H-G_2 & \ldots & -G_2 \\ \vdots & \ldots & \vdots & ...
1
vote
1answer
269 views

Is there an inverse function for F[x] = {Cos[x], Sin[x]} in Mathematica?

Mathematica has functions ArcCos, ArcSin, and ArcTan, but none of these does what I need, ...
1
vote
1answer
180 views

In there a way to derive the inverse value of CDF format MultinormalDistribution?

Is there a way to produce the inverse value of multinormal distribution function in CDF format with 0.05 significance level? I found the function called ...
1
vote
1answer
133 views

Fit to inverse function

I am trying to fit my data to an inverse function from solving a DGL: ...
5
votes
1answer
256 views

Solution to a T+U = E equation

I needed to solve really easy differential equation (in dimensionless units): $$ \mathcal{T} (\dot{\xi}) + \mathcal{U} (\xi) = \text{const.} \equiv \varepsilon ; \quad T(\dot{\xi}) = \dot{\xi}^2 ; \...
3
votes
2answers
255 views

What would be the inverse function for the following condition?

I tried the problem but i couldn't take above condition in question in terms of f(x)
1
vote
1answer
150 views

Inverting matrix of unknown size

I have a matrix that has a variable number of columns and rows (but it is always square). The matrix is: $$ \Gamma = \begin{bmatrix} \Theta & 0 & 0 & 0 & T & 0 & R_j \\ ...
0
votes
1answer
168 views

Inverse of a restriction of a non-invertible matrix

Let $A∈R^{4×4}$ be a non-invertible matrix, with $2$-dimensional kernel. How can I compute the inverse of the restriction of $A$ on a subspace where it is invertible: $A^{-1}v \,\,\,\,$ where $\,\,\,\...
0
votes
1answer
161 views

Inverse functions - how are they calculated?

Mathematica is able to calculate InverseFunction[LogIntegral] and InverseFunction[RiemannR] (and many other inverse functions). ...
0
votes
1answer
388 views

Specific entry of inverse of large matrix

Given a large (say 10x10) sparse Hermitian matrix with symbolic entries, I need four specific entries of the inverse matrix. It seems wasteful to me to compute 100 entries of which I only need a few ...
0
votes
1answer
1k views

How to find the inverse a symbolic matrix that Mathematica thinks might be singular

I have a square matrix depending on a parameter "a". When "a" has a numeric value (eg 2.1 * 10 ^ 8) through the inverse function Inverse[] I can invert the matrix. If I write the matrix as a function ...
1
vote
0answers
233 views

Speeding up inversion of symbolic matrices by invoking caching

Is it possible to reduce the computation time taken to find inverse of symbolic matrices USING CACHING TECHNIQUES accessible (if any)? I am trying to compute inverse of symbolic matrices of size ...
0
votes
0answers
38 views

How to Invert a Multivariate Interpolating Function? [duplicate]

I used NSolve on a partial differential equation with boundary conditions to get a numerical solution that Mathematica says is of the form InterpolatingFunction. I then defined a function f(x,y) which ...
1
vote
1answer
180 views

invert system of two parametric ODEs and plot results of do-loop

I can solve this system of parametric ODE (u is the parameter,while g,e and ...
1
vote
1answer
385 views

How to do Inverse formulas/Rearrange formulas in Mathematica? [duplicate]

Hi am a student in chemical engineering and I have the necessity to rearrange formulas algebraically, for example ...
1
vote
0answers
234 views

Invert a transcendental function

I have tried Reduce and Solve in Mathematica, as well as have a long list of tries in Maple, but cannot seem to get anywhere ...
0
votes
1answer
219 views

Finding the InverseFunction of a polynomial function restricted to an interval [duplicate]

I want to calculate the inverse of f[x_] := 1/2 - (x (4 x^2 - 9))/12 /; -1/2 <= x <= 1/2 f[x] is monotonic inside $-0....