# Questions tagged [inverse]

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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### Finding the inverse function of an interpolating function given by NDSolve

Consider the following solution of NDSolve ...
399 views

### Easiest way to have an approximation of binary entropy inverse

I call $H_2$ the function $H_2(x) = -x \ln(x)-(1-x) \ln(1-x)$ It is the binary entropy. I call $g(x)=H_2((1+x)/2)$ This last function is bijective on $[0;1]$. I would like to have an inverse, or ...
97 views

### Fast method for getting the inverse function of the Hypergeometric function in Mathematica

I didn't manage to obtain the inverse function for this frightening function: ...
158 views

### Mapping colours to numbers

Through this post I've learned how to make a function to map a colour gradient to an interval of numbers like ...
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### Inverse of a 3x3 Matrix [closed]

So I know the definition of the Inverse of a Matrix A is that there exists matrix B such that AB=BA=I3, where I3 is the identity matrix. If A is invertible, then the matrix B is called the inverse of ...
263 views

### Taylor expansion of two variable function without cross terms

I have the matrix symmetric matrix ...
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### Where is this difference between the solutions of DSolve and NDSolve coming from?

I am trying to solve this DE: DSolve[{r'[t] == r[t]^2/3 (1 - r[t]), r[0] == 2}, r[t], t] // Simplify For which I get the solution ...
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### Inverting a series with both positive and negative powers

I have an asymptotic series expansion that I would like to invert of the form $t_2 z + t_3 z^2 + t_4 z^3 + \frac{A_1}{z} + \frac{A_2}{z^2} + ... + \frac{A_9}{z^9} + \mathcal{O}(z^{-10}) = w$ i.e. I ...
170 views

### How to invert boolean byte coding function?

I've got simple byte coding function: y = x and E0 or x and 1F xor 05 Now I want to express x = ...? Is it possible using Mathematica (for more complex ones), please? TIA Correct answer (right?): ...
219 views

### Is there a built-in function to inverse Thread?

Namely, while Thread @ f[{a, b}, {x, y}] gives {f[a, x], f[b, y]} the InverseThread (if it existed) should reverse the ...
194 views

### Treat symbols as elements of a non-commutative field

I want to invert a matrix, {{a,b},{c,d}}, where a,b,c,d are elements of a non-commutative field (for example invertible matrices)...
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### Inverse Function in Mathematica

How to find bConst in the following code ...
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### Solving for $\beta$ in $\tan\gamma = C \tan\beta$, $0 \leq C \leq 1$, where $\beta$ must be in same quadrant as $\gamma$

I am pretty weak with Mathematica, so please, nothing overly complicated. The ArcTan[x, y] function allows for a full range of $2 \pi$ in the output. However, for ...
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### Finding input of the function $f(a,b,c) = (d,e)$ such that $|d-e|$ = constant for $d\in[d_0,d_1]$

The actual question contains a few more parameters than mentioned in the title, but the idea will remain very similar. Lets begin abstractly; I have a certain function $f(a,b,c) = (d,e,g,h)$. I am ...
930 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: ...
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### 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 ...
486 views

### Implicitly inverting a function from numerical solution [closed]

I have the following piecewise continuous function: ...
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### Function inversion [closed]

I have an expression of this kind ...
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### 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 ...
311 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 ...
154 views

### InverseFourierTransform very slow

I determined a distribution dist = SmoothKernelDistribution[ListOfValues];. Then I determined the FT of the PDF, which is the ...
19k 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} } using the ...