# Questions tagged [operators]

Questions about using or composing operators--functional mappings from one state or vector space to another.

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### when is f@g not the same as f[g]?

I have always thought that f@g will give the same result as f[g] in all cases, and it is just a matter of style which one to use ...
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### V10's Operator Forms - what are they good for?

V10 introduces an operator form for several functions perhaps primarily due to their role in queries as part of introducing data science functionality. At first pass it seems a lot of effort to add ...
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### Is there a comprehensive list of functions with operator forms?

As of version 10, Mathematica sports operator forms for many functions like Map, SortBy, ...
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### Redefining a built-in operator

Is there a way I can redefine the || operator such that a||b will be 1/(1/a + 1/b)? Is it ...
3k views

### Creating the Nabla operator (also known as Del operator) as an operator

How can I define the nabla operator (also known as Del operator) as a an operator, acting on everything to the right of the operator! Also taking \[Del]^2 would ...
746 views

### Define an operator with the distributive property

I would like to define the operator with distributive, associative, and commutative properties - so that Mathematica can symbolically simplify expressions I use ...
189 views

### Position-based Inline syntax for Curry

I would like to update an existing pseudo-curry function: • /: h_[pre___, •, post___] := Function[expr, h[pre, expr, post]]; that I use inline like this - the ...
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### How to write an operator that acts on pure function (to give another pure function)

I would like to write an operator oper that acts on a pure function f with an undetermined number of arguments, with the syntax <...
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### How to define the Poisson bracket in Mathematica

If $f,g$ are functions of the independent variables $\{q_1, q_2, ..., q_N, p_1, p_2, ..., p_N\}$, then the Poisson bracket is defined as: \begin{equation*} [f, g] = \sum_{i=1}^N \left(\frac{\partial ...
859 views

### How to make a binary function associative? (Or define an n-ary function?)

Suppose I have a simple function that I assign to an operator f[a_, b_] := a + b CirclePlus = f Then I want to write ...
308 views

### Defining an operator in Mathematica?

How to define the following operator in Mathematica? $$\hat{\nabla}^4=\left(\frac{\partial^2}{\partial\hat{r}^2}+\frac1{\hat{r}}\frac{\partial}{\partial\hat{r}}\right)^2$$
337 views

### HoldForm[Operator ##] on some list

Recently in response to this question Mr.Wizard suggested an unusual way to summing numbers. This doesn't seem to be documented. ...
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### How to find (numerical) value of a derivative at point?

I have the following function: f[0, 0] = 0 f[x_, y_] := Exp[-(x^2 + y^2)^(-1)] How do I find its partial derivatives at any given point, including $(0,0)$? This ...
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### How to construct custom operators with precedence?

I need to combine data structures in operations analogous to addition, subtraction, multiplication and division (and more). I need more than one operation of each type, i.e. more than one method of ...
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### How to change coordinates of a differential operator?

I'm doing a basic quantum mechanics problem and am trying to learn how to do it in Mathematica. Any help would be much appreciated. $\vec{L} = \vec{x} \times \vec{p}$ where $\vec{x}$ has components:...
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### What is the mathematical meaning behind D[f]?

y = a + b x; I can understand this output of the ordinary differentiation of y w.r.t. x <...
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### Computing with matrix differential operators

I am looking the achieve a working set of Mathematica functions that would allow me to take products, commutators, etc. of (2x2) matrix differential operators and apply them to vector-valued functions ...
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### Why can't I define a commutator operator in this way?

I am trying to define some operators I use frequently. For example, I defined a KroneckerProduct operator as $\otimes$ as follows: ...
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My objective is to work out commutators like this $$[f(x,y)\partial_x^2+g(x,y)\partial_x+h(x,y),a(x,y)\partial_x^2+b(x,y)\partial_x+c(x,y)]$$ or $$[f(x,y)\partial_x^2+g(x,y)\partial_x+h(x,y),a(x,y)\... 4answers 6k views ### How to write a differential operator in Mathematica I have a very basic question. I am trying to code the LHS of the differential equation:$$\Big[\frac{1}{\sin\theta}\frac{d}{d\theta}\big(\sin\theta\frac{d}{d\theta}\big)-\frac{m^2}{\sin^2\theta}+n(n+...
I want to be able to define an operator $(a(x) d/dx + b(x))^n$ where $d/dx$ is the derivative operator and $a(x)$ and $b(x)$ are known functions and $n$ is a positive integer. Related Query: How ...