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

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58
votes
6answers
2k views

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 ...
44
votes
2answers
2k views

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 ...
26
votes
3answers
513 views

Is there a comprehensive list of functions with V10 operator forms?

Version 10 sports operator forms for many functions like Map, SortBy, Select which allow you ...
22
votes
5answers
3k views

Having the derivative be an operator

How do I create an operator which acts like a derivative to everything to the right of it: for example: $ \left( \partial_x + \partial_y + z \right ) x \psi $ How do I make that evaluate to: $x \...
22
votes
11answers
2k views

Generating an ordered list of pairs of elements from ordered lists

I have a pair of ordered lists. I want to generate a new ordered list (using the same ordering) of length n by applying a binary operator to pairs of elements, one from each list, along with the index ...
21
votes
3answers
1k views

How is + as an infix operator associated with Plus?

How is + associated with Plus? Suppose I want to define a head FooBar and have it ...
15
votes
2answers
1k views

What happens when you divide by ##?

I've been playing around with sequences a bit. In particular with using ## with unary and binary operators. Let's start simple, the following all make some kind of ...
15
votes
2answers
1k views

How to define a non-standard algebra in Mathematica?

I want to define an algebra, where there are three elements: 0, 1 and $\infty$ and two operations, addition and multiplication defined, both commutative: $$\begin{align*} 0+0&=0\\ 0+1&=1\\ ...
11
votes
3answers
527 views

Replace operators

/. can be used to replace variables but how can one replace operators. For example in a * b, ...
10
votes
9answers
661 views

How to find range in which a number falls, from given list of numbers?

How can one find the range in which a number falls, from given list of numbers? ...
10
votes
4answers
357 views

Element-wise test on List elements

This question could sound pretty silly but I can't find a way to apply element -wise tests to a list. For example if I digit ...
10
votes
1answer
240 views

Question about Rules and Pattern (The operator patt/;test)

Maybe this question is so trivial but it has confused me. I'm studying the What the @#%^&*?! do all those funny signs mean? and in the Rules and patterns under ...
10
votes
1answer
143 views

Using MapIndexed[List] on a dataset fails — why?

The following works: MapIndexed[List]@{1, 2, 3} (* {{1, {1}}, {2, {2}}, {3, {3}}} *) This works too: ...
9
votes
3answers
367 views

Operate over list of pure functions

I have list of pure functions (All functions are InterpolatingFunction) i.e {{a, b}, {c, d}, {e, f}, ...} and I would like ...
9
votes
1answer
2k views

How do I expand a sum?

I have a problem with Mathematica's symbolic manipulations. As an example, consider the following expression: $$\sum _{i=1}^n -2 x_i \left(-a x_i-b+y_i\right)=0$$ How do I get Mathematica to expand ...
9
votes
2answers
309 views

Change associativity of the @ operator

The @ operator in Mathematica is right-associative by default, i.e. f@g@h evaluates as f@(g@h) Is it possible to make the ...
8
votes
3answers
2k views

Using D to find a symbolic derivative

I need to do the following: Define a function Take the derivative of this function and have a look at the symoblic representation Substitute in some values With the bonus that I want to use the ...
8
votes
3answers
350 views

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 ...
8
votes
2answers
949 views

Defining quantum-mechanical Bra and Ket operations

I have the following ket in the Fock basis: $\vert3, 0 ,1\rangle$, where each entry defines the number of photons in a particular mode and can take any one of the following numbers: 0, 1, 2, 3. As a ...
8
votes
1answer
222 views

Why `Drop` and `Take` do not support a operator form

Since Mathematica 10 introduced the operator form, I have been a big fan of it. Whenever I use some buit-in functions, I first look up whether they support operator form. To me, it was quite ...
8
votes
1answer
143 views

Define multilinear operator

In Maple it is possible to define a multilinear, orderless operator with: define(A,'orderless',multilinear): I can't seem to find the equivalent in Mathematica. ...
7
votes
5answers
274 views

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 <...
7
votes
2answers
313 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 ...
7
votes
2answers
270 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. ...
7
votes
1answer
226 views

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 ...
6
votes
2answers
1k views

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:...
6
votes
1answer
397 views

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 <...
6
votes
4answers
799 views

Exponential of a Differential Operator

In Mathematica, is it possible to exponentiate a differential operator such that the operator will act on a function, $f(x,p)$? Specifically, I wondering if I can get Mathematica to do this: $\exp(c\...
6
votes
2answers
2k views

why I can't define a commutator operator in this way?

I am trying to define some operators I used frequently. For example, I defined a KroneckerProduct operator as $\otimes $ as follows: ...
6
votes
1answer
506 views

Defining the Moyal Product in Mathematica

What would be the best way to define the Moyal Product, $f(x,p)\star g(x,p)$, in Mathematica? $f(x,p)\star g(x,p)$ may be written as $f\star g=\sum\limits_{n=0}^{\infty}\frac{1}{n!}\left(\frac{i\hbar}...
6
votes
1answer
71 views

Custom operator form for system functions?

There are some functions for which an operator form would make sense but isn't implemented. For example, I'd like to make this work: RandomSample[3] @ Range[10] ...
5
votes
2answers
243 views

Associativity of `/@` [duplicate]

Why are the following not equivalent: Map[Line, Map[(Print[#]; #) &, {{{2, 1}, {1, 1}}, {{-2, 1}, {3, 1}}}]] which produces ...
5
votes
3answers
386 views

ComplexInfinity/Indeterminate error when evaluating derivative

Motivation: I want to find the coefficients for the polynomial that is obtained when one adds together the first $n$ natural numbers to the power of $a$; that is, when you consider $1^{a} + 2^{a} + \...
5
votes
3answers
1k views

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 ...
5
votes
2answers
5k views

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 ...
5
votes
2answers
687 views

Scalar product operator of complex vectors

What is the scalar product operator for complex vectors (or matrices) in Mathematica? The usual $Dot[]$ doesn't work. E.g. here is what the Mathematica gives $$\{1,0\}.\{I,0\}=I$$ but the answer ...
5
votes
1answer
136 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 ...
5
votes
1answer
99 views

Computing list elements that refer to earlier elements and two other lists without iteration

I am attempting to compute the elements of a list, $\{a_i\}$ given lists $\{b_i\}$ and $\{c_i\}$ using the following formula: $a_i = \frac{1}{c_1}(b_i - \sum_{j = 2}^{i}c_{j}a_{i-j+1})$ for $1\leq i \...
5
votes
0answers
78 views

Operator which can be interpreted as binary and unary

I'm a bit lost with the way how e.g. the + operator is implemented in Mathematica as binary (infix) and unary (prefix) operator depending on the context, since I would like to define a similiar ...
5
votes
1answer
158 views

Can Mathematica Operators be combined in a linear fashion for readability? [duplicate]

Here's a simple example. Suppose we want to find the off-diagonal matrix of m: m={{1,2},{3,4}} This can be solved fairly simply by extracting a list of the ...
4
votes
2answers
272 views

Question on operator: // N

I've seen a notebook with the following: ...
4
votes
1answer
144 views

Operator-Input Form for Lists?

The documentation on Operator-Input Forms shows the following example which suggests that there is an alternative, convenient, operator-style, tidy technique for inputting lists. However, there is ...
4
votes
1answer
160 views

Factoring a differential equation into an operator product

Following the fundamental theorem of algebra, I can (as stated here in Sec. 1.1.4) factor an $n$th-order linear ordinary differential equation $$ a_n \frac{d^n x}{dt^n} + a_{n-1} \frac{d^{n-1} x}{dt^{...
4
votes
1answer
468 views

Define operator algebra

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)\...
4
votes
2answers
90 views

How best to write an exponential of differential operators?

I want to evaluate a term like this, $$\left.\exp\left({1\over 2}\sum_{i,j=1}^{n}(A^{-1})_{ij}{\partial \over \partial x_i}{\partial \over \partial x_j}\right) f(\vec{x})\right|_{\vec{x}=0}$$ and I ...
4
votes
1answer
112 views

Products of Differential Operators

I have a differential equation defined as the product of operators which I want to expand out into a polynomial in powers of $z\frac{d}{dz}$ $\qquad \prod_{n=1}^p(z\frac{d}{dz}+a_n)$ However when I ...
4
votes
1answer
732 views

Creating the Nabla operator as a operator

How can I define the nabla-operator as a an operator, acting on everything to the right of the operator! Also taking \[Del]^2 would give the second derivivates. I wish to be able to write \[Del]f[...
4
votes
1answer
113 views

Avoid writing explicit form of operator

I would like to evaluate the following (simplified) expression with Mathematica : $\frac{\delta}{\delta J} \exp[(J(x)+K(x)) \Delta (J(x)+K(x))]$ where $\Delta$ is a differential operator independent ...
3
votes
4answers
3k 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+...