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0
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0answers
31 views

Operator product

I have this problem: I define the gradient operator as: gradiente = {D[#, x] &, D[#, y] &, D[#, z] &} Now, if I want to apply the operator on a ...
0
votes
0answers
27 views

How to calculate a symbolic expression with non-commutative operators? [duplicate]

I am working on a quantum mechanics problem in my school tutorial and have come across operators that are not commutative ($a\, b\, !\mathbin{\kern-4mu=} b\, a$, where $a$ and $b$ are unknown ...
5
votes
0answers
87 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 ...
2
votes
1answer
84 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 ...
1
vote
1answer
173 views

Shorthand for operations?

Mathematica has a large number of built-in symbols, and I am unsure when there is a shorthand for the operation I am trying to perform. Question 1: Is there a shorthand for the function ...
0
votes
0answers
48 views

Applying the square root of operator on polynomial functions

I am trying to apply an "operation" on polynomial functions: apply the operator $(\frac{\partial f}{\partial x}-y\frac{\partial f}{\partial z})^2+(\frac{\partial f}{\partial y}+x\frac{\partial ...
2
votes
2answers
131 views

Polynomial expansion of operator

I am new to Mathematica, I am trying to generate the polynomial function of a operator. So for example, the operator $L $ is $\frac{\partial f}{\partial x}+\frac{\partial f}{\partial y} $, and I want ...
1
vote
0answers
33 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 $z\frac{d}{dz}$ $\prod_{n=1}^p(z\frac{d}{dz}+a_n)$ However when I try to ...
13
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 ...
5
votes
2answers
232 views

Associativity of `/@` [duplicate]

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

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 ...
5
votes
1answer
92 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 ...
8
votes
3answers
327 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 ...
5
votes
3answers
259 views

Element-wise list operation on list of lists [closed]

Suppose a function F operates on list A: $$A=\{a_1, a_2,\cdots, a_n\}$$ I have a list of lists, B: $$B=\{A_1, A_2,\cdots,A_m\}$$ Is there a syntax to specify that F should operate on members of B, ...
17
votes
2answers
300 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 ...
2
votes
2answers
55 views

Column Operation - Subtract part of nested list from part of another nested list [duplicate]

I have two lists with x- and y-coordinates with different z-coordinates of the form {{x0, y0, z0_1}, {x1, y1, z1_1}, ..., {xn, yn, zn_1}} and ...
4
votes
0answers
74 views

Operator and VariationalMethods [closed]

I'm trying to get the variational derivative $\delta E$ respect to $\Phi$ of this functional $$ E[\Phi] = \int d^3r\ \left[ -\frac{\hbar^2}{2m}\nabla^2\Phi + V(\vec{r})\Phi^*\Phi + ...
4
votes
1answer
97 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 ...
10
votes
1answer
123 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: ...
37
votes
5answers
1k 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 ...
3
votes
1answer
109 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 ...
1
vote
1answer
105 views

How to solve an operator form of an integral equation by iteration method?

How I can obtain the $n^{th}$ approximation of the following Operator form integral equation? $F(t)=A(t)+\int_0^tds B(s)F(s)$, where $A(t)=\bigg{(}\begin{matrix}t&0\\Cos(t)&1 ...
4
votes
1answer
110 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} ...
4
votes
1answer
237 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 ...
3
votes
1answer
252 views

Gateaux (directional) derivatives and higher order differentials of a functional

I would like to calculate the Gateaux derivative of a functional (i.e. a function depending on functions). A simple example for the Dirichlet functional: $L(u(x))=\int_0^1 \frac{1}{2} (u'(x))^2 dx$ ...
4
votes
4answers
275 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: ...
0
votes
0answers
62 views

Computing integrals with differential operator

I've to compute this expression $$ \hat{H} = \frac{1}{4}g_2\int d^3R\int d^3r\ \bar{\Psi}(\vec{R}+\frac{\vec{r}}{2})\bar{\Psi}(\vec{R}-\frac{\vec{r}}{2})\left[ \delta(\vec{r})\nabla_{\vec{r}}^2 ...
4
votes
2answers
266 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 ...
3
votes
1answer
67 views

Extract differential operator from differential form

Let's say I have : a*u''[x]+b*u'[x] where a and b are constant I would need to get ...
3
votes
1answer
140 views

Custom operators; custom pattern matching with pure functions

What I'm trying to achieve in Mathematica is the creation of a binary operator whose operands are both pure functions over the natural numbers. The result of the operator should be another pure ...
1
vote
1answer
107 views

Operator operation

There are two basic operators r={x,y,z} and p=-I*h*{D[#,x] , D[#,y], D[#,z]} &. The angular momentum operator is defined as ...
6
votes
1answer
378 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 ...
1
vote
0answers
65 views

Is there any way to define a new binary operator? [duplicate]

I am looking to define a new operator that would work similarly to the + or - operator. My end goal is to make a dice operator for calculating random distributions in the normal d20 fashion (e.g. 5d6 ...
3
votes
2answers
432 views

Differential operator squared

I defined a one-dimensional momentum operator $\hat{p}=-i\hbar\frac{\partial}{\partial{x}}$ in Mathematica p = -I * h * D[#, x]& and I want to get the ...
0
votes
0answers
43 views

How do you explicitly define Box Operator (D'Alembert operator)? [duplicate]

I wanted to see how one can define a box operator in mathematica? $$ \Box\phi=(-\frac{\partial^{2}}{\partial t^{2}}+\frac{\partial^{2}}{\partial x^{2}}+\frac{\partial^{2}}{\partial ...
4
votes
0answers
121 views

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

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 ...
5
votes
3answers
644 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 ...
1
vote
0answers
28 views

custom precedence for custom infix operator with InfixNotation [duplicate]

I am trying to define several custom operators with custom precedence to implement geometric algebra. Loading the notation package << Notation` I can ...
1
vote
1answer
109 views

Linearity of a function in Mathematica

I have a function which has something like myFunc[q,a state[c,d]] a could be anything, and I want to tell Mathematica that ...
1
vote
0answers
65 views

Define an operator without Built-in Meanings containing a Power function [duplicate]

I would like to define the following operator: $$ \left[T^{(j_{1})}\otimes U^{(j_{2})}\right]_{m}^{(j)}=\sum_{m_{1},m_{2}}\left\langle j_{1},m_{1};j_{2},m_{2}\big|j,m\right\rangle ...
1
vote
0answers
123 views

Defining an operator

Let s be a positive integer and let DifferenceDelta be this function with step = 1. Define ...
0
votes
1answer
81 views

What's wrong with my implementation on CountryData

I was wondering, *for which countries is the proportion of Phone line users to population greater than or equal to that of the United States?* This is what I inputted below, but the list of countries ...
1
vote
0answers
51 views

Parallelizing an associative binary operation

I have an associative binary operation '.', which I often use in this sort of way: result = expr1 . expr2 . expr3 . expr4 The ...
3
votes
1answer
270 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 ...
4
votes
2answers
200 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. ...
17
votes
3answers
654 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 ...
3
votes
1answer
116 views

Displaying the meaning of an operator using Information

I'm using CircleTimes ($\otimes$) operator defined as a_\[CircleTimes]b_ := KroneckerProduct[a, b] so I can use ...
32
votes
2answers
1k 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 ...
9
votes
6answers
412 views

Performing Computations on Sets

I would like to find a permutation of $\quad S=\{\frac{1}{10}, \frac{1}{2}, \frac{4}{7}, \frac{3}{5}, \frac{2}{3} \}\quad$ that maximizes the sum of theses elements raised to unique powers: ...