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

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1
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1answer
54 views

How to do matrix operation if the first matrix is an operator? [duplicate]

Suppose I have: mM = {{D[#, x]&, D[#, y]&}, {D[#, y]&, D[#, z]&}} v = {f[x, y, z], g[x, y, z]} I want to get $u=mMv=\{\frac{\partial f}{\partial ...
11
votes
5answers
471 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 ...
1
vote
1answer
67 views

What are rules in Mathematica and what are its uses? [closed]

I'm new to Mathematica. I have been going through the official reference and came across this article on rules to which I was led by a Google search on how to ...
3
votes
1answer
467 views

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

I would like to calculate the Gâteaux 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
1answer
155 views

Defining a matrix with elements acting as operators

This question is directly related with my previous one. I'll try to be more specific here. I have a matrix {{a[x],b},{c,d}}, where ...
3
votes
2answers
133 views

Replacing multiplication of matrix elements by application of these elements as functions

I want to realize the following idea in Mathematica. I've got a matrix {{a,b},{c,d}} which is multiplied to a vector {h,k} ...
6
votes
1answer
72 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] ...
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+...
2
votes
2answers
73 views

Why is the square of a differential operator not evaluated automatically?

I defined an operator: py[f_[x, y]] := (I*h*D[f[x, y], y] - x) // Expand (not important, but it represents a simplified component of a quantum momentum in a ...
5
votes
1answer
140 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 ...
3
votes
2answers
123 views

Computing powers of the operator using symbolic computation

Suppose $t\in\mathbb{R_+}$ - some parameter, $V: \mathbb{R}\to\mathbb{R}$ - some function. I have an operator $S:f\mapsto S[f]$ that maps a function $f$ to a function $S[f]$: $$ S[f](x) = f(x+\sqrt{t})...
26
votes
3answers
517 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 ...
0
votes
1answer
83 views

what do those signs #1, #1^2, #1^3, & mean here? [duplicate]

I have read common pitfalls page and the documentation page but I still don't understand what do those signs mean here? ...
3
votes
3answers
141 views

General function for the expansion of a polynomial of operators

This question is motivated by a Quantum mechanical problem - but in explaining the problem - I assume no knowledge of quantum mechanics. I want to define a function that can expand and simplify the ...
4
votes
2answers
92 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 ...
0
votes
1answer
80 views

Differential equations expressed in operator form [duplicate]

Is it possible to make a workable operator representation of differential equations in Mathematica? I think it would make solving my differential equations easier, but I have no idea how to do it. ...
1
vote
1answer
65 views

How to get Burgers hierarchy for any value of n

The Burgers hierarchy is defined by D[u[t, x], t] + α D[((∂/∂x) + u[t, x])^n u[t, x], x] How can I get the equation for the value of ...
4
votes
1answer
114 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 ...
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 ...
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: ...
1
vote
1answer
73 views

How can I define operators that have the behavior I want? [closed]

I need to define some operators with properties like idempotence and distribution over union and intersection so that Mathematica can symbolically simplify expressions. How do I define such operators? ...
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\\ ...
0
votes
1answer
111 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 ...
2
votes
1answer
128 views

Not commuting operator calculation

I am working on some operator calculation; I do not want the commutation relation. so xy ≠ yx. I found the mathematica code from https://reference.wolfram.com/language/ref/NonCommutativeMultiply....
10
votes
1answer
243 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 ...
3
votes
0answers
139 views

Is it possible to simplify an expression in vector form, which involves crossproduct and dot product?

I often need to simplify expressions involving cross product and dot product, for example: f = Dot[Cross[Cross[p1 - p, e1], Cross[p2 - p, e2]], Cross[p3 - p, e3]] ...
8
votes
1answer
148 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. ...
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 ...
7
votes
1answer
232 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 ...
0
votes
1answer
64 views

How to put a levelspec in operator form? [closed]

All variable argument functions need Function wrapped around them in operator form, but is there any other way to achieve this: ...
2
votes
1answer
50 views

Changing the grouping of an user defined infix operator

How can I change the default grouping on an operator without a built-in meaning? I've created my own infix operator by defining LeftArrow. ...
7
votes
2answers
271 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. ...
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 ...
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 ...
8
votes
3answers
352 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 ...
7
votes
5answers
278 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 <...
2
votes
1answer
103 views

Expand a product of operators

Lets suppose I have a family of operators $f_i$, and unknown c-numbers $a,b,c$. I want to expand such products: $(f_1+f_2+c)(f_3+f_2+b)$ into $b c+b f_2+b f_1+c f_2+c f_3+f_2^2+f_1 f_2+f_2 f_3+f_1 f_3$...
0
votes
2answers
129 views

How may I define e.g. Tilde[x,y] to have certain properties?

I would like to define, e.g., the Tilde[x,y] operator to have certain properties, and then investigate whether certain expressions involving that operator are True or not. For example, if I specify ...
0
votes
1answer
97 views

Symbolic matrix calculation [closed]

I have question about a matrix calculation like $\mathbf{b}^{t}\,\Sigma\,\mathbf{b}$, where $\Sigma$ is a 7 by 7 matrix, and $\mathbf{b}$ is vector of 7 elements, and each element in the vector $\...
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 ...
8
votes
2answers
986 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 ...
5
votes
0answers
81 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 ...
3
votes
1answer
71 views

Cannot normally underline slash characters and hyperlinks

Really, if you evaluate Style["/", Underlined] or type / and set the font of the character to be underlined through Format|Font..., you get $/$, not $\underline{/}$....
7
votes
2answers
315 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 ...
0
votes
1answer
85 views

Define action of noncommutative product of operators

I have objects wrapped with head fv. So they are things like fv[{1, 2}, {3, 4}, {5, 6}] I then defined two operators, a and <...
4
votes
1answer
755 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[...
1
vote
1answer
220 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 ...
2
votes
2answers
278 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 ...
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 ...
3
votes
1answer
381 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 ...