Questions tagged [operators]
Questions about using or composing operators--functional mappings from one state or vector space to another.
206
questions
4
votes
3answers
344 views
Iterated differential operator
I would like to implement the following differential operator in Mathematica,
$$\prod_{j=1}^n \left({d \over dx}-j\right)$$
On a case by case basis, I can just expand it out and write things in terms ...
1
vote
0answers
47 views
Precedence of @@ vs /@ [closed]
How do I find what I think is called the "precedence" of a given operator. That is, for the following code:
...
3
votes
2answers
50 views
Define the behavior of operators without built-in meaning
I need an operation $\tilde{}$ that lifts another operation (for example, the sum, but this does not have to be limited to real numbers) in the sense that $\widetilde{ (x \oplus y)} = \tilde x + \...
2
votes
0answers
23 views
Define an operator with the distributive property that works in general expressions
This is a follow up to this question. In that question they use TagSetDelayed to give a symbol the distributive property. In my case this becomes
...
4
votes
1answer
101 views
Partial transpose of 8x8 density matrix?
Please could someone help me to knew how to compute the partial partial-transposition of the following matrix?
mat = Table[ρ[i, j], {i, 1, 8}, {j, 1, 8}]
0
votes
1answer
43 views
How to define derivative operation of a series acting on normal function
In some cases, I have to do derivarive of higher order acting on some function successively.
Here is a toy example:
I have a function named myfunc:
...
2
votes
1answer
30 views
Is associativity of operators documented?
Operator precedence is documented. Operators without built-in meanings are documented.
The word "associative" apparently does not appear in either page. It's easy enough to do an experiment to observe ...
0
votes
0answers
37 views
Defining and Squaring an Operator using Mathematica
Hello I have a question regarding the possibility of defining a operator using Mathematica. Essentially what I would like to do is define the following,
\begin{gather*}
{\mathcal D := \frac{1}{(x^2+...
0
votes
0answers
61 views
Evaluating a differential expression using Mathematica
I am attempting to calculate the following expression in Mathematica, but I am having a bit of difficulty doing so. I want to calculate the following expression
\begin{gather*}
\left(x^2\sqrt{1-...
3
votes
2answers
77 views
How to check if all the members of a list lies in specific ranges based on another list?
There are two lists as follows:
lista = {i, j, k};
listb = {{1, 2}, {3, 4}, {5, 6}};
If i in ...
1
vote
0answers
39 views
Create an operator that holds its arguments [duplicate]
How can I create an operator that holds its arguments?
I am looking to define something similar to
oper[x_][expr_] := Hold[expr]
I am expecting the following ...
-5
votes
3answers
429 views
How to calculate the divergence of stress matrix in polar coordinate system correctly
I calculate the divergence of stress matrix in polar coordinate system by the method of coordinate transformation as follows :
...
7
votes
2answers
308 views
Defining an operator in Mathematica?
How to define the following operator in Mathematica?
$$\hat{\nabla}^4=\left(\frac{\partial^2}{\partial\hat{r}^2}+\frac1{\hat{r}}\frac{\partial}{\partial\hat{r}}\right)^2$$
3
votes
1answer
59 views
How to expand (not replace) the “+”, “>” infix operator on strings? [duplicate]
I went through the similar questions to overload the behavior of built-in operator, like How to overload the operator "*" as KroneckerProduct. The answers given there are usually to use new ...
19
votes
1answer
164 views
Why does OperatorApplied by default reverse the arguments?
Perhaps this is just one of those Mathematica curiosities, but I'd like to know why by default
OperatorApplied[f][x][y] === f[y,x]
versus the more usual way one ...
0
votes
0answers
18 views
Problem with makeOperator which yields Polynomials of an operator
Hi Is it possible to improve the macro provided by Jens Polynomial expansion of operator
...
0
votes
0answers
44 views
Nest function n times
A trivial example would be
f[x_]:=x
Nest[f, 7, n]
which would of course be 7 because it is independent of ...
0
votes
3answers
114 views
How to use `Through` function to pass through derivative operator
Because of the need of the operation rules of variational notation, I want to achieve the following effects:
Through[(f + s)'[x]]
Through[(f + s)''[x]]
I want to ...
2
votes
2answers
65 views
How can I concisely define a matrix-form partial derivative operator?
I have a vector
$\boldsymbol{u}(x,y) = \begin{bmatrix} u_x(x,y) \\ u_y(x,y) \\ \end{bmatrix}.$
I would like to get
$\boldsymbol{\sigma}(x,y) = \begin{bmatrix} \sigma_x \\ \sigma_y \\ \tau_{xy}...
4
votes
2answers
192 views
Can C-like function call syntax be easily achieved for particular function names?
I'm trying to use Mathematica as a tool to prove that some C code is equivalent to another (up to roundoff errors). For this I need to somehow paste C expressions like ...
0
votes
0answers
65 views
Simplifying a differential equation acting on a product of functions
I have a function $f(x_1, \ldots , x_n)$ in $n$-variables that satisfies a fourth order linear differential equation (say $Df=0$). The function $f(x_1, \ldots, x_n)$ is of the form $f(x_1, \ldots, x_n)...
0
votes
0answers
46 views
Using FullSimplify to simply expressions involving differential operators
I am trying to simplify some long formulas involving differential operators in $n$ variables. For example, I want to simplify
$$\left(\frac{\partial}{\partial x}-\frac{\partial}{\partial y}\right) \...
0
votes
1answer
78 views
Simplifying $\left(f\left(x\right)\frac{\partial}{\partial x}\right)^nf\left(x\right)$ into a summation
In case you're wondering how to get differentials to act like operators in Mathematica, I stumbled across a package Carl Woll made to solve this issue in this question. There's a a more recent version ...
0
votes
0answers
33 views
How to transform polynomial to differential operator?
How to transform the multiariate polynomial to corresponding differential operator?
For instance, for a polynomial $ \frac{1}{2} z_1^2 z_3^6 $ is the goal operator $ \frac{\partial ^8}{\partial ^2x_1\...
0
votes
0answers
33 views
Implicit definition of a coordinate in differential equation [duplicate]
I would like to solve the following differential equation
$\frac{d^2 \psi(r_*)}{dr^2_*} + (\omega^2 - V(r)) \psi(r_*)=0$
and the boundary conditions are $\psi(\inf) = \psi(-inf) = 0$. The problem is ...
0
votes
1answer
85 views
Multiply function-valued matrices
I would like to create a notebook for calculations in supersymmetric quantum mechanics. The basic building blocks are two functions (or maybe better: operators):
...
10
votes
4answers
386 views
Operator currying: how to convert f[a,b][c,d] to {a+c,b+d}?
This question is related to this golfing question (but I'm not interested in golfing, only in functional operator composition):
How can we convert f[a,b][c,d] to <...
3
votes
1answer
106 views
Best way to apply a list of functions to a list of values?
This question is closely related to questions 83720, 17460, and 11298.
How would you write the operator
F = Through[#1[#2]] &
in the prettiest, fastest, or ...
0
votes
1answer
75 views
How to substitute integral operators into polynomials?
Suppose I have a polynomial
$a_0+a_1 f(x,t) + a_2 f(x,t)^2 + ....$.
In code,
a0 + a1 y + a2 y^2 + a3 y^3 /. y :> Integrate[Subscript[y, k] E^(I k y), k]
<...
0
votes
0answers
37 views
Defining a function through an ODE containing unspecified operators
I want to do some algebra using a function only defined through a DE containing unspecified operators. The DE is
$$
\partial_zu(z) = \left[\hat{D}+\hat{N}(z,u)\right] u(z).
$$
Here $u$ lives in ...
0
votes
2answers
167 views
How to construct — based on physics-type notation — a magical simplex $\mathcal{W}$ of bipartite qutrits?
I have a short Mathematica program:
...
3
votes
2answers
147 views
Append a function of an expression as operator form using Curry?
I fielded this q to tech support but didn't get a conclusive answer yet:
Is it possible to use Curry specifically to modify ...
1
vote
0answers
58 views
Distribute && over a list [duplicate]
I cannot find an operator "RO" so that given a list, say {a,b,c},
RO[&&,{a,b,c}]
produces
a && b && c
2
votes
4answers
158 views
Skipping indices in a product
I have a matrix $A$ for which I want to compute the quantity $T\lambda_j = \Pi_{\lambda_i\ne \lambda_j} \frac{A - \lambda_i I}{\lambda_j-\lambda_i}$, where $\lambda_i$ ($\lambda_j$) denote the ...
0
votes
1answer
44 views
Performing a simple operation with operators [closed]
I have a map defined as
$\qquad \Phi(X) = a^2\, Tr[X] |0\rangle \langle 0| + b^2\, Tr[X] |1\rangle \langle 1| + a\,b\, Tr[\sigma_z X] |0\rangle \langle 1| + a\,b\, Tr[\sigma_z X] |1\rangle \langle ...
2
votes
1answer
120 views
Problem with defining a simple linear operator
I need to define a linear operator, which should have very simple linearity:
myOp[Plus[f_, g_]] := myOp[f] + myOp[g]
myOp[a_ f_[x_, t_]] := a myOp[f[x, t]]
where ...
1
vote
2answers
115 views
Simplify differential expressions
One can differentiate a two dimensional vector like this,
ClearAll["Global`*"]
u[x_, y_] := {f[x, y], g[x, y]}
Div[u[x, y], {x, y}]
with output
...
2
votes
1answer
40 views
Define different actions for the same operator depending on the nature of its arguments
I am working with terms of the form
A**B1**B2
where A, B1, and ...
2
votes
1answer
131 views
Defining an operator with given properties
In symbolic derivations with Mathematica, one often needs to define an operator with some desired properties, which will be used to stand for a general function or transform.
For example, I would ...
1
vote
1answer
78 views
Define custom operator and specific application
I want to define a specific operator that will act in generic functions that depend, say, in the variable z. My problem is that I want when a specific function is ...
1
vote
1answer
90 views
A program for finding the summation of an analytical expression
Consider the Baker-Hausdorff formula for two operators $A$ and $B$:
$$e^BA e^{-B} =A+[B,A]+\frac{1}{2!}[B,[B,A]]+\frac{1}{3!}[B,[B,[B,A]]]+....,$$
where $[A,B]=AB-BA$. In the case of my problem, $[B,...
2
votes
2answers
55 views
Defining a differential operator that acts on a non-commutative basis
Given a non-commutative basis ${x_0,x_1,x_2}$ I'd like to define a differential operator that acts as so
$$ \Delta_i (\sum_{n=0}^\infty c_n x_i^n) = \sum_{n=1}^\infty c_n x_i^{n-1}, \quad \Delta_i ...
21
votes
4answers
970 views
What is the definition of Curl in Mathematica?
I have a usual mathematical background in vector and tensor calculus. I was trying to use the differential operators of Mathematica, namely Grad, ...
2
votes
2answers
352 views
=== not working properly [closed]
I've been trying to check the identity using wolfram Mathematica and I've found the following
...
1
vote
1answer
92 views
Reduction of differential operators
Suppose my code outputs the expression
$$\frac{f^{(0,2)}(r,\phi )+r \left(f^{(1,0)}(r,\phi )+r f^{(2,0)}(r,\phi )\right)}{r^2}$$
This is simply the Laplacian $\nabla^2f(r, \phi)$. Is there a way ...
0
votes
0answers
282 views
Commutator of differential operators
Let $P_x = \frac{\hbar}{i}\frac{d}{dx}$, after specifying the commutator relation symbolically $[X, P_x] = i\hbar$, I can ask Mathematica to calculate commutator algebra. My question: is there a way ...
0
votes
1answer
88 views
Divergence and gradient operators in two dimensions
Divergence of a vector $\mathbf{a}$ can be numerically written as,
\begin{eqnarray}
\nabla \cdot \mathbf{a} \approx \sum_{i=0-9} w_i\mathbf{a(x+c_i)}\cdot \mathbf{c}_i
\end{eqnarray}
The lattice ...
0
votes
2answers
113 views
Sum over integer partition with variable function argument
Define
$$\hat{X}(Y) = [X,Y]
$$
I have known matrices $S_i$ and $V$. I am trying to use Mathematica to define a function which calculates
$$
\sum_{\substack{n_1, \ldots, n_k>1\\ n_1+\ldots n_k = ...
0
votes
1answer
83 views
Lowering operator for spherical harmonics [duplicate]
I need to be able to generate all of the $ l=2 $ spherical harmonics using the lowering operator. The specific question is listed below. Any assistance would be much appreciated!
Thanksenter image ...
0
votes
1answer
293 views
Partial trace and Partial Transposition of a matrix easily? [closed]
Could someone help me to understand as to how to compute the partial trace and partial-transposition of an arbitrary matrix? I mean, is there any code to carry out these operations in Mathematica?
...
