Questions tagged [operators]

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

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Apply central difference formula to a variable twice

I am working with finite difference methods analytically and I would like to be able to perform operations on subscripted variables. I would like to generate the following expression by applying a ...
Hefaestion's user avatar
4 votes
3 answers
264 views

How can I construct a determinant-type differential operator?

How can I construct a determinant-type differential operator, where the multiplication of elements in the determinant represents the composition of multiple differential operators? \begin{align*} \...
D.Matthew's user avatar
  • 217
0 votes
1 answer
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Nested RowBox in MakeExpression reports error when I define my own curl operator, but the single RowBox in MakeExpression works well

I want to define my own vector notation so that the input \[Del] \[Cross] a outputs curl[a] while the ...
ymma's user avatar
  • 1
1 vote
1 answer
89 views

Doing algebra with differential operators

I'm doing some work on stochastic processes, where I use random functions which are defined by their properties over averages, i.e $$\langle f(t) \rangle =0 \\ \langle f(t) f(t')\rangle = \alpha(x,y) ...
J Pin's user avatar
  • 11
0 votes
1 answer
83 views

Could Mathematica analytically work with operators (such as $\nabla$) and vectors?

I have the following expression: $$(\nabla+\vec{P})^2$$ where $P=(r\cos\theta sin\phi,r^4\sin\theta,r\cos^3\phi)$ I would like to open the brackets and simplify the expression. Are there in ...
Mam Mam's user avatar
  • 1,753
1 vote
3 answers
115 views

Is it possible to prevent two functions from commuting?

I have an expression of the following type: x f[a] g[b] where x is a number but f[a] and <...
Pxx's user avatar
  • 691
7 votes
7 answers
2k views

Can I use == to compare two list element wise?

I have the following lists Y and EY with actual and estimated outcomes. ...
M.E.'s user avatar
  • 323
2 votes
1 answer
102 views

How to define an operator like ⊕?

For example, I define the circle plus as a_\[CirclePlus]b_ := a + b^2; a__\[CirclePlus]b_ := (a[[1 ;;-2]]\[CirclePlus]a[[-1]])\[CirclePlus]b; But when I try ...
Curious Cat's user avatar
1 vote
1 answer
47 views

How can I define an operator and plot its iterates?

I am trying to define a function (an operator) that "integrates then translates" a function. More specifically, for an input f[x], I want to integrate it as \int_0^x f[t] dt, then translate ...
user122916's user avatar
1 vote
0 answers
215 views

How to define momentum operator for use with creation and annihilation operators in quantum mechanics

I am having trouble writing the momentum operator in the differential form to complete a piece of code shown here so that I can show a commutator [P,Q] = I . Here is what I have done so far, and I ...
kevin Tah N.'s user avatar
1 vote
2 answers
137 views

Replace with non-commutative product

I'm trying to evaluate some scattering amplitudes terms in Mathematica using the spinor helicity formalism. For that, I need to turn products like $\epsilon_i\cdot k_j$ into spinor product which can ...
Marcosko's user avatar
  • 239
11 votes
2 answers
206 views

How to make a function with two patterns listable?

Suppose that I have a function that has two patterns: disksConstantRadius[radius_][points_] := Disk[#, radius] & /@ points (noting that this would be better---...
Craig Carter's user avatar
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1 vote
0 answers
87 views

How to define a vector operator?

I know how to define a single-variable differential operator like Clear[Op] Op[x_] := a D[#, {x, 1}] & and I can do operations like ...
z.v.'s user avatar
  • 189
7 votes
1 answer
276 views

What does the operation Map[({...}=#;{...})&, ] do?

With reference to the answer by @Bill to the question posted here, I am trying to understand the following three lines ...
seeker's user avatar
  • 539
2 votes
1 answer
293 views

What's wrong with or? [closed]

Consider Clear[x]; x = 2; x < 2.9 || x > 3.1 This yields True So, everything is o. k. (interesting) But when you replace ...
user7427029's user avatar
1 vote
1 answer
97 views

How do I make an operator that acts on a function with the function's argument explicitly given?

I am trying to make a finite difference operator such that it would behave similar to the partial derivative $\partial_{x}f[x]$. $\delta_n[f[n],m] := \frac{f[n+m]-f[n]}{m}\ .$ I couldn't find a way to ...
Questioneer's user avatar
1 vote
1 answer
58 views

Using Through function with vectors

I have the vectors defined as follows: v1={x1,y1,z1}; v2={x2,y2,z2}; v12=v2-v1; v21=v1-v2; I am passing an integer function for iteration purpose as follows: ...
Aschoolar's user avatar
  • 883
2 votes
1 answer
124 views

How to give a property to a list of functions?

For example, I have defined a bunch of binary functions Sum1, Sum2, Prod1, ...
Yifeng Huang's user avatar
2 votes
1 answer
82 views

Visualizing order of operations

TreeForm[HoldForm[ (9-2^2+10 8)/9]] produces this: Is there a way to use Divide instead of ...
Geremia's user avatar
  • 478
2 votes
2 answers
99 views

Product of different differential operators

I need to define a multivariable differential equation of the type $$ \mathcal{D}=\Theta_1^2-z_1(-\Theta_1+\Theta_2+\Theta_3+\Theta_4)(1+\Theta_1+\Theta_2+\Theta_3+\Theta_4)\\ \;\;\;\;\;\;\;\;\;\;\;\;\...
Forum's user avatar
  • 21
0 votes
1 answer
30 views

Confusing abnormalities observed when counting a specific operator in an expression [duplicate]

Recently I have met with some confusing abnormalities when trying to determine if there is a specific operator (usually Plus[] ) in an expression by programming. ...
AlbertLew's user avatar
  • 473
2 votes
1 answer
84 views

How to convert an expression of several variables into an operator

Given the expression How can I define the following operator like g[u_, v_] := eq1 The correct definition is
Jose Nuñez's user avatar
3 votes
2 answers
161 views

How to subtract a list from certain sublists of a list? [closed]

I have a problem in doing an operation on this vector {{2,3},{3,4},{5,6}}-{1,1} I want to minus this to get the result ...
Ahmed's user avatar
  • 369
0 votes
1 answer
132 views

Second order differential operator in Mathematica

I am trying to write the code for the following expression in Mathematica: $$\partial_{x} e^{-g x}=-g e^{-g x}+e^{-g x} \partial_{x}\,.$$ I was able to do so with the help of the following links with ...
Sam's user avatar
  • 3
0 votes
0 answers
54 views

How to write the expression for first order differential operator in Mathematica?

How to write the expression for first order differential operator in Mathematica? What I mean to say that I want to evaluate $$\frac{\partial}{\partial x}f(x)=f'(x)+f(x)\frac{\partial}{\partial x}.$$ ...
Sam's user avatar
  • 3
3 votes
1 answer
92 views

Define an operator for long equations

I'm trying to workout a long expression with derivations, the thing is I can't seem to transfer this problem to code. What I need is a operator $D = l^\mu \frac{\partial}{\partial x^\mu} $ where $l^\...
Nitaa a's user avatar
  • 698
7 votes
1 answer
460 views

What operator is this?

I was looking at some sample code in a YouTube video and saw an "operator" (not sure this is the right term) consisting of a horizontal bar with circles on the ends. I searched through the ...
Robert McCormick's user avatar
0 votes
2 answers
68 views

How to define specify parameter functions of a Sturm-Liouville operator & plot its effect on specific functions?

I have a Sturm-Liouville operator: $$\mathcal{Ly(x)}=-\frac{\mathrm{d}}{\mathrm{d}x}\left(p(x)\frac{\mathrm{d}}{\mathrm{d}x}y(x)\right)-q(x)y(x)$$ but I do not yet know the parameter functions $p(x)$ ...
zabop's user avatar
  • 137
0 votes
0 answers
60 views

Is there a concise way to generate a continuous less-than relationship?

Actually, I have a ton of variables, Let me simplify it to 4 in this post. vars = {a, b, c, d}; 0 < Less @@ vars < 10 0 < (a < b < c < d) < ...
yode's user avatar
  • 26.3k
0 votes
2 answers
120 views

How can I remove the attributes "Orderless" from function Times stably and reliably?

Recently I have been doing some algebra of partitioned matrices, where product like below is common: where $A_{11}, A_{12}, X, Y$ are all partitioned matrix blocks thus all are matrices in essence. ...
AlbertLew's user avatar
  • 473
3 votes
1 answer
90 views

A possible issue in combination of the Infix operator ~ with Sequence [closed]

There are other similar questions on this site about using the Infix operator for more than two arguments, which I have read. But there is one thing that I wasn't able to understand and couldn't ...
polfosol's user avatar
  • 952
1 vote
0 answers
111 views

Use self-defined operator symbol simplify formula

Mathematica is very useful and powerful in symbol compute, but some output isn’t concise if we didn’t simplify. Can i predefined some operator? eg. Lie bracket. Here is a minimum example. Suppose ...
lumw's user avatar
  • 583
0 votes
1 answer
56 views

Defining Numerical Integral Functional [closed]

In some sense the question is a combination of defining an operator and defining numerical integration with parameters. For example, I want to define $I[f] = \int_0^1 f(x)dx$. and tried ...
Fan Zheng's user avatar
  • 101
1 vote
2 answers
64 views

System of rules transformingn a multivariate polynomial onto corresponding partial derivative operator

I take a complex multivariate polynomial, and I want to transform it into the corresponding differential operator. I.e., I am looking for the set of rules transforming variables to derivation, ...
Slepecky Mamut's user avatar
1 vote
1 answer
546 views

Simplifying quantum operators (ladder operators with multiple modes)

Similar to this question, I am interested in working with an implementation of quantum ladder operators. I've been trying to use this "Quantum Mathematica Package" to solve some lengthy ...
Steven Sagona's user avatar
3 votes
0 answers
191 views

Commutator of QFT Operators $[\hat{a}_p, \hat{a}^\dagger_k]$ and 4-Momentum Integrals

I just recently started looking into CAS (i.e. i have very little experience in Mathematica), specifically for doing basic calculations in Quantum Field Theory. For that i would like to define $\hat{a}...
fN ktn's user avatar
  • 131
0 votes
2 answers
165 views

How to create an operator which is a composition of a sequence of operators?

Suppose I have a sequence of operators $\partial_x$, $\partial_x^2$,..., $\partial_x^n$. I want to define an operator which is a composition of these $D_x^{(n)}=\partial_x\circ\partial_x^2\circ\cdot\...
vichitravir's user avatar
7 votes
1 answer
175 views

Applying Operators inside complex expressions to argument with Through

I am developing some functions to help me work with Quantum Mechanics Momentum Operators. Here, for simplicity, I represent them with these simple functions because the actions of the operators ...
Jorge's user avatar
  • 83
1 vote
2 answers
160 views

How to make a change of variable $y=x^2$ in the differential operator $\frac{d^2}{d y^2}$?

I have this differential operator $$\frac{d^2}{d y^2}\qquad (1)$$ I want to make a change of variable $y=x^2$ in $(1)$ so that I get this differential operator $$ \frac{1}{4 x^2} \frac{d^2 }{d x^...
Phys96's user avatar
  • 361
0 votes
1 answer
59 views

Evaluating a scalar product of a vector and a differential operator vector

I created a scalar product of a vector $\in \mathbb{R}^2$ and of a vector consisting of a differential operators ...
Uwe.Schneider's user avatar
2 votes
4 answers
334 views

Coordinate transformation can this be done with AffineTransform?

Looking for alternatives or improvements for accomplishing the following: Given the position of points A, B, and C in both the x-y and u-v planes, determine transformation functions to map values ...
user6546's user avatar
  • 1,027
1 vote
0 answers
47 views

Performing operator expression on a function

What I want. I write an operator expression, and Mathematica performs it on a function. Examples: E^(b D): f[x] -> f[x+b] ...
Anixx's user avatar
  • 3,553
5 votes
2 answers
399 views

Dealing with infinite matrices in Mathematica?

Is there a mechanism of dealing with infinite matrices in Mathematica, and in particular, with linear operators, corresponding to those matrices? For instance, automatic simplification of operator ...
Anixx's user avatar
  • 3,553
1 vote
0 answers
80 views

Whole 2 line code, producing a bug (infix operator)

Copy the following code, and create new 0 byte file, and paste the code and save it to TEST.nb ...
imida k's user avatar
  • 4,047
1 vote
1 answer
25 views

Generating composed operators using Table

Given an operator with two argumentsf[#1,#2]& and some positive (evaluated) integer n, I want to generate the operator ...
atabler's user avatar
  • 113
1 vote
0 answers
83 views

Composition of functions and operator forms of built-in functions

I am trying to replicate the behaviour of some of the built-in operator forms (for Map, Apply etc) but struggling to understand ...
EstabanW's user avatar
  • 658
1 vote
0 answers
57 views

Differential operator in Mathematica

I am fairly new to Mathematica and I wanted to know if I can define the following operator $E:=(x^2\sqrt{1-K(x^2+y^2+z^2}+y^2+z^2)\gamma^{1}\partial_{1}+(y^2\sqrt{1-K(x^2+y^2+z^2}+x^2+z^2)\gamma^{2}\...
lastgunslinger's user avatar
0 votes
0 answers
86 views

How to implement this operator in Mathematica?

I am interested to implement this operator: $$(\ln D)[f] =\left(\frac{i \pi}{2}-\gamma\right) f(x)+\frac{1}{2}\,\text{P.V.}\int_{-\infty}^\infty \left(\frac{1}{x-x'}-\frac{1}{| x-x'| }\right)\,f(x')\,...
Anixx's user avatar
  • 3,553
0 votes
0 answers
69 views

Can I apply functions to infinite matrices or linear operators in Mathematica?

I do not know how can I apply functions to infinite matrices or linear operators. For instance, having the derivative operator, what is its sine? For instance, for finite derivative operator we have $$...
Anixx's user avatar
  • 3,553
5 votes
1 answer
324 views

How can I direct sum matrices into the middle of one another another?

I would like to execute the mathematical operation of the direct sum of matrices in the case where the matrices are not appended one after the other along the diagonal, but instead mixed among one ...
TQM's user avatar
  • 53

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