Questions tagged [operators]
Questions about using or composing operators--functional mappings from one state or vector space to another.
268
questions
76
votes
3
answers
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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 ...
- 143k
67
votes
6
answers
3k
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 ...
- 6,076
39
votes
6
answers
8k
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 \...
- 1,581
37
votes
3
answers
983
views
Is there a comprehensive list of functions with operator forms?
As of version 10, Mathematica sports operator forms for many functions like Map, SortBy, ...
- 8,774
28
votes
3
answers
3k
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 ...
- 585
26
votes
4
answers
2k
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, ...
- 1,727
23
votes
11
answers
3k
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 ...
- 2,832
19
votes
1
answer
241
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 ...
- 2,099
17
votes
2
answers
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 ...
- 8,774
17
votes
2
answers
2k
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:
$$\begin{align*}
0+0&=0\\
0+1&=1\\
...
- 3,585
15
votes
6
answers
3k
views
Element-wise test on List elements
This question could sound pretty silly but I can't find a way to apply element -wise tests to a list.
For example if I digit
...
- 337
15
votes
3
answers
845
views
Is it possible to define custom compound assignment operators like ⊕= similar to built-ins +=, *= etc?
I would like to do something like this:
...
- 7,213
15
votes
4
answers
3k
views
Exponential of a Differential Operator
In Mathematica, is it possible to exponentiate a differential operator such that the operator will act on a function, $f(x,p)$? Specifically, I wondering if I can get Mathematica to do this:
$\exp(c\...
- 992
15
votes
2
answers
436
views
Custom operator form for system functions?
There are some functions for which an operator form would make sense but isn't implemented. For example, I'd like to make this work:
RandomSample[3] @ Range[10]
...
- 31.5k
15
votes
2
answers
978
views
What is the best way to define Wirtinger derivatives
Wirtinger derivatives ( also called Cauchy operators) in complex analysis are widely used tools. They are defined in the case of one dimensional complex plane as follows
$$\frac{\partial}{\partial z}=...
- 363
14
votes
2
answers
597
views
How I can define this operator in Mathematica?
I want to define an operator $G$ such that
$$G(f):=\begin{cases}f(\{x\}),&\lfloor x\rfloor\text{ is even}\\\frac1{f(\{x\})},&\lfloor x\rfloor\text{ is odd}\end{cases}$$
for any function $f$, ...
- 1,107
13
votes
13
answers
2k
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?
...
- 1,866
11
votes
3
answers
6k
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 ...
- 70.6k
11
votes
4
answers
671
views
Change Operator Precedence of --> operator
I am trying to use --> operator with highest precedence
...
- 961
11
votes
3
answers
2k
views
Replace operators
/. can be used to replace variables but how can one replace operators.
For example in a * b, ...
- 2,073
11
votes
2
answers
12k
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 ...
- 977
11
votes
2
answers
209
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---...
- 4,415
11
votes
2
answers
338
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 ...
- 2,285
11
votes
1
answer
17k
views
Difference between = and := [duplicate]
I wanted to know the difference between two operators:
= and :=
I couldn't find the ":=" operator on the list at https://reference.wolfram.com/language/tutorial/Operators.html
Can someone help?
...
- 111
10
votes
3
answers
534
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 ...
- 36.5k
10
votes
4
answers
468
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 <...
- 47.5k
10
votes
2
answers
5k
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 ...
- 2,640
10
votes
1
answer
459
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 ...
- 967
10
votes
2
answers
512
views
Which operators are missing from the official precedence table?
I often use the Operator Input Forms page as a reference for operator precedence as well as which (used or unused) operators exist. However, I just noticed that at least one operator is missing from ...
- 8,774
10
votes
2
answers
486
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 ...
- 5,120
10
votes
1
answer
577
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.
...
- 127
10
votes
2
answers
2k
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}...
- 992
10
votes
1
answer
226
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:
...
- 235k
9
votes
1
answer
1k
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 ...
- 111
9
votes
1
answer
223
views
Position-based Inline syntax for Curry
I would like to update an existing pseudo-curry function:
• /: h_[pre___, •, post___] :=
Function[expr, h[pre, expr, post]];
that I use inline like this - the ...
- 15.1k
8
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.
...
- 333
8
votes
3
answers
805
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 ...
- 279
8
votes
3
answers
5k
views
Creating the Nabla operator (also known as Del operator) as an operator
How can I define the nabla operator (also known as Del operator) as a an operator, acting on everything to the right of the operator!
Also taking \[Del]^2 would ...
- 109
8
votes
2
answers
322
views
How can I define operators that implement the algebra of sets?
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?
...
- 111
8
votes
2
answers
9k
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 ...
- 949
8
votes
1
answer
564
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 ...
- 135
7
votes
5
answers
1k
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 <...
- 19.7k
7
votes
3
answers
516
views
Iterated differential operator
I would like to implement the following differential operator in Mathematica,
$$
\prod_{j=1}^n \left({\mathrm d \over \mathrm d x}-j\right)
$$
On a case by case basis, I can just expand it out and ...
- 81
7
votes
6
answers
464
views
Applying several functions to the same argument
Is there a more concise way of achieving the following result (possibly without d |->)?
...
- 16.7k
7
votes
2
answers
3k
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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:...
- 81
7
votes
3
answers
4k
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 ...
- 3,054
7
votes
2
answers
834
views
Defining an operator in Mathematica?
How to define the following operator in Mathematica?
$$\hat{\nabla}^4=\left(\frac{\partial^2}{\partial\hat{r}^2}+\frac1{\hat{r}}\frac{\partial}{\partial\hat{r}}\right)^2$$
- 71
7
votes
2
answers
1k
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
...
- 523
7
votes
2
answers
390
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.
...
- 2,073
7
votes
1
answer
464
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 ...
