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38
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 ...
34
votes
2answers
2k 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 ...
18
votes
11answers
1k 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 ...
17
votes
3answers
722 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 ...
17
votes
2answers
318 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 ...
16
votes
5answers
2k 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 ...
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 ...
11
votes
3answers
395 views

Replace operators

/. can be used to replace variables but how can one replace operators. For example in a * b, ...
10
votes
9answers
582 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? ...
10
votes
1answer
127 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: ...
9
votes
6answers
419 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: ...
9
votes
2answers
282 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 ...
8
votes
3answers
2k 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 ...
8
votes
3answers
335 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 ...
8
votes
1answer
1k 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 ...
7
votes
2answers
214 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 ...
6
votes
2answers
898 views

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 ...
6
votes
1answer
381 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 ...
5
votes
3answers
274 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, ...
5
votes
2answers
236 views

Associativity of `/@` [duplicate]

Why are the following not equivalent: Map[Line, Map[(Print[#]; #) &, {{{2, 1}, {1, 1}}, {{-2, 1}, {3, 1}}}]] which produces ...
5
votes
3answers
350 views

ComplexInfinity/Indeterminate error when evaluating derivative

Motivation: I want to find the coefficients for the polynomial that is obtained when one adds together the first $n$ natural numbers to the power of $a$; that is, when you consider $1^{a} + 2^{a} + ...
5
votes
4answers
351 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: ...
5
votes
3answers
725 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 ...
5
votes
2answers
3k 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 ...
5
votes
2answers
1k 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: a_$ \otimes $b_:=a.b-b.a and this works fine. Then I want to ...
5
votes
1answer
95 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 ...
5
votes
0answers
53 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 ...
5
votes
0answers
95 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 ...
4
votes
2answers
247 views

Question on operator: // N

I've seen a notebook with the following: ...
4
votes
2answers
208 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. ...
4
votes
1answer
122 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
270 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 ...
4
votes
2answers
325 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 ...
4
votes
1answer
101 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 ...
4
votes
0answers
86 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
0answers
125 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 ...
3
votes
2answers
488 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 ...
3
votes
2answers
65 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 ...
3
votes
1answer
117 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 ...
3
votes
1answer
299 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: $L(u(x))=\int_0^1 \frac{1}{2} (u'(x))^2 dx$ ...
3
votes
1answer
155 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 ...
3
votes
1answer
304 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 ...
3
votes
1answer
121 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 ...
3
votes
1answer
161 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 ...
3
votes
1answer
72 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 ...
2
votes
2answers
161 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 ...
2
votes
2answers
474 views

Replacing values of a function

I have recently starting using Mathematica and have recently come to what seems as an impasse in my understanding of the language. If this is too "tell me how to do it" I would certainly understand. ...
2
votes
2answers
57 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 ...
2
votes
1answer
33 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 ...