Questions tagged [function-construction]

For questions on writing functions (pure or using Set/SetDelayed) for any purpose, including the features that may be incorporated in those functions, such as options, patterns and conditions.

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Passing input arguments to a function

I want to pass input arguments to a function In python I do, def solution3d(a, b, c, d): I looked at the documentation here https://reference.wolfram.com/language/...
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What are some ways to overload Min in order for it to work with user defined expressions?

I have defined size to work with discrete size labels: ...
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37 views

Defined function keeps the variable

I'm a beginner at Mathematica, and I have a problem finding the roots of a function for a specific variable (using Jens' findAllRoots function). Due to the nature of my problem, I need to compute ...
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2answers
64 views
+100

Better way to rename arguments to a functional form so that duplicate arguments are sequentially enumerated

I need to modify expressions that such as f[w, w, a, y, x, a, x, a] into f[w1, w2, a1, y, x1, a2, x2, a3]. In short, I have ...
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Normalized functions

I'm looking for a smart way to define normalized functions. I usually write f[x_] := f[x] = A Sin[x]/x; Then I integrate the function ...
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How to define some functions automatically?

I want to use Gauss-Seidel iteration to solve this problem. $$\left\{\begin{array}{l} 8 x_{1}-3 x_{2}+2 x_{3}=20 \\ 4 x_{1}+11 x_{2}-x_{3}=33 \\ 6 x_{1}+3 x_{2}+12 x_{3}=36 \end{array}\right.$$ ...
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2answers
74 views

How can I fix my Simpson's rule integration code?

I was tasked with writing a function on Mathematica similar to NIntegrate, but that uses the Composite Simpson's Rule as its method for doing the calculation. The ...
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1answer
87 views

How to find formula from a table?

I recently started using mathematica for simple tasks like simplifying etc. First of all let me say if this breaks any rules I apologize since I'm a novice in using this and I'll remove the question. ...
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Plot Expression returned from Function

Suppose we have a function that does something with its parameters, and then returns an expression containing an equality. I want to then use that expression in (Contour)Plot to visualize it. The ...
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2answers
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Procedures on Functions That Remember Values They Have Found

This one can not remember the value. Code 1. f[x_] := f[x] = f[x - 1] + f[x - 2]; f[1] = f[2] = 1; f[5] ?f The 2nd one can keep the value it finds. Code 2. ...
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2answers
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A table of plots of different functions

I want to create a Table of individual Plots where the table's index-variable is a series of functions. For example: Take two ...
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1answer
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Controlling Expansion of Functions

Suppose I had the following definitions const /: N[const] = 1 / Pi^2; f /: N[f[x_]] := const / x^2; g /: N[g[x_]] := Pi * Sqrt[f[x]] * x^2; Now for this example, ...
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Good Practice in Defining Numeric Functions

I would like to define numeric functions for Mathematica such that they behave 'nicely' in much the same way as the built-in numeric functions do. For example, consider the following numerical ...
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1answer
112 views

Extract Jacobian from FindRoot?

I have to solve a system of fixed point equations and then calculate the eigenvalues of the Jacobian at the fixed point. There are about 50 equations with 50 variables and they contain a lot of ...
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57 views

How to take limits in Fourier series?

I have a Fourier series which produces an impulse train of period j+1. In principle, it is given by ...
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1answer
44 views

How can I define a function using ArrayFlatten without using SetDelayed?

I created a matrix F2 using SparseArray and ArrayFlatten as follows: ...
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functions with mutiple variables and lines of calculations

I am almost a new user of Mathematica, my question is that how can I have something like a function or exactly a function that for example gets two inputs (a) and (b), then calculates a+b and a*b. In ...
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29 views

Problem with FormulaLookup and FormulaData

I'm not getting an answer when I type either: FormulaLookup["BinomialDistribution"] or ...
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1answer
53 views

Can't make this “If” clause work

I am writing a code that creates a population with a probability to die for each citizen. They all start with some age, and after each application of the function, it either kills a person or adds +1 ...
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1answer
64 views

How should I define the Cayley transform?

I am a beginner to Mathematica. I am trying to define a function which would evalute the Cayley matrix transform, namely taking a matrix $M$ such that $I + M$ is invertible to $(I-M)(I+M)^{-1}$. I ...
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1answer
31 views

Define a function of multiple arguments at a given point

Trivia I am using Taylor series expansions to solve a system of PDEs for a number of functions $f_1(z, \phi), f_2(z, \phi) ...$ The expansions are generated by ...
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Defining an mathematical operator

I'm trying to learn mathematica to use in my thesis. I have basic problems with definitions, calculations etc. Let me ask a question. I want to define anti derivative operator and derivative operator, ...
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1answer
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General definitions of deeply nested functions without SetDelayed, “UpUpValues”

I'd like to assign an "UpUpValue" in a way generalized to any nested head surrounding the value for which the UpUpValue would be defined. That is, if a function ...
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2answers
86 views

Symbolic properties of Re and Im

I want to define a function f such that f[x] is real whenever x is real. So I define ...
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1answer
51 views

How to include Do loop inside the With statement?

I wanted to create a matrix by following way: ...
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2answers
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Defining a function of a function with arbitrary variable name

Is there a way to pass a function into a function you write such that the function can be of an arbitrary variable? What I want to do is something like... ...
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3answers
74 views

Strange Behavior of Compile[] inside With[]

Consider, in the examples below, the difference between defining $n$ as a global variable or as an argument to function comp[], which includes a compiled function ...
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1answer
119 views

How can I get the progressive application of list of rules?

I have a very long list of rules, and using this list of rules I want to see how some elements evolve as I successively apply the next rules on the previous rule. Here is the simpler version of my ...
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Is there a function to convert a trigonmetric expression to an algebraic expression suitable for ComplexPlot?

According to H. A Priesley: "both $cosθ$ and $sinθ$ can be written as simple algebraic functions of $z$": $cosθ =\frac{1}{2} (z + \frac{1}{z}) \tag1$ $sinθ =\frac{1}{2i} (z − \frac{1}{z})\...
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1answer
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How to get smooth square root of complex valued function?

Let $f(x)$ be smooth complex valued function with real argument $x\in[0,1]$. I want to get square root $g(x)=\pm\sqrt{f(x)}$ where the sign is chosen so that g(x) is smooth. How can I do that? In ...
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Functions of several variables composition

If we have two functions $G,F:\mathbb R^2\to\mathbb R^2$ then the mechanism $F\circ G(x,y)=F(G(x,y))$ gives us a new map $F\circ G:\mathbb R^2\to\mathbb R^2$ called its composition. In a "...
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3answers
387 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 ...
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How to define tensors similar to Riemann tensor in xAct xTensor xTras

I'm working on a project where we deal with objects very similar to Riemann tensor. In fact they are Christoffel symbols for higher spins. I'm using xTras for modeling problems in wolfram mathematica. ...
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1answer
119 views

How can I emulate Orderless attribute?

Suppose I want an expression to automatically sort its arguments. This can be done via SetAttributes[f, Orderless] f[3, 2, 1] (*output is f[1, 2, 3]*) Just as an ...
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4answers
196 views

How to use each replacement only once in a list of replacements

I have a list of replacements and some list they are acting on. However, some RHS of the replacements rules are identical (the LHS is not). I want to use those rules one after another (perhaps cycling ...
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How to find the Inverse of numeric Function that was created from NDSolve

I'm a newbie to Mathematica and i do have a simple question. I have a function H that was created numerically as solution form NDSolve (like H(R)), and i'm trying to create the Inverse function R(H) ...
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1answer
48 views

How do I introduce an assumption when defining a piecewise function?

Define m as an integer. I want to specify a Piecewise function f[x,n] that takes value ...
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0answers
63 views

Prime Matrix with determinant of powers $2^x$

Mathematica has commands for finding prime matrices, for example, here is a matrix with randoms in the range $<100$: RandomPrime[100, {3, 3}] This $2 \times 2$ ...
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1answer
32 views

Method to determine a set contains rational whose denominator is 2

Suppose S is a set of (complex) numbers. I want to know whether S contains rational whose denominator is 2. For example, when S={1,2,3,4,1/4}, return "False". when S={1,2,3,1/4,-5/2}, return ...
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2answers
97 views

Shortest way to take first half of list and/or split list into n parts

What is the shortest way to take the first half of a list? Or to split a list into n equal parts? If the length is not 0 mod n, I would prefer to leave out the left ...
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3answers
172 views

How to write a custom function to judge whether a bivariate function is differentiable at a certain point?

We know that the necessary and sufficient conditions for a multivariate function to be differentiable at a certain point are complicated: Suppose the function $z = f (x_ 1, x_ 2, ..., x_n) $ is ...
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1answer
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Defining an iterated differential operator with compositions

I'm a bit new to Mathematica so this question might be a bit basic. Still, I could not find an answer. I wish to define a symbolic differential operator. Currently, I do something like the following: <...
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2answers
112 views

How to program a situation like the following in mathematics and generalize the process to other configurations?

Distribute the numbers from 1 to 10(view image) so that the sum of each row and each column is the same and a) the maximum possible b) the minimum possible (I put it from 1 to 10 for ease) I know it ...
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1answer
65 views

Tensorial functions

I need to solve a system of ODEs for a function that has a complicated tensorial structure. I believe that NDSolve can deal with this scenario since version 9. Yet, ...
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2answers
129 views

How does `DirichletConvolve` relate to Dirichlet convolution?

Mathematica's Help documentation on DirichletConvolve is economical, to say the least. It claims the function "gives the Dirichlet convolution of the ...
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1answer
47 views

Difference Between Set and Pattern in Mathematica

Ok, sorry if this is too basic, I'm somewhat new to Mathematica, but I keep making errors in my code because I'm not understanding the namespaces. So this part I thought I understood. ...
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1answer
55 views

NumericQ and unknown number of variable in a module-block

I have the following problem I want to address in an elegant way. I have a function of many variables f[x, y, z,...] I want to find the minimum with ...
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2answers
57 views

Better way for constant expressions in functions than storing as global variables?

For example, I wrote a function like this: inversions[list_] := Complement[ Subsets[{1, 2, 3, 8, 4, 7, 6, 5}, {2}], Subsets[list, {2}] ] But as you see, ...
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1answer
174 views

Having difficulty plotting linear system of equations

I have a function eqsfromMatrix[..] that generates linear equations from a matrix which I would like to plot but there seems to be no direct way to plot them. I ...
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1answer
46 views

Cannot get conditional Take[…] from List[…] to work inside a user-defined function

Abstract I have a function eqsfromMatrix[...] that does exactly as it sounds. It returns a list of equations given matrix m for ...

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