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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1answer
338 views

How to define a pure function with a Module?

I was not able to use a self defined (using Module and For loops) piecewise function to fit data. It seems that the problem is that I have to define a pure function. I would like to learn how to ...
1
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0answers
45 views

Using anonymous functions instead of module or block. Bad idea? [duplicate]

Here is an example function which returns True if a point p is on an (open) line segment (A, B) assuming that Orientation[A, p, B] returns 0 if the three points are collinear: ...
3
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2answers
122 views

How to apply multiple/complicated requirements for a pattern in a function input [duplicate]

In this question. I suggested that to test whether the input of a function was a matrix of numbers one could create the following test: ...
0
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1answer
76 views

Have the kernel load a user-defined function by default [duplicate]

I wrote a very simple function that I would like to act as if it were one of the default functions that came with Mathematica, so that you don't have to load or import any package before you make use ...
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0answers
54 views

Question regarding function definition overloading / argument passing test [duplicate]

It is possible to define function dependently to passed argument type or condition this argument fulfills (somewhat like overloading): ...
38
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5answers
1k views

Why is there no PositionFunction in Mathematica?

Too often I have seen the programs of inexperienced users greatly slowed by using Position in an iterative fashion, when far faster would have been to compute a ...
5
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3answers
248 views

Applying a function with the HoldAll attribute inside NestList

I'm trying to write an update function, which can be applied to a list and then to NestList it. As the function has to manipulate the given variable I figured I ...
4
votes
2answers
590 views

Write a function that returns the logarithmic derivative

How can we write a function that if we input an expression f, it returns the log derivative $\frac{1}{f} \frac{df}{dx}$. We have to use a conditional or pattern test so that the function accepts any ...
36
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2answers
1k views

Variable naming changes everything

Bug fixed in 10.0.0 I am having a rather unusual problem I do not understand with Mathematica where renaming one of the variables of my function causes the function to stop "working". Here is the ...
6
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2answers
2k views

How to define a polynomial/function from an array of coefficients?

I have the coefficients of my desired polynomial in an array CoefArr (I'm new to mathematica, so I think of everything as arrays, it is actually a list I believe) starting with the constant at index ...
2
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2answers
127 views

Putting a matrix inside function

I want to fit a function to some data and inside the function there's a list here's my data ...
0
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2answers
900 views

How can I define a function which is the sum of other functions?

I have a function which is summation of another function over different i,j iterators. U[r] = Sum[V[r, i, j], {i, 1, 5}, {j, 6, 10}] and ...
4
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3answers
175 views

How can I combine two Pick expressions into one?

I want to speed up my code, i.e., replace Select by Pick. I think using two Pick ...
2
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1answer
1k views
2
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3answers
296 views

Map several functions in one routine

I have several functions, let's assume they are: func1[x_]=x; func2[x_]=3*x-5; func3[x_]=0.1*x^2; and a lot more like these. For each and every one of these I ...
5
votes
4answers
553 views

Any rule of thumb for converting a simple mathematical expression into a pure function?

By simple mathematical expression I mean one with a few functions and few variables copied into MMA in a mechanical way from a math book. For example this one, giving the distance between two points ...
7
votes
4answers
581 views

How can I shorten this code to rotate a line segment around its center?

I have a list of line segments stored in the form: { {{x11,y11},{x12,y12}} , {{x21,y21},{x22,y22}} , ... , {{xn1,yn1},{xn2,yn2}} } Now I want to rotate all of ...
0
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2answers
1k views

Why function cannot be defined inside For loop? [closed]

I have a following code (which is simplified version of what I am doing): For[i = 1, i <= 5, i++, f[x_] := Sin[x]^2 Print[{i, f[i]}] ] And the question ...
2
votes
2answers
108 views

Rising Recursion Relationships

Lets say I want to compute the following function in mathematica: $G[n,k]=G[n+1,k-1] + G[n+2,k-2]$ where I know that $G[n,0]=n$ and $G[n,1]=n^2$. So, for example, $G[3,2]=G[4,1]+G[5,0]=4^2+5$ or, ...
0
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1answer
109 views

Function giving negative value when it should be positive [closed]

I am trying to evaluate $$\displaystyle J=A\sum_{k=0}^{n-2}(-1)^k{n-2 \choose k}B^{n-2-k}\left(\frac{C_1}{k+n}-\frac{C_2}{k+n+1}+\frac{C_3}{k+n+2}-\frac{2}{k+n+3}\right)$$ in Mathematica as a function ...
0
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2answers
832 views

Fast Autocorrelation Computation

I want to compute the Autocorrelation Function (ACF) of a data table with $10^6$ entries. I know that there is a built-in function in Mathematica for that, but because I do not know how exactly it is ...
12
votes
3answers
589 views

Pass by reference for an option argument

Pass by reference can be faked by using HoldAll or something similar in the definition of a "Function". But can pass by reference be faked for symbols passed as ...
8
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1answer
1k views

Stereographic Projection

Say I want to represent points of the complex plane in the sphere $\Bbb S^2$ using stereographic projection. That is, the Riemann sphere: Specifically, it would be nice to be able to: Given the ...
32
votes
1answer
646 views

How can I make threading more flexible?

Threading automatically with Listable functions requires the argument expressions to have the same length (or for one of them to be atomic). For nested lists the ...
21
votes
3answers
897 views

How to program a F::argx message?

How useful is it to program a user-built function in a package to produce a red warning message F::argx if you give the wrong number of arguments to that function? ...
1
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1answer
103 views

NMaxmize with a list of variables

I want to use NMaximize to find the maximum value of a function with multiple variables. The problem is I would like to set this up so the number of variables is only decided when the function sees ...
4
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2answers
98 views

Creating functions from output of other calculations

Apologies in advance if the title is vague, I'm not really sure what to call this. I have a function (call it 'foo') that generates a largeish polynomial, and it is natural to make the variables be ...
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1answer
179 views

Finding coefficients that make certain functional expression vanishing

My problem is to find a procedure that gives coefficients which make certain functional expression vanishing. For example if I have a polynomial $P(x)$ of one variable $x$ given by $P(x)=a_0+a_1 ...
42
votes
10answers
8k views

Generating a Sierpinski carpet

I am trying to draw a Sierpinski_carpet. I have code that works, but I think there is a more elegant way to do than my way. Maybe I couls use Tuples or ...
8
votes
2answers
3k views

Gram-Schmidt Process for Polynomials

I want to implement the Gram Schimdt procedure to the vector space of polynomials of degree up to 5, i.e. I want to find an orthogonal basis from the set of vectors $v=(1,x,x^2,x^3,x^4,x^5)$. The ...
0
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1answer
90 views

Given a sequence of expressions, how can I convert them all into functions?

I have a sequence of expressions 1, x, x^2, ..., x^5 I want to define a sequence of functions out of it, what should I do? Namely I want to define a vector of ...
12
votes
4answers
471 views

How to pass a list of arguments into HoldAll

I have a list of arguments (which in reality is lengthy): arguments = {a, b, c} arguments2 = {a_, b_, c_} f[Sequence@@arguments2] := a + b + c Note: It seems ...
9
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2answers
448 views

How can I get the right hand side of a delayed expression?

Imagine there is a given function f, defined with SetDelayed, say f[x_] := Sin[x]^2 + Cos[x]^2. Is it possible to get rhs of ...
4
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2answers
197 views

How to only work on sublists with non-zero (or positive) values

i have a large compositional dataset which contains non-zero and zero values. here is a sample: ...
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1answer
126 views

Dynamically show a specific number of the fractional part's digits

What is the fastest way to cut off all n z digits of the fractional part of a real number? (For example 12390.20934230) I came up with this so far: ...
13
votes
3answers
1k views

What is Mathematica's equivalent to MATLAB's filter function?

The MATLAB code filter(0.5,[1, -0.5], [1:10]) is equivalent to Rest@FoldList[(#1 + #2)/2. &, 0, Range[10]] I don't ...
8
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2answers
168 views

Possible to scope an anonymous function within Module?

This is my first question. I'm fairly new to Mathematica and completely new to SE, so I apologize if this question is trivial. I'm working on a problem that requires a function to be redefined ...
2
votes
3answers
361 views

Defining a function to determine when convergence is guaranteed

I'm investigating how many iterations are needed for a particular orbit to reach a fixed point of a function. Since I have many functions to test, I want to define a function in Mathematica that will ...
3
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2answers
487 views

Why does the first derivative of a piecewise continuous function have discontinuities?

I have this piecewise continuous function which is also continuously differentiable over time : ...
0
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1answer
127 views

Strange function definition result [duplicate]

I'm relatively new to Mathematica, and I'm trying to define a function f(k) that would do the following: For any positive integer $k$, a finite sequence $a_i$ of fractions $\frac{x_i}{y_i}$ is ...
2
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2answers
376 views
34
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4answers
819 views

Enforcing correct variable bindings and avoiding renamings for conflicting variables in nested scoping constructs

Using global variables the following turns an "expression" into a Function: expr = 2 x; Function[x, Evaluate[expr]] Of course ...
5
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1answer
230 views

How to find the name of the current function

I would like to know the name of the current function from within that function. For example, consider the following code ...
1
vote
1answer
266 views

Function definition and delayed assignment

I need to define the following function MyWavelet[n_]["PrimalLowpass", prec_ : MachinePrecision] := Table[(-1)^(j - 1) h[[2*n - j]], {j, 0, 2*n - 1}] which ...
4
votes
4answers
363 views

Differentiating space curves

I'm trying to do some very basic differential geometry of space curves. For example, a space curve $\gamma:\mathbb R\to\mathbb R^3$ has unit tangent and normal vectors given by ...
2
votes
4answers
3k views

How to write a differential operator in Mathematica

I have a very basic question. I am trying to code the LHS of the differential equation: ...
3
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1answer
161 views

Using NestWhileList to determine smallest prime value in series

I have a function recursively defined as follows: $a_{n+1}-1=(a_n-1)\times lpf(a_n)$, whe $lpf(x)$ is the least prime factor of $x$. Now, given an initial value of $a_0$, I would like to find the ...
7
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1answer
3k views

Module with “local functions”

I am trying to use a Module having "local functions", i.e., those which I need to define only inside this module. So I tried this: ...
5
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3answers
235 views

Creating a nonperiodic function in mathematica

I want to create a non-periodic square wave with values of 1 and -1(not necessarily alternating). For e.g. I want to convert an arbitrary array like {1,-1,-1,1,-1,1,-1} into a function. I tried ...
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1answer
80 views

Confirming the existence of a function related to a matrix

Is it possible to get an answer to the following question in Mathematica? Let $M$ be a $n$ by $n$ matrix, is there a function $m:\mathbb{N}\times \mathbb{N}\rightarrow \mathbb{Z}$ such that ...