# Tagged Questions

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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3answers
93 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 ...
2answers
116 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 ...
2answers
385 views

### Variable naming changes everything

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 example of the code ...
2answers
76 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 ...
2answers
65 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 ...
2answers
88 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 ...
3answers
131 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 ...
1answer
77 views

### Mathematica plots a discontinuity in piecewise function that does not exist [duplicate]

I have the following function defined: ...
3answers
96 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 ...
4answers
220 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 ...
4answers
257 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 ...
2answers
145 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 ...
0answers
64 views

### How can I get tabular output for the results of my simulation? [closed]

I have code that simulates a simple Markov Chain and looks like this: ...
1answer
56 views

### User-defined NormFunction in FindFit -

I would like to use a different Norm instead of a p-Norm in FindFit (Mathematica 9). For example, instead of using Sqrt[Sum[(x_model - x_data)^2]] I'd like to use Sum[x_model/x_data]. I can ...
2answers
66 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, ...
1answer
65 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 ...
2answers
125 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 ...
3answers
127 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 ...
1answer
155 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 ...
1answer
127 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 ...
1answer
55 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 ...
2answers
73 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 ...
0answers
44 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 ...
9answers
6k 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 ...
2answers
231 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 ...
1answer
75 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 ...
4answers
134 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 ...
2answers
152 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 ...
1answer
190 views

### How can I define a Step-Wise function in Mathematica (Not using Heaviside Step Function)? [closed]

I need to define a function, which has very different behaviour in different regions. There are about 13 different regions. A sample of my function is the foloowing table: I want to define it as a ...
2answers
92 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: ...
1answer
66 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: ...
3answers
376 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 ...
1answer
63 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 ...
3answers
104 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 ...
1answer
149 views

### Why does the first derivative of a piecewise continuous function turns out with discontinuities?

I have this piecewise continuous function which is also continuously differentiable over time : ...
1answer
74 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 ...
2answers
87 views

### Defining a function by pieces using list of interpolated functions in order to use FindRoot

I have two lists with the interpolated functions ...
4answers
237 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 ...
1answer
127 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 ...
0answers
73 views

### How can I obtain the function described by given set of central moments?

I want to investigate how my function P behaves with different probability functions rho as input variables. This means ...
1answer
102 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 ...
4answers
202 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 ...
4answers
277 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: ...
1answer
78 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 ...
1answer
108 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: ...
3answers
94 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 ...
1answer
66 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 ...
1answer
77 views

### How could we define a function recursively?

Let us first consider the constructon of the following simple iteration ...
1answer
111 views

### Downvalues vs. Scoping for Functions

Regarding my recent question on using a default value for a function argument when a pattern was not met yielded some interesting answers, but the general consensus was "Yes this can be done, but ...
1answer
160 views

### How do I make function A create and return function B?

My basic need is I have to take lots of data and other information and assemble it into a function (static parameters). I then need to call the function many times for numerical results for many ...
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