Questions about the use of built-in Mathematica functions, including pure functions.

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31
votes
2answers
1k 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 ...
11
votes
4answers
930 views

Pure Functions with Lists as arguments

Assuming I have two function: example 1: add[{x_, y_, z_}] := x + y - z add[{1, 3, 5}] If use pure function,I know I can write it as : ...
9
votes
3answers
3k views

How can I differentiate Numerically?

Mathematica has two ways to integrate: Integrate and NIntegrate. But what about D? ...
28
votes
2answers
800 views

Is there a name for #1@#2&?

Why does the pure function # @ #2 & have no name? I'm asking because sometimes I find inelegant to write expressions like ...
19
votes
1answer
197 views

How to get Cases to wrap results in an arbitrary head?

A number of functions provide for results to be wrapped in an arbitrary head. This is very important in cases where the results should not be evaluated. Take ...
11
votes
1answer
479 views

user defined functions, how to save them for future use?

I need certain user defined functions over and over. I was wondering how can I define and where and how to save them such that each time I start a notebook, these functions are available and need not ...
16
votes
2answers
2k views

Is there an equivalent to MATLAB's linspace? [duplicate]

Does Mathematica have an equivalent to Matlab's linspace? I want to make a list with "start", "stop" and "number of points". What is the neatest way of doing this?
16
votes
2answers
1k views

Sum or Product with Exclusions

Is there a built-in feature for handling things like: $$\sum_{i=0}_{i\ne j}^n\frac{a-a_i}{a_i-a_j}$$ and $$\prod_{i=0}_{i\ne j}^n\frac{a-a_i}{a_i-a_j}$$ or should I work out some sort of ...
15
votes
1answer
1k views

Error checking and trapping techniques with Throw and Catch

Mathematica provides several mechanisms for checking arguments and trapping errors in a function definition. Typical methods are : Definitions with argument patterns, definitions with ...
10
votes
1answer
374 views

Two ways of map a function on the list: Which one is faster?

There are 2 ways to make a function listable on the list: Use Map or use SetAttributes. My question is, which one is faster, ...
10
votes
3answers
319 views

How to “ignore” an element of Map or MapIndexed

Say I have some function that I'm applying every element in a list to... if that element matches some criteria: ...
6
votes
4answers
531 views

Function argument to default under certain condition

Inspired by this and this question (and how I handle this in practice), what is the best way to default a function value when a certain condition is met? For example, if a function is defined as: ...
21
votes
3answers
467 views

Is there a bug in Pick?

I wanted to use the Pick function with a condition. But there seems to be an issue here. Take a look at this: ...
10
votes
5answers
354 views

Transform a list of functions to a composition

How do I apply a list of functions in a nested way? Example: functionList = {f1,f2,f3} RequiredCommand[functionList,Pi] such that the required command returns ...
9
votes
2answers
364 views

Nest , Fold … is there an extension for more than 2 arguments?

Fold is an extension of Nest for 2 arguments. How does one extend this concept to multiple arguments. Here is a trivial example: ...
7
votes
4answers
480 views

Solving $L=\frac{3}{2} \sqrt{4 \pi ^2 A^2+W^2}-\frac{\sqrt{5 W \sqrt{4 \pi ^2 A^2+W^2}+6 \pi ^2 A^2+3 W^2}}{\sqrt{2}}+\frac{3 W}{2}$ for $W$

When I solve the aforementioned equation for $W$ or $A$ on Mathematica I get a long and ugly equation in return, namely one of the solutions for $W$ is: (attempt to read at your own health) ...
-1
votes
1answer
337 views

Gamma Incomplete Function representation in Mathematica and Matlab

I am confused about Gamma Incomplete function calculation in Mathematica and MatLab: For example, in Mathematica: Gamma[5,3] = 19.56 But in MatLab: ...
8
votes
1answer
334 views

ReplaceAll[] and Limit[] don't give correct results for this expression under extreme variables [duplicate]

Possible Duplicate: Funny behaviour when plotting a polynomial of high degree and large coefficients 1/x^2 + (3 + x)/(6 (1 - Exp[x] + x)) ——This is a ...
3
votes
4answers
491 views

How to completely delete the head of a function expression

Is there any way to completely remove the head of an expression function? For example, how would I remove the head Cos from ...
3
votes
1answer
261 views

NestList with a list inside?

I'm new to Mathematica, and was looking for more efficient ways to implement the Do loop below. a, ...
3
votes
2answers
818 views

Function returning Null along with other unexpected expressions

When I use some function, at the end along with the output I get some NULLs returned that I don't understand the reason for and are highly undesirable. For example, when I define the reversal of list ...
15
votes
2answers
255 views

What are Root objects with multiple polynomials?

In Mathematica 9 a new flavor of Root object with multiple polynomials was introduced. For example, ...
24
votes
1answer
245 views

What does Internal`InheritedBlock do?

What does the function Internal`InheritedBlock do? How is it different from the regular Block?
10
votes
5answers
506 views

How to find first list element that differs from average of N previous elements by more than a given amount?

Given a list of real numbers, I need to write a function that returns the value of the first element in the list that differs from the mean of the previous $N$ elements by greater than $P$ standard ...
16
votes
4answers
6k views

Finding Limits in several variables

Is there a way to find a limit of a multivariable function, like $$\lim_{(x,y)\to (0,0)} f(x,y)$$ with Mathematica? When $f$ is continuous, we can use $$\lim_{(x,y)\to (0,0)} ...
15
votes
1answer
385 views

How to represent a continuous monotonic phase of Airy functions?

Note: In this question I am concerned only with real-valued variables and functions. DLMF, §9.8 Airy Functions, Modulus and Phase, formula $9.8.4$ defines the phase of Airy functions: ...
13
votes
1answer
15k views

How to express trigonometric equation in terms of of given trigonometric function?

How can I express a trigonometric equation / identity in terms of a given trigonometric function? using following trigonometric identities ...
9
votes
1answer
524 views

What is the difference between prefix/postfix notations and map?

I am new to Mathematica and just experimenting with the different programming constructs. I have been looking at Map and how to evaluate a function for a list of ...
21
votes
2answers
457 views

Why is Query so much slower than Part?

Time for another of these(1),(2) as yet another new-in-10 function appears to have poor performance compared to older alternatives. This time: Query appears to be ...
11
votes
2answers
797 views

Growth of functions

Does somebody know if Mathematica can be used to calculate the growth of functions, that is in Big O, Theta, and Omega and find proper $n_{0}$ and $c_{1}$, $c_{2}$ respectively?
9
votes
3answers
223 views
4
votes
3answers
623 views

Simplify function notation

I have some calculations with arbitrary functions. In the output, Mathematica always shows the functions with its arguments. I would like to tidy the notation a bit, by hiding the arguments in the ...
15
votes
2answers
838 views

Why do certain values in ArcSin not fully evaluate?

This is a continuation of: Why do certain fractional values in TriangleWave not evaluate? The analysis by R.M and rasher revealed that problem to reduce to the behavior of: ...
14
votes
5answers
365 views

Partitioning a list of numbers the Mathematica way

I have two sorted lists, one list will be called the "fences" and the other the "values" Fences could be: $\{1, 5, 9, 14\}$ Values could be $\{-1, 1, 3, 4, 6, 9, 10, 13, 14, 15\}$ I want to ...
13
votes
11answers
1k views

Divide all but the maximal element in a list by 10?

I have a list of numerical data, and I want to write a program that will keep the maximum as it is, but reduce the rest by certain factor (such as 10). For example: ...
11
votes
4answers
513 views

Plot the minimum of a list of functions

This is my first question on any stack-exchange site and I'm also very new to using Mathematica software so please excuse/correct me if I mess up. I would like to take a list of functions of a single ...
11
votes
4answers
324 views

Using With to scope over pure functions

Consider this example: given an option for a function func as "x" :> (a&), how can one assign different values to ...
8
votes
3answers
631 views

Difference between @ and @@

I am confused by the commands @ and @@. From the documentation, I learnt that @@ is the ...
8
votes
2answers
265 views

Tally repeated evaluation of function

How can I tally the result of repeated evaluation of a function? n=100000; f[]:=RandomInteger[{1, 4}] Tally@Table[f[], {n}] When ...
5
votes
3answers
1k views

Make a differentiable smooth sawtooth waveform

So, I am trying to understand the effect of sawtooth waveform on a mechanical system model. For example, a system of a plate and a box on it. And then we try to oscillate the plate. In order to do ...
15
votes
2answers
236 views

A bug in Commonest in version 10

Bug introduced in 10.0.0 and fixed in 10.0.2 m_goldberg demonstrated that in Mathematica 10 Commonest does not behave as the documentation indicates that it ...
10
votes
1answer
288 views

Get the name of a symbol passed to a function

I'm trying to get the name of a symbol passed to a function with this: f[x_] := {SymbolName[x], x} SetAttributes[f, HoldFirst] x = 5; f[x] But ...
10
votes
2answers
876 views

Determine whether some expression contains a given symbol

Given a symbol t and an expression expr, how can I determine whether or not the symbol t ...
10
votes
1answer
224 views

How to pass composite function list to SortBy?

In order to sort alphanumeric-as-string data of the form {"T3", "T14", "T1", "E2"}, so that "T14" comes after ...
9
votes
2answers
322 views

Define Log so that negative reals evaluate on lower edge of branch

I need to get Mathematica to evaluate the logarithm of a negative real number using the lower branch instead of the upper branch, so that while ...
7
votes
3answers
316 views

Why can't D[] be used in place here? [duplicate]

Possible Duplicate: General::ivar is not a valid variable when plotting - what actually causes this and how to avoid it? Beginner question: Why can't I use ...
6
votes
3answers
229 views

How to rename a built-in function?

I want a built-in function renamed without loss of any properties, I want the shorter name to appear in all results and to be recognized as input. Is it possible?
5
votes
2answers
938 views

How to find the non-differentiable point(s) of a given continuous function?

For example, the non-differentiable point of the function $f(x)=|x|$ is at $x=0$. How to find the non-differentiable points of a continuous function that is defined numerically?
4
votes
0answers
93 views

Make Mathematica show function template's arguments in different lines (i.e. in column) by default?

I feel a bit uncomfortable with Mathematica 10's layout. I mean, I'm impressed how powerful functional programming can be and so on, but it's me or those programs are often just a bunch of nested ...
3
votes
2answers
238 views

Selecting for 2D points that are within a threshold distance of an upper- and lower-bound number of points

I have a very large set of 2D points: numberOf2DPoints = 10^6; pointList = RandomReal[{0, 1000}, {numberOf2DPoints, 2}]; I'd like to find a way to quickly ...