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

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1
vote
4answers
2k views

Solve trigonometric equation

I'm looking for a solution (graphic, numeric or analytic) for a function of the form: $$a^2\tanh(x)=\tan(ax),\quad a ≥ 1,\ x > 0$$ preferably using Mathematica. Any advice?
6
votes
5answers
262 views

How to nest my own “times” function to get powers

I have a "times" function. I'd like to create a power function using it. It should look like this for an 6th power: ...
1
vote
2answers
92 views

Expressions containing globally undefined symbols inside a function where they are defined

Consider the following code. f[a_,b_]:=x; Clear[a,b]; x=a+b; f[1,2] It returns a+b. However, from a certain viewpoint, one ...
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 ...
25
votes
1answer
255 views

What does Internal`InheritedBlock do?

What does the function Internal`InheritedBlock do? How is it different from the regular Block?
11
votes
4answers
958 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
807 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
203 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
507 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
3k 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?
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 ...
11
votes
1answer
400 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, ...
7
votes
4answers
698 views

How make f[{x,y}] evaluate as f[x,y]? [duplicate]

I frequently encounter the situation where I have a function of two real variables defined, e.g.: f[x_, y_] := 9 - x^2 - y^2 But then I need to feed into ...
4
votes
3answers
658 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 ...
10
votes
3answers
328 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
547 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
473 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: ...
9
votes
2answers
378 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
527 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
361 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
339 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
562 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
268 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
891 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
269 views

What are Root objects with multiple polynomials?

In Mathematica 9 a new flavor of Root object with multiple polynomials was introduced. For example, ...
14
votes
3answers
829 views

Fitting ellipse to 5 given points on the plane

Five points are required to define a unique ellipse. An ellipse has five degrees of freedom: the $x$ and $y$ coordinates of each focus, and the sum of the distance from each focus to a point on the ...
13
votes
1answer
16k 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 ...
10
votes
5answers
513 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 ...
22
votes
2answers
464 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 ...
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
393 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: ...
9
votes
1answer
552 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 ...
11
votes
2answers
833 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
231 views
15
votes
2answers
863 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
369 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
550 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
328 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 ...
9
votes
3answers
683 views

Difference between @ and @@

I am confused by the commands @ and @@. From the documentation, I learnt that @@ is the ...
8
votes
2answers
299 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 ...
3
votes
2answers
2k views

Define a color function using Piecewise

How can I define a ColorFunction for my ContourPlot using Piecewise? For example after ...
15
votes
2answers
241 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
302 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
934 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
225 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
323 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
318 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 ...