Questions tagged [faq]

Frequently Asked Question – a tag for original questions which have a multitude of duplicates

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455
votes
37answers
100k views

What are the most common pitfalls awaiting new users?

As you may already know, Mathematica is a wonderful piece of software. However, it has a few characteristics that tend to confuse new (and sometimes not-so-new) users. That can be clearly seen from ...
175
votes
9answers
59k views

Elegant operations on matrix rows and columns

Question The Mathematica tutorial has a section 'Basic Matrix Operations', describing operations like transpose, inverse and determinant. These operations all work on entire matrices. I am missing a ...
119
votes
6answers
123k views

Get a “step-by-step” evaluation in Mathematica

Is it possible in Mathematica to get a step-by-step evaluation of some functions; that's to say, outputting not only the result but all the stages that have led to it? If so, how does one do it? ...
91
votes
4answers
4k views

Replacement inside held expression

I wish to make a replacement inside a held expression: f[x_Real] := x^2; Hold[{2., 3.}] /. n_Real :> f[n] The desired output is ...
90
votes
4answers
12k views

Plot draws list of curves in same color when not using Evaluate

This example comes from the Mathematica documentation for Plot under Basic Examples. Can someone please explain why these are each plotted as a different color in ...
89
votes
6answers
87k views

How do I clear all user defined symbols?

Is there some way to do this other than going to Evaluation -> Quit kernel and firing a new one up?
55
votes
4answers
8k views

Can I simplify an expression into form which uses my own definitions?

This seems like a simple thing to do, but I couldn't find anything relevant from Mathematica documentation. So suppose I have an expression: a*b/(a + a*Cos[a/b]) ...
53
votes
8answers
20k views

How to avoid returning a Null if there is no “else” condition in an If construct

I need to use If but with only one option that is if "a" then do "b", else do nothing. So I wrote If[a,b] but the problem is ...
51
votes
7answers
73k views

Assign the results from a Solve to variable(s)

I understand Mathematica can't assign the results of a Solve to the unknowns because there may be more than 1 solution. How can I assign the 4 values of following result to variables? ...
50
votes
3answers
4k views

Changing Values in an Association using Map

I am trying to change the value of one key in an association based on the value of another key in that association. So if my association starts as: ...
48
votes
6answers
10k views

Finding real roots of negative numbers (for example, $\sqrt[3]{-8}$)

Say I want to quickly calculate $\sqrt[3]{-8}$, to which the most obvious solution is $-2$. When I input $\sqrt[3]{-8}$ or Power[-8, 3^-1], Mathematica gives the ...
47
votes
4answers
9k views

Why does MatrixForm affect calculations?

This is a really newbie question, but it has me confused. Why does this code work without // MatrixForm and doesn't work with ...
47
votes
4answers
2k 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 ...
44
votes
5answers
3k views

How to create symbols from strings and set values for them?

I am trying to convert a list of string names into symbols, which will then be used to store data. I have 24 files (where the name of each file is a member of the list mentioned above) that I need to ...
41
votes
3answers
2k views

Funny behaviour when plotting a polynomial of high degree and large coefficients

I am trying to plot a polynomial of degree $29$ on the domain $[0,1]$, with fairly large coefficients: ...
41
votes
3answers
12k views

How do I work with Root objects?

I want to solve the trigonometric equation : $$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$ I tried Solve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x] It returns the ...
41
votes
4answers
3k views

Function in Table

I need a table with the elements made of pure functions and list elements. This is a simplified example: I need a list as: ...
41
votes
5answers
18k views

What is the most efficient way to add rows and columns to a matrix?

Say I have a matrix m and a vector v. ...
40
votes
5answers
42k views

Plotting Complex Quantity Functions

Trying to plot with complex quantities seems not to work properly in what I want to accomplish. I would like to know if there is a general rule/way of plotting when you have complex counterparts in ...
38
votes
4answers
4k views

Can a function be made to accept a variable amount of inputs?

I have a function that takes two inputs and processes them for a single output. What I need is one that can take a varying number of inputs. and process them to a single output. Is this possible in ...
35
votes
3answers
26k views

How can I plot implicit equations?

If you enter the following into Wolfram | Alpha, you get nice graphs: graph 4 x^4 + y^2 = 2 How do you do this in Mathmatica? I realize that these are not ...
35
votes
1answer
1k views

Why are all the lines commented when I create a Mathematica script?

When I created a Mathematica script, I found that all my lines were commented out (when opened with vi or gedit or any other ...
34
votes
4answers
9k views

How to modify function argument?

Usually in programming languages, function arguments are normal local variables, which can be modified. Is this not true in Mathematica? ...
30
votes
2answers
2k views

Plot Option Precedence while combining Plots with Show[]

I like to build sophisticated plots by combining simpler ones with Show[]. Typically this involves setting non-default Plot-Options with the different Plot-Commands,...
29
votes
5answers
6k views

Plotting several functions

I'd like to plot a function of one real and one integer variable, but I don't want them all shown in the same 2-D plot - I'd like to see them as separate curves so I can see both "axes", more like how ...
28
votes
6answers
3k views

How are parameters evaluated for a Plot in Manipulate

I am trying to get my head around how Manipulate evaluates functions in a Plot. I have read the introduction to Manipulate, and introduction to Dynamic, but I still ...
28
votes
1answer
3k views

How does Return work?

It is not completely clear to me how Return[] works. The documentation says: Return[expr] returns the value expr from a ...
27
votes
6answers
14k views

Replacing composite variables by a single variable

To replace a single variable by another variable, one can simply use the the replace all (/.) operator (e.g., ...
26
votes
4answers
31k views

How do I identify the source of a “Tag times protected” error?

I have some code that looks like Table[ a = 1; b = {2, 3} c = i;, {i, 2} ] which gives an error: Set::write: Tag Times in c {2,3} is Protected....
26
votes
1answer
18k views

What do the X and Y axis stand for in the Fourier transform domain?

In Wolfram Mathematica the function Fourier has the following declaration Fourier[list] And after a list is given to the ...
24
votes
3answers
19k views

General::ivar is not a valid variable when plotting - what actually causes this and how to avoid it?

I was just evaluating a couple of expressions and started to get errors like this: ...
23
votes
5answers
4k views

Extracting variables from an expression

I'm looking for a way to extract a list of variables from an expression, for example with an input like: ...
23
votes
3answers
770 views

Nested definition: How can I define a function with a passed-in expression?

Here's a simplified version of what I'm trying to do: ...
23
votes
2answers
1k views

Ordering problem

Let's look at the following example. Ordering[{0, 20 Sqrt[5], 40 Sqrt[5], 20 Sqrt[5], 20 Sqrt[10]} // N] gives the right answer ...
21
votes
7answers
1k views

Combining values in one column (or part) when values in another column (or part) match

Consider the following: ...
21
votes
3answers
6k views

How do I convert an argument list to a sequence of arguments?

I think this is a basic question, but I am having difficulty finding the answer in the documentation. Thread is not what I am looking for, I think. Suppose that I ...
19
votes
2answers
5k views

Error entering equation in DSolve

I entered a command incorrectly as follows: DSolve[{y'[x]=y[x]},y[x],x] I am now experiencing: ...
16
votes
5answers
11k views

Matrix Multiplication in context of row and column vectors

I've been looking at some matrices in Mathematica and I've noticed something very weird: they're extremely temperamental when it comes to dot products! For example, if I have the following, ...
15
votes
4answers
2k views

Splicing a list of arguments into a function with Sequence

Not sure if this has been asked, but I have a fairly simple operation that I don't know the syntax for. Say I have an array with some values, and a function f that accepts an arbitrary number of ...
14
votes
5answers
8k views

How to plot periodic function's graphic?

How to plot periodic function's graphic? For example, $f(t) = t$ when $-5<t<5$ and $f(t+10) = f(t)$. ...
12
votes
2answers
516 views

Unexpected behavior of rule matching a pattern

I am a beginner exploring the world of Mathematica. I expected the following code T[6, 5, 4, 1, 2, 3] /. {T[a___, 1, b___] -> Length[List[b]]} should return ...
12
votes
2answers
2k views

Evaluating an If condition to yield True/False

I would like to decide whether an option passed to my custom function has the value Automatic or something else. This is my attempt: ...
11
votes
4answers
1k views

Capital Letters that are built-in symbols

I'm trying to search for an answer to "What is the complete list of single capital letters that represent built-in Mathematica commands, symbols, or uses?" For example: C, D, E, I, N, O Is this ...
11
votes
3answers
9k views

Replace very small numbers by zero in the output of a list

I have a long nested list, but many elements are numbers of order 10^-18 or less, e.g. ...
11
votes
2answers
748 views

Dr. StrangeNumbers or: How I Learned to Stop Worrying and Love Floating Point Arithmetic

The following is the program. ...
10
votes
2answers
899 views

Programming with Dynamic

I don't understand the following: f[a_, b_] := a + b ls = {1, 2, 3}; MapThread[f, {ls, {10, 20, 30}}] This yields ( as expected ) {11,22,33} If I change ...
10
votes
1answer
593 views

Confused by (apparent) inconsistent precision

$$ e^{\pi \sqrt{163}} \approx 262537412640768743.99999999999925 $$ E^(Pi Sqrt[163.0]) N[E^(Pi Sqrt[163.0]), 35] NumberForm[E^(Pi Sqrt[163.]), 35] returns <...
9
votes
1answer
3k views

White regions in DensityPlot — is this a bug with ColorFunctionScaling?

Is this a bug with ColorFunctionScaling? When I try to supply my own ColorFunction Mathematica seems to partially ignore it, ...
8
votes
2answers
2k views

A problem about function N

Toady,I have a problem about N,described as below: For example N[1/3, 5] (* ==> 0.33333*) and ...
8
votes
1answer
493 views

Preventing cell height adjustment when rotating 3D graphics

I have a large dataset of scattered x,y,z coordinates. I am trying to use ListPointPlot3D to identify outliers in 3D. This involves generating a plot and then ...