# Questions tagged [faq]

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

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### 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 ...
68k 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 ...
154k 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? ...
20k views

### Why should I avoid the For loop in Mathematica?

Some people advise against the use of For loops in Mathematica. Why? Should I heed this advice? What is wrong with For? What ...
5k 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 ...
101k 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?
14k 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 ...
92k 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? ...
24k 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 ...
10k 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]) ...
5k 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: ...
11k 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 ...
10k 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 ...
17k 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 ...
3k 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 ...
3k 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: ...
4k 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 ...
4k 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: ...
46k 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 ...
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 ...
21k 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. ...
34k 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 ...
10k 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? ...
2k 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 ...
8k 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 ...
17k 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., ...
3k 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,...
25k 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: ...
4k 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 ...
46k 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....
7k 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 ...
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 ...
29k 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 ...
2k 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 ...
5k 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: ...
887 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: ...
6k 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: ...
2k views

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

Consider the following: ...
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 ...
14k 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, ...
10k 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 $f(t+10) = f(t)$. ...
558 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 ...
12k 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. ...
3k 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: ...
2k 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 ...
794 views

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

The following is the program. ...
4k views

### White regions in DensityPlot?

When I try to supply my own ColorFunction Mathematica seems to partially ignore it, and the white color "burns through" if the function is too "sharp&...
1k 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 ...
$$e^{\pi \sqrt{163}} \approx 262537412640768743.99999999999925$$ E^(Pi Sqrt[163.0]) N[E^(Pi Sqrt[163.0]), 35] NumberForm[E^(Pi Sqrt[163.]), 35] returns <...