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549 votes
37 answers
130k 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 ...
53 votes
4 answers
21k 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 ...
minthao_2011's user avatar
  • 4,503
602 votes
19 answers
156k views

Where can I find examples of good Mathematica programming practice?

I consider myself a pretty good Mathematica programmer, but I'm always looking out for ways to either improve my way of doing things in Mathematica, or to see if there's something nifty that I haven't ...
110 votes
4 answers
16k 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 ...
trayres's user avatar
  • 1,225
181 votes
8 answers
22k views

List of compilable functions

Is there somewhere a list on the functions that Compile can compile, or the cases in which a particular function can be compiled that I haven't found? I'd be glad ...
Rojo's user avatar
  • 42.6k
257 votes
9 answers
19k views

What are the use cases for different scoping constructs?

Mathematica includes three functions that I know of which can be used to effectively (if not actually) define a variable and give it a value within a local scope: ...
David Z's user avatar
  • 4,911
205 votes
3 answers
53k views

Alternatives to procedural loops and iterating over lists in Mathematica

While there are some cases where a For loop might be reasonable, it's a general mantra – one I subscribe to myself – that "if you are using a ...
Mr.Wizard's user avatar
  • 271k
122 votes
3 answers
9k views

What is a Mathematica packed array?

A simple sounding question with a few sub questions: What is the difference between unpacked vs packed array? Are packed arrays more space efficent, how much so? Are packed arrays more time ...
nixeagle's user avatar
  • 2,263
113 votes
4 answers
26k 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 ...
Szabolcs's user avatar
  • 234k
52 votes
4 answers
12k 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 ...
Alexey Kalmykov's user avatar
205 votes
14 answers
74k 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 ...
sjdh's user avatar
  • 7,717
211 votes
26 answers
17k views

What are some useful, undocumented Mathematica functions?

There have already been some questions about some undocumented functionality in Mathematica. Such as (please add to these lists!) How can one find undocumented options or option values in Mathematica?...
92 votes
5 answers
15k views

What does the construct f[x_] := f[x] = ... mean?

This question mentions "x := x = trickery". What does defining a function as f[x_] := f[x] = ... do and what is it good for?
Chris K's user avatar
  • 20.1k
50 votes
5 answers
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 ...
einbandi's user avatar
  • 4,024
220 votes
2 answers
14k views

What is the distinction between DownValues, UpValues, SubValues, and OwnValues?

When reading through the documentation, you often encounter the phrases DownValues, UpValues, ...
rcollyer's user avatar
  • 33.9k
125 votes
7 answers
7k views

What is the most convenient way to read definitions of in-memory symbols when we don't have the source files? (Spelunking tools)

Note: I put Simon's implementation on GitHub. Contributions welcome! When trying to read the definition of already defined (package or built-in) symbols using ...
Szabolcs's user avatar
  • 234k
53 votes
4 answers
8k views

Dynamic Euler–Bernoulli beam equation

I am trying to solve for the vibration of a Euler–Bernoulli beam. The equation is $\frac{\partial ^2u(t,x)}{\partial t^2}+\frac{\partial ^4u(t,x)}{\partial x^4}=0$ For the boundary conditions I ...
Hugh's user avatar
  • 16.2k
50 votes
9 answers
13k views

About multi-root search in Mathematica for transcendental equations

I have some questions for multiroot search for transcendental equations. Is there any clever solution to find all the roots for a transcendental equation in a specific range? Perhaps ...
yulinlinyu's user avatar
  • 4,805
32 votes
6 answers
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 ...
ShaunH's user avatar
  • 807
64 votes
8 answers
106k 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? ...
stevenvh's user avatar
  • 6,856
106 votes
5 answers
6k 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 ...
Alexey Popkov's user avatar
161 votes
12 answers
55k views

1 Plot, 2 Scale/Axis

I would like to plot those two datasets on top of each other. But they have very different range on the $y$ axis. How can I have two different axis? I found the following on the help menu but quite ...
500's user avatar
  • 5,529
77 votes
4 answers
15k views

Plotting implicitly-defined space curves

It is known that space curves can either be defined parametrically, $$\begin{align*}x&=f(t)\\y&=g(t)\\z&=h(t)\end{align*}$$ or as the intersection of two surfaces, $$\begin{align*}F(x,y,...
J. M.'s eventual burnout's user avatar
76 votes
4 answers
21k views

How do I save a variable or function definition to a file?

Is it possible to save a function which was created via Interpolation of some data in such a way that I can use this function in a new Mathematica session without ...
partial81's user avatar
  • 3,081
60 votes
1 answer
3k views

What's inside InterpolatingFunction[{{1., 4.}}, <>]?

I'm curious what's inside the InterpolationFunction object? For example: ...
xslittlegrass's user avatar
84 votes
9 answers
7k views

Updating Wagon's FindAllCrossings2D[] function

Stan Wagon's Mathematica in Action (second edition; I haven't read the third edition and I'm hoping to eventually see it), demonstrates a nifty function called ...
J. M.'s eventual burnout's user avatar
67 votes
4 answers
6k views

How do I evaluate only one step of an expression?

I am looking for a simple, robust way to evaluate an expression only one step, and return the result in a held form. The definition of a single step is ambiguous, and this itself is probably worthy ...
Mr.Wizard's user avatar
  • 271k
69 votes
10 answers
3k views

Injecting a sequence of expressions into a held expression

Consider the following toy example: Hold[{1, 2, x}] /. x -> Sequence[3, 4] It will give Hold[{1, 2, Sequence[3, 4]}] ...
Szabolcs's user avatar
  • 234k
46 votes
4 answers
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: ...
yulinlinyu's user avatar
  • 4,805
32 votes
1 answer
37k 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 ...
user253956's user avatar
139 votes
8 answers
8k views

Can one identify the design patterns of Mathematica?

... or are they unnecessary in such a high-level language? I've been thinking about programming style, coding standards and the like quite a bit lately, the result of my current work on a mixed .Net/...
Verbeia's user avatar
  • 34.2k
183 votes
6 answers
24k views

How to compile effectively?

What are the best practices of compiling functions? I understand that this is a vague question, but let me list some aspects that might trigger useful answers. Some of these have already been answered ...
István Zachar's user avatar
113 votes
2 answers
30k views

What is the difference between Reduce and Solve?

Solve and Reduce both can be used for solving equations. Just by working with them, I know there are some differences between ...
lachis83's user avatar
  • 1,639
165 votes
5 answers
16k views

Are you interested in purchasing David Wagner's "Power programming with Mathematica"?

I recently contacted McGraw-Hill to see if they have a mechanism in place for printing out-of-print books that are still of interest. Specifically, I asked about "Power programming with Mathematica" ...
134 votes
9 answers
30k views

Creating Mathematica packages

I'm building a package to help me write packages and their documentation. In this post I explained how to make a package and its documentation. In the answer I provided I describe how to build a very ...
jmlopez's user avatar
  • 6,470
145 votes
7 answers
180k 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? ...
Cydonia7's user avatar
  • 2,519
111 votes
4 answers
7k views

Flatten command: matrix as second argument

One thing I could never wrap my head around is how Flatten works when provided with a matrix as the second argument, and the Mathematica help isn't particularly ...
David's user avatar
  • 14.9k
60 votes
4 answers
11k 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]) ...
Echows's user avatar
  • 981
53 votes
6 answers
12k 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 ...
jtbandes's user avatar
  • 1,422
16 votes
2 answers
3k views

Boundary condition with spatial derivative is ignored by NDSolve

Consider the following differential equation: $$\begin{align*}&\rho C_p\left(\frac{\partial T}{\partial t}\right)=k\left[\frac{\partial^2 T}{\partial x^2}\right]+\dot{q}\\ &\text{at }x=0,\;\...
Feyre's user avatar
  • 8,577
32 votes
2 answers
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,...
uli's user avatar
  • 1,365
32 votes
3 answers
30k 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: ...
user avatar
66 votes
2 answers
7k views

Analogue for Maple's dchange - change of variables in differential expressions

Update Finally in v13.1 the function DSolveChangeVariables is introduced, try it out! DChange in the answer below is still a ...
xzczd's user avatar
  • 65.4k
56 votes
2 answers
8k views

Do I have to code each case of this Grid full of plots separately?

I have written some custom functions to draw multi-panel graphs like this one: It's done by passing a matrix of (custom) plotting functions to a MultiPanelGraph ...
Verbeia's user avatar
  • 34.2k
181 votes
5 answers
18k views

Performance tuning in Mathematica?

What performance tuning tricks do you use to make a Mathematica application faster? MATLAB has an amazing profiler, but from what I can tell, Mathematica has no similar functionality.
John's user avatar
  • 2,429
70 votes
5 answers
31k views

Creating legends for plots with multiple lines?

So I have a graph with multiple lists, for e.g. data = {{1,2}, {3,4}, {3,5}, {2,3} . . .} If I then do ...
Eiyrioü von Kauyf's user avatar
123 votes
7 answers
17k views

Struct equivalent in Mathematica?

I really miss having something like a struct in Mathematica. I know of (and regularly use) a couple of programming techniques which feel like a ...
Cassini's user avatar
  • 5,556
46 votes
2 answers
10k views

What is the difference between Set and SetDelayed?

I have a problem with defining a function and most of time I get confused by Set or = and ...
DSaad's user avatar
  • 1,173
89 votes
11 answers
20k views

How to check if a 2D point is in a polygon?

Background: I use code from An Efficient Test For A Point To Be In A Convex Polygon Wolfram Demonstration to check if a point ( mouse pointer ) is in a ( convex ) polygon. Clearly this code fails for ...
nilo de roock's user avatar
88 votes
3 answers
6k views

Extract values for ViewMatrix from a Graphics3D

Under More Information in the help page of ViewMatrix the following entry can be found With the setting ViewMatrix->Automatic...
halirutan's user avatar
  • 113k

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