How to manipulate expressions structurally, not necessarily complying with the rules of algebra.

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58
votes
3answers
2k 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 ...
28
votes
2answers
2k views

Scan vs. Map vs. Apply

I cannot understand the difference between Apply, Scan, and Map. I have tried to play with ...
48
votes
2answers
1k views

Head and everything except Head?

I have been working on picking expressions apart using Head and Part and encountered a little mystery. Consider the canonical ...
26
votes
3answers
9k views

Is it possible to change the color of plot in Show?

For example: p = Plot[Sin[x], {x, 0, 1}] Is it possible to write options in Show to change the curve's color for example into ...
11
votes
4answers
2k 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: ...
5
votes
5answers
227 views

Is there an analogue of the Variables command for general expressions?

The command Variables[poly] gives me a list of all variables that appear in the expression poly, which involved sums, ...
5
votes
1answer
981 views

Behavior of expression evaluation in Plot

I'm confused with Mathematica's way of parsing expressions. I've been struggling with this for a while and never found an exhaustive answer, sometimes things don't parse the way I think they would ...
18
votes
1answer
337 views

Why is ReplaceAll behaving like this?

I'm learning to use the ReplaceAll function and I found the behavior of which is quite confusing. For Sqrt[f[x, y]] /. f[___] -> u Mathematica returns ...
11
votes
3answers
947 views

Pattern matching a pattern with patterns

Confusing title, I know. But the question is, if we have two patterns which have the same general structure but different names used in the patterns and different names: ...
8
votes
3answers
1k views

How to manipulate gauge theory in Mathematica?

I want to know if there is a way of typing into Mathematica an expression like the following, $$\epsilon^{\mu \nu \lambda} f^{abc} A^a_\mu A^b_\nu A^c_\lambda + g\epsilon^{\mu \nu \lambda} A^a_\mu ...
19
votes
3answers
776 views

How can I completely ban usage of some functions in output and mandate use of others?

For example, I hate that Mathematica uses Pochhammer symbol in outputs and prefer all the expressions in Gamma function. How can ...
12
votes
5answers
1k 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 ...
18
votes
1answer
704 views

List manipulation to build a functional expression

Since Mathematica deals with Head[a, b] as an expression in this way The first Part of Head[a, b] is ...
12
votes
2answers
782 views

Displaying a series obtained by evaluating a Taylor series

Description of problem I would like to use Mathematica to display the series obtained by substituting a value for $x$ in a Taylor series expansion. The terms of the series will be rational numbers, ...
7
votes
2answers
419 views

Summa package problem

I need to use the features of the Summa package but it doesn't work in Mathematica 9. It gives the error Cannot open Utilities`FilterOptions` My question is: ...
2
votes
4answers
311 views

Print all numbers from a sequence which don't contain the digit 7

so i have this: Cases[RecurrenceTable[{a[n + 1] == 7 a[n] + n, a[1] == 1}, a, {n, 7}], Except[7]] But i noticed that it will only exclude numbers that are 7, and ...
15
votes
3answers
615 views

Comparing Mathematica expressions like diff

I am looking for a way to compare (or "diff") two Mathematica expressions, similarly to how to diff utility can compare two text files and report the differences. Has anyone already written such a ...
14
votes
1answer
508 views

Transform an expression into a graph that can be plotted with TreeGraph (not TreeForm)

I would like to plot an expression (like TreeForm does), but using the new TreeGraph functionality. ...
8
votes
4answers
575 views

Counting multiplications (complexity function)

I'm trying to count the number of times multiplication appears in an expression (for the purpose of constructing a ComplexityFunction that would help me simplify a terrible algebraic expression for ...
28
votes
8answers
1k views

How do I get my equation to have the form $(x-a)^2 + (y-b)^2 + (z-c)^2-d = 0$?

I want Mathematica to express the equation $$-11 - 2 x + x^2 - 4 y + y^2 - 6 z + z^2=0$$ in the form $$(x - 1)^2 + (y - 2)^2 + (z - 3)^2 - 25=0$$ How do I tell Mathematica to do that?
13
votes
3answers
2k views

How can I transfer mathematical expressions between Mathematica and Maple?

Is there a simple way to copy mathematical expressions between Mathematica and Maple (or at least in one direction)? I mean only expressions built from numbers and predefined mathematical functions, ...
13
votes
6answers
308 views

Construct an infix operation from a list

Inspired by this question, if I have a list {a, p, b, q, c} where p and q are binary ...
9
votes
1answer
2k views

How do I expand a sum?

I have a problem with Mathematica's symbolic manipulations. As an example, consider the following expression: $$\sum _{i=1}^n -2 x_i \left(-a x_i-b+y_i\right)=0$$ How do I get Mathematica to expand ...
6
votes
6answers
250 views

Trying to write out the prime factorization of a number with CenterDot and Superscript

I am trying to use CenterDot and Superscript, in conjunction with Apply to write out the prime factorization of any given integer. Everything works well UNLESS the prime factorization of the number ...
3
votes
1answer
232 views

Separating exponential terms

Suppose I have a lot of expressions multiplied by factors such as: $$e^{-i\theta[1]-i\theta[2] - i\theta[3]-i\theta[4]-i\theta[5]}$$ I would like to separate this into a product of exponentials of ...
21
votes
1answer
430 views

How can I see which transformations Simplify attempts?

The documentation for Simplify[expr] says that it performs a sequence of algebraic and other transformations on expr, and returns the simplest form it finds. How can I see which transformations it ...
9
votes
2answers
5k views

How to expand tan(x+y) as normal form?

TrigExpand@Tan[x + y] gives $\frac{\sin (x) \cos (y)}{\cos (x) \cos (y)-\sin (x) \sin (y)}+\frac{\cos (x) \sin(y)}{\cos (x) \cos (y)-\sin (x) \sin (y)}$ but I ...
13
votes
2answers
338 views

How to do algebra on summations of variable expressions?

Is there any easy, general way to handle algebra on variable Sums? For examples, Gaussian Mixtures or Fourier Series: ...
8
votes
2answers
282 views

How to reduce the number of operations needed to evaluate an expression? [duplicate]

For some numerical calculations in C++ I have, for example, this complicated expression to evaluate. Given as Mathematica input, in its original form it is ...
5
votes
1answer
318 views

Embedding StreamPlot in Graphics3D

I am trying to visualise the action of the infinitesimal generator of a Lie group on the solution of a 2-ODE system drawn in the 3D space (t,y1,y2): t is time and y1,y2 are the two dependent ...
13
votes
2answers
564 views

How to embed an image into a string?

Note: The bug described in the post is in Mathematica 9, and has been fixed in 10.0. The documentation for String contains the following statements: Strings ...
9
votes
3answers
2k views

How to extract expression from ConditionalExpression

p1 := y /. {First[Solve[x^2 + y^2 + x == 1, y, Reals]]} ...
5
votes
2answers
229 views

Passing list of options to Plot

I'm looking for a way to create a variable that I can use to hold all of the graphics directives for, say, a plot command. For example, I have 8 plots with variations on the following: ...
4
votes
2answers
529 views

Simplifying expressions involving Sum

I am trying to use Mathematica to simplify a symbolic expression involving Sum. The expression is defined as follows: ...
3
votes
3answers
448 views

Conjugating symbolic expression

I am trying to conjugate a symbolic expression, and I have explicitly stated the real terms. However, I simply can't get it to work: ...
2
votes
1answer
113 views

Simplifying Expressions for FindMinimum

I am currently trying to apply the FindMinimum function to find the lowest energy of an expression. My current expression as of now is relatively complicated. It is the summation of 48 similar terms, ...
2
votes
2answers
201 views

How to change the Integer to a special form in an expression?

I have an expression. I want to change all the Integers to a new form. The rule is, x_Integer->x._f. But we should consider some special cases. For example, ...
1
vote
3answers
207 views

How to manage list of list of rules?

Considering we have a list: str = "{1 -> {a -> aa, b -> bb}, 2 -> {2a -> \"{b -> bb}\"}}" Bringing this to expression gives: ...
21
votes
2answers
740 views

List of atomic expressions

I was surprised to see Graph objects are atomic. Is there a way (through documentation or programmatically) to find all atomic heads? The ones I know of are: ...
12
votes
1answer
175 views

Is there a way to control which special forms Normal converts?

Normal documentation reads: Normal[expr] converts expr to a normal expression, from a variety of special forms. But is there a way to control which special ...
12
votes
2answers
740 views

Google Code Jam: Mountain View code review

After participating in Google Code Jam 2012 Round 2, it occurred to me that the Mountain View problem boiled down to solving a set of linear inequalities, which could be done in Mathematica. I've only ...
11
votes
3answers
219 views

How to collect expressions from cells created by Print?

I have a notebook where evaluation of a certain cell produced hundreds of adjacent output cells using Print. I need to create a list containing all expressions from ...
11
votes
1answer
475 views

How to convert a notebook cell to a string retaining all formatting, colorization of identifiers etc?

I have an opened Mathematica notebook containing several cells. Suppose, I am interested in one of them -- it may contain a complete or incomplete expression (e.g. with syntax errors, highlighted ...
10
votes
2answers
358 views

Get rational and irrational parts

Consider an expression of the form $a + b \sqrt{2}$, where $a,b \in \mathbb{Q}$. How can I extract $b$ (or equivalently $a$) from this expression?
10
votes
1answer
139 views

What are the scoping rules for function parameters shadowing System` symbols?

Here are some very contrived code snippets, highly unlikely to appear in real code, but still I am curious why they behave like this: ...
7
votes
1answer
104 views

When is the righthand side of a RuleDelayed evaluated?

The documentation on RuleDelayed states that lhs :> rhs represents a rule that transforms lhs to rhs, evaluating rhs only after the rule is used. Consider the following rule: ...
6
votes
1answer
195 views

How to efficiently find all combinations of the letters in an alphabet given a condition

Problem: I want to find all unique expressions with n number of terms that contain all the digits (or characters) in alphabet. ...
6
votes
1answer
338 views

Using FunctionExpand to evaluate symbolic derivatives

Some symbolic derivatives of certain special functions are not expanded automatically, but FunctionExpand often helps to get a derivative-free closed form ...
3
votes
1answer
219 views

Change values in equation with slider

I want to make an equation where the values adjust to my slider which I inserted with manipulate. Well, I tried, but when I use the slider the equation starts to fall apart. Actually this should ...