Questions about Mathematica's rule-based replacement functionality, including functions such as Rule (->), Replace, ReplaceAll (/.) and ReplaceRepeated (//.).

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6
votes
2answers
350 views

Matrix exponential via Cayley-Hamilton Theorem

I'm attempting to calculate the exponential of a matrix via Cayley-Hamilton theorem. (Following the "concrete example" from http://en.wikipedia.org/wiki/Cayley%E2%80%93Hamilton_theorem) I am having ...
6
votes
3answers
230 views

What's wrong with naming a rule?

Please have a look at the code below. The second Manipulate uses the name rl of the replacement rule given in the first line, ...
6
votes
3answers
188 views

How to prevent substitution in a part of an expression?

Background: I am trying to write a program that can execute scheme in Mathematica. Now I have things like {"+", 3, {"-", 2, {"'", {"*", 1, 3}}}}. The syntax ...
6
votes
2answers
199 views

How can you resize all the images in a notebook section?

I've pasted a large number of photos and they are too big which makes scrolling hard. Is there a way to automatically have Mathematica size them to 10% or something reasonable without have to click on ...
6
votes
1answer
573 views

How to speed up calculations with large number of replacement rules?

In my program I have an expression which looks like: ...
6
votes
2answers
456 views

Conditionally replace rows in lists

I have a sequence of matrices/lists ...
6
votes
3answers
894 views

Arithmetic operation on the value returned by Solve

I want to modify the value that is returned by Solve. Example: SolC1 = Solve[Sin[ π x / L] == 1, x] {{x -> L/2}} I need to add n to x so that x becomes ...
6
votes
3answers
193 views

How to make Missing[] invariant for some functions without redefining them

Missing[...] "is a symbolic object, with no default evaluation rules defined." Missing data can be tagged and enables use of filters like DeleteMissing. So it's worthwhile to normalize various types ...
6
votes
5answers
184 views

Setting value of a rule

How do I change the value of a rule? For example, If I have a = x->3, how do I reset the value of x/.a to 4, so that ...
6
votes
1answer
246 views

Conditional string replacement

I have a list of text and need to replace an element based on the text that appears in the element before it. Example of my list: ...
6
votes
2answers
308 views

Apply Trig Identity to Transform Sum of Sinusoids into Phase-Shifted Cosine Function

I'm trying to solve for the output of a simple RC low-pass filter, with Cos[w t] input. The convolution of the input with the RC transfer function gives me the right output, but I'd like to be able to ...
6
votes
1answer
233 views

Better replacement rules to perform this change of variables?

In cosmology, it is common to work with both a normal time variable t and a “conformal” time variable τ, which is defined such ...
6
votes
1answer
225 views

Generating replacement rules programatically

I would like to generate sets of replacement rules programatically for predefining some permutations. So a function ...
6
votes
2answers
147 views

What is the Difference Between Rule (->) and RuleDelayed (:>)?

I am new to Mathematica so this question may seem rudimentary. Sorry for that! :) I want to implement the well-known property of Kronecker's Delta $$\Sigma_{i=1}^{n} a_i \delta_{ij}=a_j,\quad 1 \le ...
6
votes
2answers
105 views

Condition and RuleDelayed

On this site I found, for example here, some very interesting questions and answers on the use of delayed rules with conditions. I would very much like to understand these answers, but so far I failed ...
6
votes
2answers
1k views

Speeding up mathematica by subsitituting numerical values

According to this Wolfram Blog post, one can speed up Mathematica code by substituting numerical values as soon as possible. How does one substitute before the main expression is evaluated? The ...
5
votes
4answers
365 views

ReplaceAll is not working correctly

The line of code -E^(-I k) x /. {-x -> -x, -E^(-I k) x -> -E^(I k) x} is not properly replacing the exponential of (-I k) with the exponential of (I k), as ...
5
votes
5answers
446 views

Random character change in a random place

I would like to ask for help in a Random Replace of character. For example: ORANGE and change 1 character randomly (random place and random character from ORANGE) in it into any character of ORANGE, ...
5
votes
3answers
2k views

How to replace all occurrences of an element in a list?

Consider the following: list={1,2,2,2,3}; I would like to replace all 2 with the string "Test". ...
5
votes
5answers
214 views

Converting set of characters into numbers using list of replacement rules

I am trying to convert a text, as an example "aaaa" into a set of numbers as defined in a list of replacement rules, for example letterstonum . letterstonum takes in letters a to z and returns the ...
5
votes
4answers
300 views

How to split a list with respect to its nested sublists?

I have a problem with the following task: having some nested list list = {{k6},{k1,k3,k5},{k7}} I would like to replace all sublists by their permutations and ...
5
votes
3answers
504 views

Simple image processing very slow

I have compared the speed of some simple image processing routines between Mathematica an IDL. 1. Reading of a grey scale png image of (720,577) pixels: The image is: Mathematica: ...
5
votes
3answers
186 views

How to replace an element in a list with an element in another list with matching indices

I have a list like this l = {1 + 2*s, 2 + 3*s, 4 + 1*s}, and I have calculated s = {1, 2, 3}. I need to replace ...
5
votes
2answers
533 views

Replace rule with function? Derivatives don't evaluate

Say I have an expression (call it expr) involving a function, f[x]. I'd like to be able to evaluate that for a particular choice of ...
5
votes
3answers
355 views

Replace x, but not x[a] [duplicate]

I want to replace all occurences of the symbol x with x[a], as long as it is not in the form ...
5
votes
2answers
134 views

ReplaceAll performance problem: packed arrays on the LHS are unpacked when the RHS is too long

The following is one of the most mysterious performance problems I encountered and came up while extending the booleval function mentioned here. I am looking for a ...
5
votes
3answers
2k views

Replace function and its derivatives found with Solve

If I have an equation eq = f[x] + g[x] == 0 and I solve for f[x] sol = Solve[eq,f[x]] ...
5
votes
3answers
182 views

How to change symbols in differential equation with a single rule?

Problem Suppose I have a differential equation such as $\qquad f'(x)+f(x)=0$ and I want to change it into $\qquad y'+y=0$ My Method Using rule = f[x] -> y,...
5
votes
1answer
205 views

How can I make a “self-referential” replacement operation self-contained?

Fairly often I find use for replacement rules that call themselves on the right-hand side of the rule, e.g.: ...
5
votes
1answer
372 views

replace items in a list with items in a another list

Suppose I have a list A={x1,x2,x3}, a list B={3,4,5}, and a function f[x]=x1+x2+x3. Is there ...
5
votes
1answer
347 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 variables....
5
votes
2answers
125 views

Why does Rule behave like this?

Why does {x, x^2, x^3, a, b} /. x^n_ -> f[n] result in {x, f[2], f[3], a, b} when ...
5
votes
3answers
329 views

When I use Rule, why doesn't this work?

k.k.k //. {k.k -> k} works perfectly, so the output is just k. But, when I use Esc.<...
5
votes
1answer
660 views

Apply color function to matrix plot

I want to apply the following color rules to a large table of numbers. I have extracted a part of the table to use as an example. I would like to assign 5 different colors to 5 different ranges of ...
5
votes
2answers
203 views

BezierCurve in EdgeShapeFunction fails when used on multiedges graph

I would like to create a network graph with curved edges. To do this, I wrote this function: ...
5
votes
1answer
228 views

Replace rule does not match

I have the following expression -3 I Ez Re[Ex] + 3 I Ex Re[Ez] And I wish to write this in the form -3 Re[I Ez Conjugate[Ex]]....
5
votes
3answers
104 views

How can I pass replacement rules to a package-defined function and have it understand their context?

I am writing a package where I would like to be able to pass replacement rules to a function inside the package and have the function manipulate its symbols using those replacement rules. However, I'm ...
5
votes
2answers
105 views

Replace expression in series expansion [duplicate]

A test case: I'm trying to replace an expression inside a series expansion: Series[f[x],{x,x0,4}] ./ (x-x0)->h but it still returns ...
5
votes
1answer
205 views

Simplifying a b = 1 in non-commutative products?

Yesterday, I try to define some rules for non-communicative multiplication, here. I find some quite helpful rules, but things still do not work properly; the distributive rule can't be applied (e.g.: <...
5
votes
1answer
449 views

Why does this pattern for combining two lists require triple underscores (___) to work?

I understand that __ is a list of one or more elements, and that ___ is 0 or more elements, but when I try this rule with 2 ...
5
votes
1answer
109 views

How to make a postordered ReplaceAll that operates just once per subtree?

The answers to this question provide code for a function I'll call postOrderReplaceAll to replace from the inside-out: ...
5
votes
4answers
210 views

How to replace all symbols except several?

I'm doing some heavy symbolic calculations and for preliminary simple tests I need to replace all coefficients except chosen with 1, e.g.: ...
5
votes
1answer
264 views

Why does the replace all (/.) evaluate differently in plot

I'm plotting this function: Plot[(2 (l/2 π)^2 ((2 π f)/c)^2 /. {f -> (f 10^9), l -> .01, c -> 3 10^8}), {f, 17.5, 26.5}] but it does not plot ...
5
votes
1answer
1k views

How to Make a change of variables

I have the following expresion $$\hat{M}^2=-\left[\frac{1}{\sin\beta}\frac{\partial}{\partial\beta}\sin\beta\frac{\partial}{\partial\beta}+\frac{1}{sin^2\beta}\left(\frac{\partial^2}{\partial\alpha^2}...
5
votes
2answers
267 views

How to “ReplaceAll” using a set of conditional expressions instead of a list of rules [closed]

Suppose that I have two linear functions f[x_] := f0 + f1 x g[x_] := g0 + g1 x and a (possibly rather complicated) set of conditional expressions, obtained ...
5
votes
1answer
172 views

How can I substitute something using only map?

For example, I have the equation x^2 + y^2 == x*y and I want to apply the rule y -> s*x I can do it easily by ...
5
votes
2answers
142 views

Trouble with Replacements [duplicate]

I have the following line of code: Plus @@ Table[p[x], {x, 0, 20}] /. p[x_] -> Boole[MemberQ[{0, 5}, x]] The first part of this produces ...
5
votes
2answers
100 views

Creating functions from output of other calculations

Apologies in advance if the title is vague, I'm not really sure what to call this. I have a function (call it 'foo') that generates a largeish polynomial, and it is natural to make the variables be ...
5
votes
1answer
86 views

How to transform abstract finite group to permutation group?

It seems that Mathematica only has group functionality for permutation groups? Then there is a step to transform the abstract finite one to a permutation one. As an example, consider the following ...
4
votes
4answers
180 views

Rearrange graph

I have to rearrange graph described by j = {1 -> 2, 2 -> 3, 3 -> 1}; appling some function to all vertices on the right so rearrange[j] output should ...