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

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35
votes
3answers
741 views

Replace inside Held expression

I wish to make functional replacement inside Held expression like this: ...
13
votes
6answers
2k 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., ...
12
votes
7answers
2k views

How do I replace a variable in a polynomial?

How do I substitue z^2->x in the following polynomial z^4+z^2+4? z^4+z^2+4 /. z^2->x ...
5
votes
5answers
1k views

Replace values which obey certain criteria

I'd like to replace all values in a list which obey one or more criteria with another value. Example: Replace all values>30 by 30. data={{3,35},{2,7}} ...
19
votes
2answers
2k views

Extracting values from nested rules in JSON data

I have been using Mathematica to analyse some data from the StackExchange API. It is conveniently available in JSON form, which Mathematica interprets as replacement rules. However, some of the rules ...
9
votes
3answers
960 views

Replace expressions with symbols

First of all: I'm new to Mathematica, so I would appreciate it if the answers are quite complete. I have the result of calculation that is expressed in $\sin$ and $\cos$. Now, all of these can be ...
19
votes
2answers
891 views

Mathematica for Computer Scientists

Background I've coded in C/Scheme for 10 years. I have a BS CS. I've recently become very interested in pattern-matching (lisp's match macro), and term rewriting systems, which brought me to ...
13
votes
1answer
391 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. ...
25
votes
2answers
1k views

Best practice of passing a large number of parameters to functions

I have a number of functions that all take a large number of parameters. I am wondering what is the best practice of passing these parameters to those functions. I could, of course, simply specify ...
10
votes
1answer
223 views

StringReplace, ReplaceAll and Rule interact in a bizarre way

I have the following pair of things: ClearAll[foo, labeledFoo]; labeledFoo = {"FooBarBazQuux", foo}; This works like you'd expect: ...
11
votes
4answers
344 views

“Strange” behavior of Rule

According to the Help lhs->rhs evaluates rhs immediately. How to understand the output of the following code? ClearAll@x; {1, 3.5} /. x_?IntegerQ -> {x} ...
11
votes
4answers
311 views

How to replace every possible $A+B$ and $AB$ in expansion of $(A+B)^{10}-A^{10}-B^{10}$ with $x$ and $y$, respectively?

I would like to replace every possible $A+B$ and $AB$ in expansion of $(A+B)^{10}-A^{10}-B^{10}$ with $x$ and $y$, respectively. How to do it with the simplest code in Mathematica? For example, ...
1
vote
2answers
190 views

How to replace subscript symbols

I have an expression with subscripted variables. I would like to replace all those terms with other symbols. For example, $P_1 + P_2^3 \rightarrow P1 + P2^3$ I used the following code but it doesn't ...
9
votes
1answer
249 views

Performance of Dispatch and lists of Rules

The issue outlined here seems to be no longer present in version 10, if you use a Dispatch table! This because a Dispatch table ...
7
votes
3answers
158 views

Converting StringJoin to StringForm inside Hold

Let's say I have a piece of code: Hold[{code1, "asdad " <> ToString[testa] <> " adsd " <> ToString[testb], code2}] (*MWE ofc*) ...
4
votes
1answer
205 views

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

In my program I have an expression which looks like: ...
10
votes
3answers
491 views

How to properly project a Graphics object consisting of line primitives

My problem starts from attempts at depicting overlapping lines of different thickness, i.e. ...
9
votes
2answers
483 views

Simple problem with Manipulate and Plot

Would anyone have an idea why the following doesn't work: rule = {z -> x^2 + 2 x + y}; Manipulate[ Plot[z /. rule, {x, 0, 10}], {{y, 2, "y"}, 1, 5} ] But ...
8
votes
8answers
856 views

How can a power of 0 or 1 be replaced?

Consider this given example for ReplaceAll 1 + x^2 + x^4 /. x^p_ -> f[p] This returns ...
6
votes
6answers
949 views

How to simplify a complicated Sum in terms of power Sums?

For example, I have: $a=\sum _{r=1}^n x_r \left(\left(\sum _{i=1}^n x_i-x_r\right){}^2-\sum _{i=1}^n x_i^2\right)$ ...
5
votes
1answer
272 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 ...
1
vote
1answer
267 views

Arbitrary depth patterns/rules

Temporary message: I am now really confused. I am not sure how using Power and Unevaluated together works in the examples below. While answering this question, I stumbled upon the following. We ...
0
votes
2answers
112 views

How to assign special colors to the output of DensityPlot?

I have created the following function for plotting ...
8
votes
3answers
244 views

Applying a transformation rule on an Image

I haven't been able to figure out why the following doesn't work: ...
5
votes
3answers
113 views

Assign output of solve to variables [duplicate]

I have this input: Solve[x^2 + 3 x + 2 == 0, x] which gives this output: {{x -> -2}, {x -> -1}} I want the first x ...
4
votes
2answers
601 views

Replace expressions by self defined symbols

I have a list of expressions like the following: ...
2
votes
2answers
149 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 ...
1
vote
4answers
112 views

Replacing more than one element from a Sublist

The following expression allows me to extract the value of x and y: ...
20
votes
1answer
658 views

replacement rules from a pattern and a matching expression

(This seems to be a very basic necessity in a language having pattern-matching capabilities such as Mathematica, yet I struggled for many hours to find a common solution to this problem.) Suppose ...
10
votes
3answers
640 views

How to implement a regular grammar?

What is the most simple, elegant way of implementing a rewrite-system defined as: $$ \begin{aligned} \Sigma &= \{a_1, a_2, a_3, ...\} \\ N &= \{A_1, A_2, A_3, ...\} \\ \{\alpha_1 , ...
11
votes
4answers
280 views

Replacing parts of a held expression with held parts of another expression

I'm applying the Trott-Strzebonski technique in order to replace inside a held expression. ...
9
votes
1answer
69 views

Using PatternSequence on its own in ReplaceAll?

Say I have this list: list = {0, 1, 2, 0, 1, 3, 0, 1, 4} and say I want to remove consecutive sequences of 0 and 1. I'd normally go for this: ...
10
votes
2answers
225 views

How to extract a specific element from EXIF photographic metadata?

It's now possible to import photographs into Mathematica and import the EXIF data at the same time: i = Import["ExampleData/coneflower.jpg", "ImageWithExif"] ...
13
votes
1answer
458 views

rule-based implementation of an algorithm

When I first started learning about rule-based programming with Mathematica, I tried to translate this algorithm for computing the convex hull of a set of 2-D points in $O(n \log(n))$ time, to use ...
7
votes
2answers
211 views

Why does the name of a pattern affect the result of a transformation rule?

I was playing a little dirty, trying to get a template for defining a Curl[] operator. I wrote the following rule, which I knew was going to spit out a few ...
6
votes
5answers
207 views

Lowering the degree of an polynomial with an assumption that the polynomial has a factor x^2+ax+b

Let's assume $ x^{10}+x^5+1 $ has a factor $x^2+ax+b$ Then, If $x^2=-ax-b$, $ x^{10}+x^5+1 =0$. If we successively apply $x^2=-ax-b$ to $ x^{10}+x^5+1 $, we can make $ x^{10}+x^5+1 $ to degree 1, ...
5
votes
1answer
145 views

Is there a faster way to Map an Association?

Consider mapping an existing Association in a manner such as this: ...
5
votes
3answers
2k views

How to use results of NDsolve[] for further solving of ODEs?

I have a system of ODEs with 10 eqns. I can solve the first 5 independently. How can I use those results to solve for the remaining 5? An easy example would be $\dot{x}=f(x), \quad \dot{y}=g(x,y)$ ...
4
votes
3answers
807 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]] ...
11
votes
2answers
206 views

ReplaceRepeated seemingly omits some rules

Is there a simple way in Mathematica to prevent rule reordering? Let me give an example: ...
9
votes
3answers
245 views

substitution rules excluding subscripted variables

Suppose I have an expression containing p,Subscript[p,1],Subscript[p,2],etc. I want to ...
3
votes
2answers
120 views

Replacing Patterns In a List of Varying Length

I am working with an array of data that may look something like this. ...
3
votes
2answers
335 views
3
votes
1answer
180 views

Pattern matching a multivariate derivative

I can extract the parameters of a single variable derivative with the rule D[f[x], x] /. Derivative[order_][fcn_][variable_] -> {order, fcn, variable} ...
2
votes
1answer
66 views

ReplaceAll in an expression including large InterpolatingFunction

I have a large InterpolatingFunction that I'm transforming to another basis with a few simple multiplications and additions by (symbolic) constants. The ...
1
vote
0answers
60 views

Abridging Lists of Equations within NDSolve, Manipulate [duplicate]

I have a pretty little NDSolve function that I've finally decked out with manipulatable (by sliders) coefficients, which changes the graph in real time. However, I ...
8
votes
2answers
689 views

Mathematica rule substitution memory

First I present the specific programming question, and then I provide further background details. Given an expression in Mathematica, say f=3x+7y, there are two ...
7
votes
1answer
216 views

Is it possible to specify a context-sensitive, “depth-agnostic” rewrite rule?

I'm using the term "depth-agnostic" in this post to describe structural patterns featuring a "target" sub-pattern that can occur "at any depth" relative to one or more "context" sub-patterns. As a ...
7
votes
3answers
249 views

Safely nesting RuleDelayed

Say I have the following, straightforward-seeming functions: ...
6
votes
1answer
390 views

ReplaceAll inside an Iterator

I'd like to apply a set of rules to an expression defining the iterators of the table, like this: ...