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

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0
votes
1answer
138 views

simplification rule with symmetry

What rule can you think of to replace the first line by the second? I have a bunch of expression like these, which I would like to simplify. All dependent cross terms must be written in the same ...
2
votes
1answer
176 views

A Sierpinski-ish structure, via 2D automata

The project is originally based on a puzzle proposed by EIORU at http://www.ptt.cc/bbs/puzzle/M.1342451949.A.00F.html (若您懂得讀中文 / if anyone happen to read Chinese^^) last July. The descriptions, ...
0
votes
1answer
120 views

Apply rule only if applicable? Check rule applicability? Custom unapplicable rule?

How to avoid recursion in the following example? ...
0
votes
0answers
35 views

How do I replace a variable with the answer from a solve function in the form k-> number + variables? [duplicate]

Possible Duplicate: Using the result of Solve in subsequent calculations extract values from replacement list I am trying to define a variable (k1) as ...
2
votes
1answer
107 views

Confused behavior using Dispatch to sort one list relative to another

I have a need to sort the entries of one list into the same sequence as the entries in a reference list. Because I have rather large lists involving strings, I'm trying to use Dispatch to accomplish ...
20
votes
1answer
510 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 ...
2
votes
2answers
132 views

Modify a sub-part of a sub-list only

I have this list: a = {{{0, 0}, {1, 7}, {2, 0}, {3, 2}, {4, 7}}, {{0, 0}, {1, 0}, {2, 1}, {3, 2}, {4, 7}}} and I'd like to transform it to this: ...
9
votes
1answer
210 views

error when defining a compiled function with ReplacePart

I always have difficulty in writing a non-trivial compiled function. I'm using Mathematica 9. Please see the following code ...
0
votes
2answers
123 views

How to use Solve rules as a function body?

Solve gives me an expression which I want to use as the body of a function. Rather than run Solve every time inside my function ...
9
votes
2answers
200 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"] ...
8
votes
2answers
160 views

Replacing product expressions - named vs. unnamed pattern?

Suppose I have an expression of the form a b c d + x y z The FullForm of this is ...
7
votes
4answers
190 views

Generating all matrices with 1 (possibly) replaced by -1

I have a matrix $M$, whose dimension I am unsure of, which has only $\lbrace0,1\rbrace$ entries. I would like to generate all the possible matrices that result from changing (some subset) of the $1$'s ...
0
votes
1answer
134 views

Extract a value from a list of InterpolatingFunction

By running the code n = 5; U[t_] := Table[Subscript[u, i][t], {i, 0, n}]; lines = NDSolve[{eqns, initc}, U[t], {t, 0, T}] I get the output ...
0
votes
2answers
77 views

Extract a List of Co-ordinates from a List of Complex Solutions

Let's say I have this list of solutions from a previous computation: ...
2
votes
1answer
134 views

#[[1]]//FullForm = 1?

I have a set of symbolic algebraic expressions that I'm trying to get some speed into. To illustrate the issue, I'll use a simple form like { k0 X, k1 Y, k1 Z}, ...
2
votes
4answers
186 views

Extracting RHS from Rule

In an example from another question, the rhs of a list of rules can be simply extracted: ...
3
votes
1answer
109 views

$Post with ReplaceAll [closed]

I'd like to have a ReplaceAll applied to every output in my notebook. When I try this using $Post, e.g. by writing ...
0
votes
1answer
76 views

What exactly happens when adding a Blank after a built-in function used in the rules of ReplaceAll?

Well, this question is just for curiosity, personally I never use ReplaceAll like this: ...
8
votes
2answers
313 views

Using ReplaceAll on SparseArray

I'm using SparseArray in a notebook in which I am doing complex conjugation manually, i.e. writing $\sqrt{-1}$ as i and applying ...
4
votes
2answers
141 views

Confusing ReplaceRepeated & Hold

I've been bootstrapping myself to the very alien world of Mathematica and there came my first WTF moment: ...
12
votes
1answer
319 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. ...
1
vote
1answer
1k views

Converting polar coordinate expression to cartesian coordinates

An intermediate step in my analysis requires me to work in polar coordinates, but I would like to convert the results back into cartesian coordinates. The conversion is very simple but tedious for ...
7
votes
1answer
195 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 ...
8
votes
7answers
264 views

Indexed replacement

Is there some equivalence of MapIndexed for rules? Consider a substitution on 3 a + 4 b + 21 c + .... The first integer I want to replace by 1, the second ...
6
votes
2answers
261 views

Conditionally replace rows in lists

I have a sequence of matrices/lists ...
7
votes
2answers
206 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 ...
5
votes
5answers
490 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}} ...
1
vote
2answers
148 views

Using patterns in ReplaceAll to extract elements from tuples at arbitrary depths

Please consider the following: I need to extract from MyList all last parts of each 3-tuple. ...
3
votes
2answers
212 views

Creating a Nearest function programmatically

I've been trying to work out how to create a Nearest function programmatically. My goal is to produce something similar to this, a hand-assembled function: ...
5
votes
3answers
1k 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 $\dot{x}=f(x), \quad \dot{y}=g(x,y)$ ...
1
vote
3answers
316 views

How to manipulate nested expressions?

I have the following expression, only slightly complicated, and I'd like to do two things: Plot the elements of the lists (though messy, all are in the same ...
3
votes
1answer
155 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} ...
19
votes
2answers
799 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 ...
4
votes
2answers
223 views

Returning Replacement Rules in a function and using it later on

I would like a function which returns replacement rules as some internal mathematica functions are doing and use the results in other functions. I could not find any information on that and I'm ...
2
votes
2answers
345 views

How to do substitution of variable with power in Mathematica?

I want to replace $x^{i+1}$ with $z_i$. EDIT: I have some latex equations, and wish to import them to MMa. How to replace x_i (NOT $x_i$) with $x[i]$ But it seems the underscore "_" has a special ...
7
votes
3answers
216 views

Safely nesting RuleDelayed

Say I have the following, straightforward-seeming functions: ...
3
votes
1answer
134 views

Set promotes Rule to RuleDelayed?

In mentally building a model of how Mathematica works, I naively expected Set to create a Rule in a symbol's ...
9
votes
4answers
206 views

Leave expression tree formatting the same when a replacement rule is applied

If I type e1 := 3 x + 2 (1 + y) z // TreeForm, I get an expression tree. If I then type e1 /. x -> 3, I get another ...
4
votes
3answers
601 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]] ...
0
votes
1answer
114 views

Numerical rule evaluation -> {True, False} to deviation of target equation

I solve some equations numerically with FindRoot[] returning a quadruple {1,2,3,4}. Because the solver sometimes do not find any roots depending on parameterization of these equations I select only ...
0
votes
1answer
702 views

Plot is not showing [closed]

I've used Wolfram Mathematica 8 Trial version for two days. Any pointers are appreciated. Thanks in advance! EDIT: There are supposed to be 4 plots, but only 3 are showing. Everything works except ...
8
votes
2answers
174 views

Representing a value in an output as a self defined variable

I'm trying to find a way to have Mathematica always represent a numerical value as a self defined variable that I define using lhs=rhs. For example, if I execute ...
4
votes
2answers
416 views

Replace expressions by self defined symbols

I have a list of expressions like the following: ...
5
votes
2answers
597 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 ...
6
votes
1answer
283 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: ...
3
votes
3answers
545 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". ...
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., ...
19
votes
2answers
1k 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
511 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 , ...
8
votes
2answers
610 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 ...