# Tagged Questions

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

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### 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 ...
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### 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 ...
3k 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 ...
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### 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 ...
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### 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 ...
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### Using results of Reduce

Suppose I have function f: f[x_, y_] := 50000 + x 30000 + y 35000; Now I want to find the x and y when f[]<=200000. I use Reduce: ...
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### Options which require RuleDelayed

For some functions in Mathematica it is important to use RuleDelayed. One prominent example is the EvaluationMonitor for ...
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### Pattern does not match with Orderless head

Why does the following pattern matching not succeed? ...
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### 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 <...
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### 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., ...
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### Why Infinity /. _?(# < 6 &) -> 0 replaces Infinity with ComplexInfinity?

Suppose I define a matrix: mat = { {Infinity, 4, 9}, {6, Infinity, 10}, {8, 9, Infinity} }; Now I want to replace all values smaller than ...
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### How to change element color in Periodic Table?

The command ColorData["Atoms", "Panel"] generates a periodic table. As I don't want to reinvent the wheel, I asked myself how to change the color of each cell ...
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### ReplaceRepeated seemingly omits some rules

Is there a simple way in Mathematica to prevent rule reordering? Let me give an example: ...
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### A replacement problem

list = {1, x, 3, x, 4, x, x, 3, 4, 3, x, 2, 3, x, 8, 7}; If there is exactly one integer between two x I want to replace it with y: ...
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### Apply multiple functions to parts of a nested list [duplicate]

data = {{1, a, x, "one"}, {2, b, y, "two"}, {3, c, z, "three"}} I want to apply a list of four functions {f, g, h, m} one ...
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### Equivalent of ReplaceAll for Associations?

Is there a nice (built-in) way to apply Replace-style rules to key-value pairs in an association? Something like ...
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### 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 ...
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### ReplaceAll with Associations instead of Rules

I have just noticed that x /. <|x -> 123|> evaluates to 123 In other words, the association seems to behave as a ...
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### 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. ...
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### How to assign a list of numbers into letter grades

Here is my list: ...
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### 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 ...
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### 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 ...
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### 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. ...
815 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. ...
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### Is everything in Mathematica ultimately stored as a rule?

My current understanding about Mathematica is that everything, at the lowest level, ends up as replacement rules. First question: is this true? Second question: does Mathematica "gloss over" these ...
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### 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, \...
487 views

### substitution rules excluding subscripted variables

Suppose I have an expression containing p,Subscript[p,1],Subscript[p,2],etc. I want to ...
501 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} ...
1k 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 , \...
299 views

### why MatchQ is fast and Replace slow?

Consider a large expression, say a polynomial with 25 terms expr=Product[Unique["a"],{i,1,25}]; to which you apply the following replacement rule: ...
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### Dispatch displays rules incorrectly and evaluates when displaying

Bug introduced in 10.0.0 and fixed in 10.0.1 Consider this a = 3; disp = Dispatch[Unevaluated[{a -> 2}]] We see the rule ...
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### 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 ...
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### 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: ...
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### Opposite of Alternatives in a Rule

Mathematica provides Alternatives, to match one of several patterns. In a rule, this is used as p1|p2|p3:>replacement. I ...
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Executing: ...
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### 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 ...
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### Replace operators

/. can be used to replace variables but how can one replace operators. For example in a * b, ...
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### Fill out blanks with a upcoming number in a list?

I have a bunch of arrays looking like this: {"", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", ...
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### For a given expression: if it appears, remove it, but if it is absent, add it

While reformatting Szabolcs's code from (42660) I noticed this interesting operation: ...
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### Replace and Association

I'm surprised that I can't find this question already, so perhaps I'm missing something obvious. I would like to take a list of associations and remove any with value ...
283 views

### Is there a programmatic equivalent of Edit > Find…?

Most things that can be done via the front-end interface in Mathematica can also be accomplished by some function. Is that the case for find-and-replacing? That is, is there some code I could execute ...
202 views

### Timing problem with ReplaceRepeated

I have the following data: ...
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### 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 ...
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### How to replace the first occurance in an expression instead of replacing all?

Is there a function that replaces the first occurance of the expression instead of replacing all? For example, if I have HoldForm[x + 2 + 4 + x] /. x -> 4, is ...
320 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"] ...
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### 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 ...
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### What kind of patterns in a list of rules would benefit from being Dispatched?

I have a long list of rules for manipulating expressions. They are of the form: ...
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### 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: ...