# Tagged Questions

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

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 ...
327 views

### Unexpected behavior of rule matching a pattern

I am a beginner exploring the world of Mathematica. I expected the following code T[6, 5, 4, 1, 2, 3] /. {T[a___, 1, b___] -> Length[List[b]]} should return ...
1k 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 ...
357 views

### Is there a faster way to Map an Association?

Consider mapping an existing Association in a manner such as this: ...
6k 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., ...
4k 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}} ...
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 ...
354 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 <...
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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 ...
475 views

### How to switch from List of rules to Association? [duplicate]

Considering we have a list of rules: ...
489 views

### substitution rules excluding subscripted variables

Suppose I have an expression containing p,Subscript[p,1],Subscript[p,2],etc. I want to ...
534 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 ...
554 views

### Using ReplaceAll to replace a head

Why would this work to replace the head b with newHead: ...
531 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. ...
6k 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 ...
349 views

### ReplaceRepeated seemingly omits some rules

Is there a simple way in Mathematica to prevent rule reordering? Let me give an example: ...
1k 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 ...
327 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: ...
574 views

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

In my program I have an expression which looks like: ...
378 views

### Fill out blanks with a upcoming number in a list?

I have a bunch of arrays looking like this: {"", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", ...
935 views

### Replacing Tan[x] with Sin[x]/Cos[x]

Why doesn't this work? (1 - Tan[x])/(Sin[x] - Cos[x]) /. Tan[x] -> Sin[x]/Cos[x] I get back: ...
378 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 ...
167 views

### How to ReplaceAll independent of depth?

I have a big list which in principle can be described as this more compact list : ...
196 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*) ...
332 views

### Pattern does not match with Orderless head

Why does the following pattern matching not succeed? ...
637 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 ...
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 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 ...
2k views

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

For example, I have: $a=\sum _{r=1}^n x_r \left(\left(\sum _{i=1}^n x_i-x_r\right){}^2-\sum _{i=1}^n x_i^2\right)$ ...
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### 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 ...
1k views

### Replace symbols with values without evaluation

If I have assigned values to a, b and c: a=7; b=5; c=6; ...
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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, \...
334 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 ...
398 views

### Select a particular rules out of a list

rule = {beta -> 4, alpha -> 2, x -> 4, z -> 2, w -> 0.8} Select[rule, beta] Select[rule, beta &] Select[rule, beta -> _ &] How would I ...
588 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: ...
192 views

### Efficient way of setting up a rule

I tried to define a simple rule defining how λ acts on ψ[n]: myrule1 = λ ψ[n_] -> α[n + 1] ψ[n + 1]; The result I get is ...
1k 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 ...
1k 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 ...
362 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 ...
2k views

### 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 ...
376 views

### 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 ...
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. ...
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]] ...
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....
682 views

### How to replace a space by a comma

in this expression = "{1 2 3 4 5 6 7 8}", I want to replace each space by a comma , to get ...
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 ...
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: ...
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### 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}...
Here is the simple task. In reality, it's far more complicated, but it comes down to this. I want to take the expression $\frac{y}{x^2}$ and replace $x^2$ with $k$. This doesn't work: ...