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

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6
votes
5answers
217 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, ...
1
vote
1answer
239 views

Equating and solving equations that have been generated using table[]

I am in the process of trying to use Mathematica to find the coefficients of transmission and reflection for the wavefunction of a beam of particles tunnelling across any number of identical potential ...
2
votes
0answers
111 views

Generalization of a rule to N arguments

I am trying to apply a series expansion on a function x[t1,t2,...tn], with an expansion parameter a. For ...
3
votes
1answer
177 views

Shortening the syntax {var1, var2} /. # & /@ list

I noticed that I often turn out to have a list of substitutions in the form ...
-1
votes
1answer
84 views

How to make rules for changing parameters

I have one boring problem with changing parameters in printing output. If I have equation ...
1
vote
3answers
91 views

How can you form a variable from a function and its arguments?

Is there a way to make the general replacement foo[x,y,z]->fooxyz so that I can treat the x_i as variables so that I will obtain foofgh from the following: ...
13
votes
1answer
568 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 ...
1
vote
1answer
155 views

Improving the plotting time of a very complicated expression

The quatity $R$ is defined by a complicated expression in terms of $a_1,a_2,\ldots,a_n$. Now each $a_i$ is a function of $x$, $a_i(x)$. I would like to know what is the most efficient way to ...
18
votes
3answers
310 views

Options which require RuleDelayed

For some functions in Mathematica it is important to use RuleDelayed. One prominent example is the EvaluationMonitor for ...
1
vote
0answers
63 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 ...
9
votes
1answer
316 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 ...
10
votes
3answers
347 views

substitution rules excluding subscripted variables

Suppose I have an expression containing p,Subscript[p,1],Subscript[p,2],etc. I want to ...
5
votes
1answer
152 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 ...
10
votes
2answers
827 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 ...
2
votes
2answers
444 views

Mass Symbolic Manipulation with Subscripts? (from plaintext Input)

The simplest example of the change being sought is a greek letter, typed in as plaintext nu, and its may be replaced by the symbol, ν: expr = 3nu*kx*ky+ ...
11
votes
4answers
394 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} ...
0
votes
2answers
85 views

Replace expression using a tuple

Given an expression in x, y, z (for example), and a list with three elements, like ...
0
votes
0answers
57 views

Problem using replace to simplify logarithms [duplicate]

Is there a way to combine logarithm terms like 9 m Log[m]-9 m Log[M]+16 m M Log[m]-16 m M Log[M] into ...
3
votes
1answer
321 views

Replace elements in a list

Suppose that I have a list: ...
1
vote
1answer
302 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
313 views

characteristic polynomial based on differential equation

I have this differential equation: $$\ddot{x}-\frac{1}{6} \dot{x} - \frac{1}{6}x = e^t$$ When I DSolve it looks like this: ...
5
votes
2answers
136 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 ...
1
vote
1answer
103 views

given n lists, get list of applications of function to n-tuples

Is there a built in function or an easy rule to do the following transformation? H[{A[0], A[1], ...},{B[0], B[1], ...},...] into ...
1
vote
3answers
180 views

Help me to find a way to do this repetitive stuff

I'm trying to do this: ...
16
votes
1answer
299 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 ...
1
vote
1answer
184 views

Match and replace subexpression

I would like to replace the expresion $(n1-1)$ to $z1$ in following: In[1] := 2*n1*p[n1-1,n2] Out[1] := 2*(z1+1)*p[z1,n2] I have tried ...
11
votes
3answers
406 views

Replace operators

/. can be used to replace variables but how can one replace operators. For example in a * b, ...
3
votes
2answers
522 views
4
votes
2answers
92 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 ...
8
votes
3answers
253 views

Applying a transformation rule on an Image

I haven't been able to figure out why the following doesn't work: ...
2
votes
1answer
120 views

Replace an expression with a slightly tricky LHS transformation

I would like to make the substitution x^(11*y) -> r in the following equation x^(11 *y^z) - 1 to end up with: ...
5
votes
1answer
279 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
197 views

Generating replacement rules programatically

I would like to generate sets of replacement rules programatically for predefining some permutations. So a function ...
8
votes
6answers
1k views

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

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

Unique[] in RHS of rule

I have a function, explicit that takes dot product of two symbols, and replaces it with repeated dummy indices generated by ...
2
votes
2answers
119 views

Using a predicate to control the application of a rule in a replacement

How can I make a replacement rule that will only be applied to those parts of an expression that will not break a condition placed on the whole expression? For example, suppose I have ...
1
vote
0answers
44 views

plot[] with subsititution rule [duplicate]

I encounter this problem in Mathematica 9.0.1, I'm not sure if it ever happens in other version. Plot[{x, x + 1}, {x, 0, 10}, PlotStyle -> {Red, Green}] This ...
1
vote
3answers
143 views

Auto simplifications of power products

Mathematica automatically simplifies Exp[a]Exp[b] to Exp[a+b]. The problem is now that I can't do this ...
2
votes
1answer
143 views

How to transform an expression using algebraical instead of pattern rules [duplicate]

I would like to transform rules algebraically. A very simple example would be: - k^2 - 2 k x + x^2 /. {2*k -> 1} This transforms to: - $$k^2-2 k x+x^2$$ ...
8
votes
2answers
203 views

How do I write a function that can be used in a rule to modify both sides of an equation? [duplicate]

I sometimes need fine grain control over equations in Mathematica in order to help me understand how to solve a problem manually. A greatly simplified example of a session might be something like ...
1
vote
1answer
170 views

Efficient way to give symbolic elements symmetry

I have a symbolic expression that represents a set of operators. These operators have quite a bit of symmetry to simplify expressions: ...
7
votes
3answers
441 views

Piping and Replacement

I haven't been able to figure out how to use piping with certain functions. Specifically, I would like to apply a replacement at the end of a pipe, like the following: ...
0
votes
2answers
401 views

Converting a list of replacement rules into a list of real values [duplicate]

The following command outputs a list of replacement rules. ...
0
votes
1answer
137 views

How to change variable that has been defined in PDE?

I have a PDE function that contains a variable (named ka). I want to plot the result of my PDE in 1 plot using several different ka values. However, I'm not sure about how to write down this equation. ...
2
votes
2answers
488 views

Replacing values of a function

I have recently starting using Mathematica and have recently come to what seems as an impasse in my understanding of the language. If this is too "tell me how to do it" I would certainly understand. ...
4
votes
1answer
117 views

Replacing a combination of terms

I have a quite simple question. I have an expression that looks similar to $T=\frac{1}{a_1}-\frac{1}{a_2}+1$ and I'd like Mathematica to use $A=\frac{a_1}{a_2}$ to reformat the expression (if ...
3
votes
2answers
179 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 ...
0
votes
1answer
327 views

Make Mathematica wait before replacing?

How can I force Mathematica to completely evaluate a subexpression before using a replacement rule? For example, consider the following definition (for the series of ...
0
votes
1answer
164 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
217 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, ...