# Tagged Questions

Questions on expression testing and manipulation through pattern matching and constructing efficient patterns.

694 views

### Why is StringExpression faster than RegularExpression?

Edit: as noted by Albert Retey the performance difference is only seen when sub expression extraction is performed. If this test is used below the timings are similar: ...
131 views

### Flat function with repeated sequence

There are functions like Join[ ] that accept a variable number of arguments. Join is a flat function, as the order of arguments ...
264 views

### Variable scoping problem when mapping over delayed replacement

This is something that got me curious while I was playing around with Mathematica. Consider the following (contrived) example: ...
679 views

### Write a function that returns the logarithmic derivative

How can we write a function that if we input an expression f, it returns the log derivative $\frac{1}{f} \frac{df}{dx}$. We have to use a conditional or pattern test so that the function accepts any ...
179 views

### I am missing a function like HoldPattern

Temporary message: I am planning to edit this question, making the examples less confusing and by moving the things that are confusing to a separate question For any confusion about expressions that ...
208 views

1k views

### Mathematica equivalent of regex '\w{2,3}'

It beats me to write the Mathematica pattern equivalent to the regex: \w{2,3} Any ideas?
283 views

### Extracting sequences from a list?

Suppose I have a list of arbitrary length like {1, 2, 3, "Open", 3, 2, "Close", 9, 3, 4, "Open", 1, 0, "Close", 3, 5} and I am trying to extract the sequences ...
107 views

### Select gives different answers in versions 8 and 9

Consider the code below: s = Solve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x, InverseFunctions -> True]; Select[s[[All, 1, 2]], Element[#, Reals] &] In MMA ...
372 views

### I can't use PatternSequence with Cases

I have a list of integers: s = {4, 5, 5, 6, 2, 5, 3, 2, 4, 2, 1, 1, 4, 3, 4, 3, 1, 6, 3, 4}; And if I do this, both occurrences of 4 after 3 are replaced. ...
965 views

### How to collect terms with positive powers in polynomial

I am trying to collect all terms with non-negative powers of $x$ in polynomials like $\frac{1}{x^2}\left(a x^2+x^{\pi }+x+z\right)^2$ First expand the polynomial ...
352 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 <...
321 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 ...
2k views

### Removing zero values from ordered pairs

I have some processed data, which are basically a collection of ordered pairs in the form: {{x1, y1}, {x2, y2}, ..., {xn, yn}} Ordered pairs which have either a ...
192 views

### Problem with | operator in pattern matching

My first question here as I only got into Mathematica programming recently. Basically I have a large symbolic algebraic expression where I know certain variables with head pε appear with degree 2 in ...
885 views

### Adjacency List representation of a graph

I am looking to draw a graph knowing a simple adjacency representation of the graph like: A = {{1, 3}, {2, 3}, {3, 4, 5}, {4, 5}, {5}} Where ...
51 views

### transformation patterns don't work with constants

I want to do the reverse of PowerExpand and convert 2*Log[x+y] to Log[(x+y)^2]. The rule: t_ Log[x_] -> Log[x^t] works for ...
443 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 ...
171 views

### Named patterns as function argument descriptors

I have a function timeToMinutes that takes a 24-hour time as a string argument (in digital clock format, e.g., "15:47") and converts it to the number of minutes ...
425 views

### Keep Ordering of Bra Ket When Printing

I would like to keep the ordering of the bra ket-print but right now this doesn't happen. Any Idea? I tried playing with HoldForm but then i could evaluate the expression inside properly ...
268 views

### Convert logical relational expression to / from disjunctive and conjunctive forms?

I would like to convert logical relational expressions in disjunctive form, e.g., $$(x \lt -1) \lor (-1 \lt x \lt +1) \lor (x \gt +1)$$ into conjunctive form, e.g., $$(x \ne -1) \land (x \ne +1)$$ ...
405 views

### Question about using a pattern in ReplacePart

I noticed that "ReplacePart" can use pattern. For example: ReplacePart[{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}, {i_, i_} -> x] {{x, 0, 0}, {0, x, 0}, {0, 0, x}} So ...
638 views

### Soft-Match String Comparison

I have a list of names in which I would like to check for duplicates. However, within the list, the duplicates may not show up as exact duplicates of each other - for instance, ...
174 views

### Extending D for four-derivatives

I'm currently trying to consistently define rules for extending D[] to four-derivatives. As 'backend' I'm using the package TRACER (http://library.wolfram.com/infocenter/MathSource/2987/), which can ...
276 views

### Deep Pattern matching with repeating arguments

I have a function that accepts a single argument that is described by the following grammar: ...
282 views

### Using transformation rules to manipulate expressions

I'm trying out Mathematica as a replacement for LaTeX for typesetting math. It works very well, but I would like to take advantage of Mathematica's computer algebra capabilities as well. Specifically, ...
167 views

### Downvalues vs. Scoping for Functions

Regarding my recent question on using a default value for a function argument when a pattern was not met yielded some interesting answers, but the general consensus was "Yes this can be done, but ...
189 views

### How to achieve Set+Part like behaviour in custom Set function?

So I've been toiling away on my DataFrame package. I've been trying to get Set to work with it, but it seems it either can't be done (ie via ...
389 views

### Fastest way to test if a numerical array has complex elements

I am looking for the fastest way to test whether an n-dimensional numerical (NumericQ) array (in the ArrayQ sense) is complex or ...
395 views

### Patternmatching sets

How to match set-patterns against sets? A set (in the mathematical sense) is a list of elements without repetition and order of elements does not matter. For example, we have a pattern set ...
149 views

### Get DownValues that do not involve patterns?

Say I have a function with a few definitions that also implements memoization: f[x_] := f[x] = x^2 f[x_, y_] := f[x, y] = x^2 + y^2 I then apply the function to ...
678 views

### Best way to modify values in a list of rules?

Recently I had to solve a problem similar to this: Let's say I have a list of list of rules ...
817 views

### Function argument to default under certain condition

Inspired by this and this question (and how I handle this in practice), what is the best way to default a function value when a certain condition is met? For example, if a function is defined as: <...
451 views

### How can I remove matching sublists from my list?

I want to use DeleteCases (or any appropriate function) to remove elements of a list, which in turn are lists of fixed size. The rule I wish to apply is that any ...
775 views

### Position of a pattern-matched part of an expression

What you have A pattern, with certain part of it labeled As an example — Label: wally ...
145 views

### Detect highest order of derivative in expression?

Is it possible to detect the highest order (or generally all orders) of derivatives in an expression? Consider eqn = D[a[x,t],t] == D[a[x,t],x,x] How would I go ...
284 views

### Pattern matching repeated structures with named subexpression components

I am trying to write a function with a pattern that tests its arguments for a particular structure. But in that pattern I'd like to name a subpattern to make it easier to exract and operate on. The ...
130 views

### Pattern match any member of a Context

Let's say I have four functions: x, y, Xx, and Xy. ...
235 views

### Why rule does not work if Flat attribute?

The following works: ...
277 views

### Convert boolean test function to pattern?

What is a "reverse" to MatchQ? MatchQ converts pattern into boolean function. So how to convert back? Suppose I want to use ...
204 views

### How to systematically classify Mathematica expressions?

How to systematically classify Mathematica expressions? I can think of using Head[], Depth[], ...
965 views

### Pattern matching a pattern with patterns

Confusing title, I know. But the question is, if we have two patterns which have the same general structure but different names used in the patterns and different names: ...
261 views

### Is it possible to use PatternTest and Optional value on one Pattern simultaneously? [duplicate]

Possible Duplicate: How to Combine Pattern Constraints and Default Values for Function Arguments First a simple example: define a function "add" with two arguments, and its second argument ...
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 ...
141 views

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### Pattern matching not going over a list when using default values

if I execute the following command in Mathematica: {a,a^2,a^3}/.a^(n_:1)->b^(2 n) Mathematica returns: {b^2,b^4,b^6} ...
2k views

### How do I combine the data from two tables according to a rule of my own devising?

I have two matrices a = m x 5 and b =m x 5 (m is large, say 1,000) which are already sorted as below: How to generate a new matrix c = m x 5 which consists: Column 1: exact replica of Column 1 ...
679 views

### Correct way to compare arrays and do conditional evaluations

I would like to compare two arrays a=: and b= and get: using: (b/.(b_?Positive->a+b))//MatrixForm but this doesn't seem to work? Can ...
### Make mathematica treat $e_i^2$ as numeric
With NumericQ[symbol] = True, I can declare that a symbol is numeric. I want the expressions matching: $$e_{\text{i\_}?\text{IntegerQ}}^2$$ to be treated as ...