# Tagged Questions

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

58 views

### Why has FreeQ a quadratic complexity with high depth?

I am a little puzzled by the following test: ...
748 views

### Calculating weird numbers

A weird number is a number such that the sum of the proper divisors (divisors including 1 but not itself) of the number is greater than the number, but no subset of these divisors sums to to ...
150 views

### Confused by the opts : OptionsPattern[ ] pattern

I'm trying to make sense of the syntax in the clause opts:OptionsPattern[], as found in this standard "rule-based" (pseudo-)function definition pattern: ...
41 views

### What does __Rule do in Mathematica? [closed]

What does __Rule do in mathematica? I understand the __ is used for any repeated expression, but why is the Rule appended at the end? For example: Import nested JSON file Thanks!
117 views

### Match groups in regular expressions

I'm trying to understand Mathematica's pattern matching in strings, but I have some doubts. 99% of the time I need to a) check if a match occurs and b) retrieve the matched patterns. I come from ...
556 views

### Camel hump string split

Given System names of 2 or more characters: systemNames = Names["System`*"] // Select[StringLength[#] > 1 &] ; Is ...
116 views

### How to Pattern Match complicated patterns? [closed]

How can I get the output expressed in terms of p1 and p2 instead of exponentials? ...
114 views

### How to write a pattern that matches all functions

What is the correct way to match a function in an expression in the way that Cases[Sin[x] Cos[x], _Sin | _Cos, {0, Infinity}] matches ...
73 views

### Ordering in noncommutative multiply

I have an expression like s ** p1 ** p1 ** p2 - s ** p1 ** p2 ** p1 Which should be zero because the commutator between p1 ...
114 views

### How to apply ReplaceAll to denominator?

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: ...
102 views

### Pattern matching list of elements with different heads

I have a function, which I want to accept only a list of kind of elements belonging to a group. The task comes down to finding an elegant pattern suitable for easy to read function prototype. As an ...
358 views

### Pattern matching in nested lists

I'm sure this has been asked before, but I can't find the right combination of search keywords to find it. Apologies. I want to do a ReplaceAll on a list of lists, ...
60 views

### Emulating Case Pattern replacement

As most regular users, I have developed utility functions complementing the Wolfram language for frequent tasks. In particular, I have variations on Cases (see ...
121 views

### Dealing Repeated pattern in StringReplace

A problem about StringReplace When I'm running into this problem possible [bug] ...
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### Replacement of terms/Pattern matching involving products of derivatives of a function

In delving into Ramanujan summation, I'm trying to get a hold of the relations of the form \sum_{n=0}^\infty f(n)=\dfrac{h\frac{d}{dx}}{{\mathrm{e}^{h\frac{d}{dx}}}-1}\int_{0}^\infty f(x)\,{\mathrm{...
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### Where can I find mathematica documentation about @@@? [duplicate]

For example, to build a rule from 2 lists {a,b,c},{1,2,3},I use : Rule @@@ Transpose[{{a, b, c}, {1, 2, 3}}] : {a -> 1, b -> 2, c -> 3} OK, but how @@@ works ? (Black magic for me) I am using ...
54 views

### Pattern matching & simple replacement

I have a question about an expression that I want to modify. Here is the expression: ...
76 views

### Using patterns to modify TeXForm output

When I use TeXForm on a matrix I often want to replace some the output with some number of verticle and horizontal lines. Is there a way to get control over this, possibly using patterns? As an ...
91 views

### How to make Simplify/Expand work in patterns?

I am trying to calculate deriv of a complicated function and store the values for reuse. But the FullSimplify in my definition doesn't seem work all the time: ...
81 views

### Evaluation speed of apparently equivalent functions

Consider the following expressions: f[x_Integer] := x, f[x_] := x /; x ∈ Integers, f[x_?IntegerQ] := x All of the expressions above (and probably others which ...
68 views

### Generate all 3-permutations of the set {x, y, z, w, u, t} excluding the ones where 'u' is after 't' [closed]

I have to generate all 3-permutations of a the set $(x, y, z, w, u, t)$ without the ones where the element $u$ is after element $t$. So far I have generated all the the 3-permutations like such <...
308 views

### Orderless pattern matching

The MMA docs state that "In matching patterns with Orderless functions, all possible orders of arguments are tried". Why then does the following not work? ...
282 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 ...
3k views

### Using a PatternTest versus a Condition for pattern matching

My last question to the site resulted in several answers that involve using pattern matching in Mathematica, a feature I wasn't very familiar with at the time. I am currently reading Mathematica ...
2k views

### What best practices or performance considerations are there for choosing between Cases, Position, Pick and Select?

Cases, Select,Pick and Position each have different ...
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 <...
100 views

### Applying ReplaceAll to I (imaginary unit) [closed]

Why does I/.I->-I return -I but Exp[-I]/.I->-I yields ...
108 views

### Get the sum with cases

I have the following list: list = {{1, 2}, {2}, {3, 4, 1}, {5, 4}, {3, 3}, {a, b, c}, {e, f}, {g}, {}, {Sin[a], Cos[b]}}; I should use ...
327 views

### Counting subsequences (i.e., patterns) within a list?

I would like to count the number of subsequences in list. Say I have data given by: data = {1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1}; I would like to count the number ...
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 ...
109 views

### Write a function, write a pattern [closed]

I have the following list: list = {{1, 2, 4}, 6, 7, 8, {8, 2}, {3, 4}, {4, 5}, {1, 2, 3, 1}}; (a) I should write a predicate-function in combination with an ...
51 views

### Find/Write a pattern [closed]

I should find a pattern for the following expression: expr = {a^2, a^b, x^4, (x - 1)^2}; And that should be the result: ...
94 views

### Removing solutions which are particular cases of others

I have an algorithm which gives me a list of solutions (in matrix form, if it is of any importance) of an equation. Some of these solutions are particular cases of other. For example, in this list ...
96 views

### Surprising behavior when OptionsPattern is part of a larger pattern

Say we have a pattern defined as: pattern = {foo[OptionsPattern[]] ...}; We can then use MatchQ to see whether an expression ...
159 views

### Express block matrix in terms of matrix basis

I'm trying to construct a function that returns the multiplication table of a matrix Lie algebra. Assuming a basis of matrices, my definitions: ...
130 views

### Output function control and manipulation for efficient computation [closed]

I have taken note of a similar post related to modifying function parameters. I tried to adapt Kuba's solution to this post but I can't get it to work. I will illustrate my problem using a similar ...
118 views

### Why the flat f[x] is treated as ghostHead_[f[x]]?

While reading this answer I feel confused. If we do not care any specific detail of the original question, then ybeltukov's answer essentially makes use of the following fact ...
177 views

### How to trim the zeros from the right of a list? [duplicate]

I need to remove the zeros from the right of an integer list up to the first non-zero element. Such as {0,1,0,0,2,0,0}->{0,1,0,0,2}. Padding zeros can be simply ...
1k views

### Finding the period of an array of integers

A simple array of integers is given. The problem is to detect if a pattern is repeatedly occurring in the array, and find the length of that pattern. For example, for ...
3k views

### Find zero crossing in a list

I'm looking for a function that finds the index of the zero-crossing points of a list. Before I go making my own subroutine to do this, I was wondering if anyone knows of any built-in Mathematica ...
92 views

### Can we say that “all functions in Mathematica are some kind of pattern-matching-and-replacement procedures”? [duplicate]

Currently I am studying Mathematica programming, and when I study pattern matching and replacement, I find it is quite similar to functions. So can we say "all functions in Mathematica are some kind ...
508 views

### Adapting “Find and Replace” functionality to work with Patterns

I was thinking if there is something like Find and Replace (Crtl+F) functionality adapted to work with patterns. Probably not, but it seems possible to create this with some effort and skills in <...
218 views

### Assumptions with patterns

I want that Mathematica assumes every symbol like Subscript[s,i] to be evaluate as a real and positive number. I have tried ...
116 views

### Is there a way to search for Arithmetic Progressions in a list?

If you have a list of integers is there a way of searching that list to see if there is a trend of Ax+B in the list? Not using all of the numbers, just seeing what trends like that are embedded in a ...
212 views

### How to highlight the elements in a list that match a pattern?

For example, {{1,2,3},{1,2,3,1,2,3,4,5}}with pattern {1,_,3}is transformed to ...
147 views

### DeleteDuplicates in a list of 2-tuples under condition

Having a list of 2-tuples, I would like to delete such 2-tuples that have 0 at second position, but only those, whose first element is not unique in the list. E.g. ...
332 views

### Matching pair of numbers {a,-a}, where a is numeric

Imagine you have a list of pairs of numbers, such as {{2,-2}, {1,5}, {1,-3},{-3,3}} The task is to reduce the given list to a list of pairs of type ...