# Tagged Questions

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

189 views

### Is there any way to use head of Real and Integer altogether?

Is there any way to use the head of Integer and Real together like below? The below is not right, I know that, it is just for ...
197 views

### How to make a function that yields a number under power operator by using pattern matching?

Can I ask you a question related to function and pattern? I would like to make the function below work which doesn't yield return values I expect. How can it be done? ...
328 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 ...
56 views

### Remove cases where region specified incorrrectly

I am using MeshPrimitives to get a list of 3D components of a Mesh Region. Within that list, I normally get some incorrectly specified regions, such as ...
144 views

### How to debug this failing pattern-matching expression?

NB: this question is primarily about troubleshooting and debugging, and only secondarily about pattern-matching. IOW, I'm far less interested in getting an explanation for the situation described ...
96 views

### Strange result of DeleteCases in an association

The function DeleteCases can be used for associations, also with level specification. Here is an example where some values are associations: ...
121 views

### Using MapThread over 2 lists different length with criterion on minimal differences

Say I have 2 lists ...
406 views

### String matching balanced pairs of braces

I am trying to extract from a string in Mathematica all instances of \newcommand{ABC}{DEF} Where ABC and ...
919 views

### How to define a recursive pattern?

I want to translate this recursive syntactic definition into a Mathematica pattern1: $$\mathtt{x}: \begin{cases} \text{Null}\\ \{\textit{integer}, \mathtt{x}\} \end{cases}$$ In other ...
280 views

### How can I construct a recursive pattern guard?

I am modelling binary trees in Wolfram Language by writing them as three-element lists, like so: binTree = {nodeVal, leftChild, rightChild}. It does not yet matter ...
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 ...
77 views

### What is the role of the pattern object in this implementation?

In the documentation I found a nice idiom which allows me to do model fitting with interpolating functions. I think this kind of thing is amazing and a credit to the utility of an environment like ...
593 views

### Quick way to use conditioned patterns when defining multi-argument function?

I have a simple function that is supposed to only accept numeric values (i.e. complex/real numbers and constant symbols e.g. Pi, E). $$f(a,b,c)=a+b+c$$ Edit: I should have chosen a less simple ...
643 views

### How to match a cyclically repeating sequence?

I have run across several times recently where I must match a sequence that is cyclically repeating. For example, with the sequence, Sequence[a, b, c] how would ...
203 views

### Sow only if different from zero

I am trying to collect elements with Reap and Sow, where I am interested only in non-zero elements, that is I am trying something like that ...
78 views

### How to exclusively match in the numerator?

Here is an expression (one of many) that involves two complicated terms: \begin{multline}\text{expression} = \frac{\log \left(\frac{c}{d}\right) \left(2 a d F(a,b,c)+a^2 \left(a^2-2 a (b+c)+b^2+4 b ...
200 views

### Two ways to speed up slow Integrate[]s? (Can't do either)

I run into problems like this all the time on the complicated integrands I pass to Integrate. The following code works but takes a veeery looong time: ...
58 views

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

I am a little puzzled by the following test: ...
759 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 ...
154 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!
130 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 ...
562 views

### Camel hump string split

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

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

How can I get the output expressed in terms of p1 and p2 instead of exponentials? ...
116 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 ...
124 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: ...
104 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 ...
361 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 ...
125 views

### Dealing Repeated pattern in StringReplace

A problem about StringReplace When I'm running into this problem possible [bug] ...
87 views

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173 views

### 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{...
41 views

### 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: ...
81 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 ...
92 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 <...
312 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? ...
284 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 ...
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 <...
101 views

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

Why does I/.I->-I return -I but Exp[-I]/.I->-I yields ...
109 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 ...
329 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 ...