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

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18
votes
6answers
1k views

Using patterns in pure functions

Pure functions may be handy if you don't want to assign your function a name. For example I would calculate $x(x-1)$ for some numbers $x$ by ...
15
votes
6answers
964 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 ...
14
votes
3answers
387 views

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 ...
11
votes
9answers
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 ...
10
votes
3answers
382 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 ...
11
votes
4answers
291 views

Recognizing special cases of a defined function for permuted arguments

I have a number of ugly ways to implement the following pattern recognition task, but I'm looking for something elegant to keep my notebook tidy. I need to define a function of six variables ...
11
votes
1answer
382 views

Selectively clear DownValues

How can I clear a subset of a symbol's DownValues ? For example, suppose I have created some DownValues for $f$ like this: ...
9
votes
5answers
272 views
6
votes
3answers
254 views

Converting expressions to “edges” for use in TreePlot, Graph

This question is similar to this: Nested list to graph. How to "flatten" an arbitrary expression, eg expr = a[b[c, d[e][f], g], h] to a list of key-value pairs ...
3
votes
1answer
198 views

Custom operators; custom pattern matching with pure functions

What I'm trying to achieve in Mathematica is the creation of a binary operator whose operands are both pure functions over the natural numbers. The result of the operator should be another pure ...
6
votes
3answers
515 views

Function with zero or one arguments

Is there a neat way to define a function with a single optional argument that defaults to an empty sequence? For example, suppose I want to define a wrapper for ...
6
votes
2answers
313 views

Rule for orderless function Times

I have problems extending a replacement rule. Schematically, this is the situation: I have an expression and a rule, and they work perfectly together. ...
5
votes
3answers
198 views

Pattern match for nested Association

Suppose I have Association testAssoc=Association[a->Association[1->1,2->2],b->Association[1->1,2->2]] which ...
3
votes
1answer
256 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 ...
2
votes
2answers
85 views

Strange failure of Series and Derivative

I just spend three hours and posted two Questions trying to figure something out, and it turned out all the confusion was caused by this mysterious quirk. I want to expand g[x,v] in v at v=0, using ...
26
votes
1answer
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 ...
22
votes
4answers
1k views

Detecting patterns of black and white stones on a 2D board

I'm writing a program to play a game of Pente, and I'm struggling with the following question: What's the best way to detect patterns on a two-dimensional board? For example, in Pente a pair of ...
18
votes
4answers
829 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 ...
10
votes
4answers
490 views

Building a tree

Given a list of word characters, such as this one, I'd like to build a tree, similar to this makeTree function, but with the tree in a different format. So, for an input such as ...
8
votes
2answers
451 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 ...
17
votes
6answers
823 views

Split a string at specific positions

Given a string of alphanumerical characters, how to split it simply and quickly at the center of continuous letter-substrings? Is there an elegant and fast solutions out there in the "computational ...
15
votes
3answers
403 views

Highlighting pattern strings in a large text

I would like to apply Style to strings that are matched, for example, with one or more specified patterns or regular expressions, a string or a list of both, ...
14
votes
2answers
351 views

Pattern to match L, but not L[_]

I have an expression where I want to replace L but not L[_] For example, the following doesn't work and ...
12
votes
2answers
396 views

Split a Unicode string maintaining uppercase characters

I want to split a string according to a predefined set of substrings (lowercase), though the actual text can contain uppercase characters anyplace. The task is to find the matches, longer preferred ...
11
votes
4answers
646 views

Assessing argument type in set delayed function definitions

I'm wondering how to properly assess the type of arguments passed to functions defined with :=. I want my functions to be the most efficient, unambiguous and clear ...
7
votes
3answers
246 views

Pattern matching Q for rectangular data matrices

Given a List of rectangular nx3 arrays of data, each of the form {...,{x,y,z},...}, (the ellipses are not Mathematica pattern syntax, just for illustration). Some members of this list may be - by ...
6
votes
4answers
320 views

Is there a more Mathematica-y way to label these plots?

I am studying an infinite square well in the context of quantum mechanics. ...
5
votes
3answers
894 views

position of sequence of elements in list [duplicate]

Possible Duplicate: Finding a subsequence in a list Question The position of {3, 5} is the list {1, 3, 4, 3, 5, 5, 1} is 3. How can such a position ...
14
votes
2answers
1k views

Determine whether some expression contains a given symbol

Given a symbol t and an expression expr, how can I determine whether or not the symbol t ...
9
votes
2answers
283 views

Using Except with strings

Suppose that I have the following sample list, called list: list = {"bBb", "aAa", "aaa"}; Now suppose I want to select the ...
6
votes
1answer
531 views

Count sublists which match pattern

I have a list which looks like this: data={{12,0},{0,0},{20,1},{0,0}, {0,-1}}. Now I would like to count the number of sublists which: have both slots zero the ...
4
votes
4answers
513 views

Listing matrices up to symmetry

I am interested in the equivalence relation on N x N binary matrices, in which two matrices are equivalent if one can be obtained by rotating/reflecting the other. I would like to obtain a list ...
4
votes
2answers
975 views

Classifying poker hands by pattern matching

I am working on this question posed in a Mathematica course revised in 1998. Here are the instructions: Poker Hands You are to define and show working examples of a function "...
3
votes
1answer
191 views

Inheritance in Mathematica using pattern matching on UpValues

Edit: I think in my original post, I missed emphasizing the main point. This is mainly a pattern matching question. If you're interested in the 'why' of this question, please read the original post ...
9
votes
5answers
424 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 ...
7
votes
4answers
857 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 ...
4
votes
3answers
120 views

Extracting subscripts and superscripts

Suppose I have several types of expressions (in some random order) of the form Power[Subscript[g, a], μ] which is $g_a{}^\mu$ ...
4
votes
2answers
217 views

Alternatives ordering affects pattern matching in Cases?

Given expr = f[x, g[y], z] In the following query, the pattern h_[__, c_] appears as last slot in ...
4
votes
4answers
585 views

More elegant way

I read ReplaceOrRemoveInvalidOrMissingData Mathematica documentation, and I tried to apply the same approach to my dataset. I've got two problems, but one is only a style problem! There is one more ...
3
votes
3answers
92 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: ...
9
votes
1answer
259 views

How to define function that can change patterns

Given time series data as follows: data = {{{2011, 1, 13}, 10}, {{2011, 2, 14}, 17}, {{2011, 3, 15}, 20}, {{2012, 1, 16}, 30}, {{2012, 2, 17}, 40}}; ...
5
votes
2answers
235 views

Pattern matching deletion of list items [duplicate]

Possible Duplicate: How can I remove B -> A from a list if A -> B is in the list? I'm working toward building a graph and use some code to construct my rules which results in a form ...
4
votes
6answers
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 ...
4
votes
2answers
414 views

Pattern test for variables during function definition

I am having a problem with pattern testing on variables during function definition ...
4
votes
1answer
329 views

Path queries for tree-structured data

Can anyone suggest documentation or tutorials for developing path queries and indices for (XML-like) tree-structured data? Suppose data is organized hierarchically in key->value pairs, eg: ...
3
votes
2answers
150 views

Matching a case when one element in a pair is Null

I've got a dataset of laitutdes and longitudes. Unfortunately, some of the dataset was from when a time when lat/longs weren't constantly recorded. So I need to remove the invalid data before working ...
3
votes
1answer
279 views

Simplify equations with pattern assumptions

When simplifying an expression using Simplify[expr, assumptions], the assumptions has to be explicit. Is it possible to simplify an expression with pattern ...
3
votes
3answers
436 views

How to do Cases with multiple related patterns?

I would like to write a function similar to Cases, but can search for a group of related patterns together. For example, ...
2
votes
1answer
118 views

Why is there a difference when formulating patterns for Select and FirstPosition?

Select[{1, 2, 4, 7, 6, 2}, # > 2 &] Gives {4, 7, 6}. OK! So one should think that the following would work: ...
2
votes
3answers
97 views

Testing for a vector of reals [closed]

Suppose I define: RealVector[expr_]:=VectorQ[expr,NumberQ[#]&&Head[#]===Real)]; Then: ...