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

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26
votes
1answer
910 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 ...
4
votes
2answers
120 views

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} ...
1
vote
3answers
1k 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 ...
-1
votes
2answers
529 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 ...
1
vote
2answers
297 views

How to generate patterns by a list of integers

I have a list of integers {3,4,2,2}. This list will give patterns {x_,_,y_,y_,_,_,z_,z_,w_,w_,x_} and ...
14
votes
3answers
381 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 ...
8
votes
1answer
230 views

Transformation rule on a list of non-negative integers

I am trying to create a transformation rule that takes a list of non-negative integer values of any length, finds a non-zero entry in the list, adds 1 to all preceding numbers, subtracts 1 from the ...
3
votes
1answer
130 views

How to make a pattern to change x^(2/y) to (x^2)^(1/y) for any x and y?

This might have been asked before. Please let me know if it is. I was looking at an interesting Mathematica question in students forum and trying to solve it, and a chance to learn more about ...
1
vote
2answers
204 views

A function that only evaluates on lists of pairs [duplicate]

Possible Duplicate: Why doesn’t PatternTest work with Composition? I'd like my function to only evaluate when the argument is a list of pairs. It seems like ...
1
vote
1answer
216 views

Functions that operate on symbolic matrices?

I'd like to write functions that operate on symbolic matrices, and do nothing when fed anything else. ...
4
votes
2answers
175 views

How to use Optional as an omissible parameter in pattern-match?

Below is a function intended to test if an expression is a polynomial in which all the coefficients and exponents are integers: ...
3
votes
1answer
267 views

How do you pattern match a DataDistribution

I have a function, f[dist_, samp_]:=somework[dist, samp] that I want to return Null or zero if passed a null distribution. I ...
2
votes
3answers
128 views

Applying several patterns to `Split`

Please consider the following: Split[data, patterns &] patterns=Not[#=="a"]&&Not[#=="b"]&&...&&Not[#=="blabla"]; How can I define ...
8
votes
2answers
243 views

Replacing product expressions - named vs. unnamed pattern?

Suppose I have an expression of the form a b c d + x y z The FullForm of this is ...
17
votes
2answers
402 views

Pattern that matches colors

Suppose I'm writing a function that takes a color as a parameter; for example: drawShape[color_] := Graphics[{Style[Disk[], color]}]; But if the caller inputs an ...
7
votes
1answer
264 views

How does Mathematica wrap code for front-end needs? Why does this wrapping affect the evaluation?

Mathematica wraps any expression with some boxing code before showing the evaluation result in the front-end. Unfortunately, the wrapping algorithm and its position in the Mathematica end-to-end flow ...
6
votes
1answer
326 views

Pattern matching in subscripted variables

I am trying to use subscripted variables as symbols and provide assumptions elegantly for them, e.g. in order to simplify logs, I'd like to have ...
0
votes
1answer
254 views

How to collect terms of a given type (with subscript and power) in an expression?

Suppose that I have an expression: ...
2
votes
1answer
165 views

replacement rule to pull independent expression outside of Integrate

I'm trying to write a fairly general replacement rule that will pull expressions independent of the variable of integration outside of Integrate, since Simplify and ...
14
votes
5answers
755 views

Getting number of binary digits combinations without “forbidden” patterns

I need to get the number of all combinations of binary digits in an 8-digit binary number, but not including those that follow some "forbidden" patterns like these: ...
0
votes
2answers
253 views

Pattern constraint for two or more variables

Is it possible to have a pattern constraint for a function with two or more variables where the pattern is a relation between the vars being accepted e.g. ...
8
votes
3answers
505 views

How can I convert x^2 to x*x?

When I try the following code: a b^2 c /. b c -> e Mathematica gives me: a b^2 c but what I want is: ...
8
votes
1answer
236 views

Is it possible to specify a context-sensitive, “depth-agnostic” rewrite rule?

I'm using the term "depth-agnostic" in this post to describe structural patterns featuring a "target" sub-pattern that can occur "at any depth" relative to one or more "context" sub-patterns. As a ...
21
votes
5answers
666 views

How can a big table be treated as a database?

I often work with big tables that I want to treat kind of like a database. Here's an example table. ...
10
votes
4answers
397 views

How to match expressions with a repeating pattern

The expression I want to match obey a simple pattern that repeats it self a number of times. f[a]@f[b]@f[c]@...@f[X] How would you match all expressions of this ...
10
votes
3answers
657 views
37
votes
6answers
2k 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 ...
6
votes
1answer
496 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 ...
8
votes
2answers
222 views

Why does the name of a pattern affect the result of a transformation rule?

I was playing a little dirty, trying to get a template for defining a Curl[] operator. I wrote the following rule, which I knew was going to spit out a few ...
12
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 ...
14
votes
6answers
2k views

Counting negative values in list

I would like to count the negative values of a list. My approach was Count[data, -_] which doesn't work. How can I tell Mathematica to count all numbers with ...
10
votes
4answers
498 views

How to use pattern matching to assign values to Subscript[f,x_]?

I want to define two subscripted functions Subscript[f,1] and Subscript[f,2]. To keep the assignments local, I would like to ...
1
vote
2answers
171 views

Using patterns in ReplaceAll to extract elements from tuples at arbitrary depths

Please consider the following: I need to extract from MyList all last parts of each 3-tuple. ...
11
votes
4answers
588 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 ...
12
votes
4answers
361 views

The gap between MapAt and ReplacePart for 2D data tables with headers

Consider a relational table derived from survey data, where each column ("001-01" ...) represents a responder and each row (...
15
votes
3answers
471 views

Grabbing a number of characters around a string pattern

If I have some string data: text = StringTake[ExampleData[{"Text", "DeclarationOfIndependence"}], 400] "When in the Course of human events, it becomes ...
5
votes
2answers
206 views

Delete contexts from a string representation of a symbol

I want to delete the string representing the context of a symbol. For info I need such a functionality in my ShowIt function defined here I'd like to know how I ...
11
votes
3answers
739 views

Specifying string patterns in DeleteCases

It seems that DeleteCases is not compatible with string patterns, at least directly (see, for example, this question). Is this true? If so, why is this the case? ...
5
votes
3answers
670 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 ...
7
votes
1answer
228 views

Built in way to de-list singletons?

Is there a built in method to de-list singleton expressions, like this rule-based solution: expr_ :> If[Length[expr] == 1, First@expr, expr] In data ...
9
votes
3answers
660 views

Find subexpression to minimize leafcount after replacment with temporary variable

Given an expression expr, is there an automated way to find a subexpression subexpr such that replacing ...
41
votes
2answers
843 views

How is pattern specificity decided?

Mathematica has a notion of pattern specificity, which is a partial ordering on patterns. The rules (e.g. DownValues, ...
13
votes
2answers
431 views

How can I separate a separable function

I have a separable function $f[x,y]$, and I would like to find two functions $g[x]$ and $h[y]$ with $f[x,y]=g[x] h[y]$ where $g[x]$ doesn't depend on $y$ and $h[y]$ doesn't depend on $x$. Ideally, ...
10
votes
4answers
450 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 ...
9
votes
1answer
351 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: ...
5
votes
4answers
819 views

Creating lists from a string, separating words from numbers

Say I have a string that contains numbers and words, such as this one: string = "there are 1234 words and numbers 5678 in here $999"; How would I separate the ...
14
votes
4answers
699 views

Returning an unevaluated expression with values substituted in

Let's say I have a function formula[x_List] := (x[[1]] - x[[2]]) + (x[[3]] - x[[4]]); and I want to pass it a variable and get back the unevaluated formula with ...
3
votes
1answer
216 views

Pattern matching a multivariate derivative

I can extract the parameters of a single variable derivative with the rule D[f[x], x] /. Derivative[order_][fcn_][variable_] -> {order, fcn, variable} ...