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

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3
votes
2answers
137 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 ...
8
votes
4answers
413 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 ...
6
votes
4answers
463 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: ...
9
votes
5answers
306 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 ...
16
votes
3answers
550 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 ...
3
votes
1answer
95 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 ...
4
votes
2answers
232 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 ...
3
votes
2answers
104 views

Pattern match any member of a Context

Let's say I have four functions: x, y, X`x, and X`y. ...
5
votes
2answers
175 views

Why rule does not work if Flat attribute?

The following works: ...
2
votes
1answer
197 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 ...
-1
votes
3answers
184 views

How to systematically classify Mathematica expressions?

How to systematically classify Mathematica expressions? I can think of using Head[], Depth[], ...
9
votes
3answers
670 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: ...
6
votes
2answers
217 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 ...
20
votes
1answer
660 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 ...
3
votes
2answers
109 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
779 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
382 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
270 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 ...
13
votes
3answers
343 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
189 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
124 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
167 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
198 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
170 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
242 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
122 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
189 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
360 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
249 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 ...
4
votes
1answer
286 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
190 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
137 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 ...
0
votes
2answers
200 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
496 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: ...
7
votes
1answer
216 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 ...
19
votes
4answers
559 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
309 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
454 views
35
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
391 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 ...
7
votes
2answers
211 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 ...
8
votes
2answers
744 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
424 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
164 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
471 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
322 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 (...
5
votes
2answers
198 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 ...