# Questions tagged [core-language]

Questions on the basic structure of the Mathematica language (Wolfram language) including atomic data types, syntax etc

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### Central element of matrix

Let we have $(2\cdot r+1) \times (2\cdot r+1)$ matrix mat. Is there a better way to extract it's central element, rather than ...
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59 views

### Is it safe to modify system functions and distribute?

I am trying to add my definitions to FormulaData and looking through the source files It is clear that one can do that systematically by adding some DownValues to system functions and elements to ...
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135 views

### Special case of CellularAutomaton

I’m interested in multi-state CA in a closed 2D space and try to implement them using CellularAutomaton but do not understand how to do it. The first question is, ...
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### Proving Exact Answers to Logistics Map for 3-Cycles

Seems that I may have found a pair of exact solutions to the logistics map with cycles of period three. However, I’ve run into a bit of a snag in proving it because of some “ambiguities” in the ...
183 views

### List[...] + Association[...], or Association[...] + List[...], when does the order matter?

Values of a list can be added to an association's values like so, ...
435 views

### Extract result of Reap in a natural way no matter if it's empty

This feature has long troubled me, I would like to share it. If Reap has non-empty set of sown, result looks like: ...
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1 vote
60 views

### Random replacement in array

In the spirit of this interesting article of Stephen Wolfram I also decided to study some issues related to mutations. I’m working with simple {0,1} arrays and I’ve ...
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54 views

### Specific array filtering - code optimization

I have a nested list where all sublists have a length 2, eg: {{1,2}, {1,1}, {3,4}, {3,5}, ...} I need to filter it for two requirements: Delete all sub-lists ...
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### Why doesn't b = a; f[a_] := b; f[2] return 2?

As the title asks, why does b = a; f[a_] := b; f[2] evaluate to a rather than 2?
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141 views

### Catch error propagation

I'd like my function to work only for arrays with all positive members, eg: myf[arr_] := Reverse@arr /; AllTrue[arr, Positive]; So ...
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140 views

### How to implement this zip function? zip[g,{f[{a,b}],f[{c,d}]}] to f[{g[{a,c}],g[{b,d}]}]

I have a function that returns an expression in the form f[{a,b}], and I use this function twice and assemble the expression ...
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### Clearing a list of variables: Problems trying to control the order-of-evaluation [duplicate]

I am having trouble controlling the order of evaluation of mathematica expressions. What I would really like is a general solution, in the form of a pair of functions ...
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### FindClusters with custom DistanceFunction

Let we have an array of integers e.g. Range@365. Each index has a specific value by which clusterization of integers should be done. But these values cannot be ...
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### PatternTest in Function

This is probably trivial and already asked but I did not find it. How to use PatternTest inside Function (...
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### Problem with RecurrenceTable of two variables

Let we have simple recursive function: ...
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157 views

### Evaluation control of nested With, If and Integrate

Can you explain the behaviour of the following? The first With outputs unevaluated If. So in the second ...
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### Parametric Minimize strongly revisited

Let we try to run this simple code: Minimize[{Cos[x + a/2], {0 <= x <= \[Pi], 0 < a < 1}}, x] It doesn't work. But ...
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41 views

### Strange behavior of MinimalBy [duplicate]

data = {{1, 2}, {2, 2}, {3, 3}}; MinimalBy[data, Norm@# &] Output: {{2, 2}} When applying numerically : ...
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125 views

### DuplicateFreeQ VS UnsameQ

What is the exact difference between DuplicateFreeQ @ arr and UnsameQ @@ arr ? I checked on many examples and found no ...
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241 views

### Converting to a scalar pure function without getting the warning messages

I am using this from the function repository for which I need to convert one of my functions into a unique form. A simple example is like this: Suppose I have, ...
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509 views

### What's the difference between With and ReplaceAll?

A wolfram Tutorial mentions that ReplaceAll and With are similar: The way ...
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501 views

### How does this code work?

I saw this thread and upvoted many answers there. Below is the answer by kglr (not my most favorite answer there, but it looks fun). I wonder if anyone could help ...
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### BlankNullSequence (___) when input variable is Null

f[x___] := Plus[x, -x] f[Null] gives output as 0 f[] ...
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497 views

### How to check if multiplication requires carries?

For some purposes I need to know if there are there any carries in the multiplication of two numbers, especially in base-2. How can we do this in Mathematica? Thanks to all, very interesting answers! ...
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81 views

### Problem with permutations

For a given binary array like {0, 1, 1, 0,..}, I need to find the shortest permutation, sorting it in standard order ...
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### Want Map function to apply over sum of terms but not product

For a given function F, if I use Map[F,a+b+c d], Mathematica returns, as desired: F[a]+F[b]+F[c d] ; However, for ...
1 vote
35 views

### Monitor inside core function

I like DistanceMatrix: its performance is surprisingly high, even for a big data. However, for a huge arrays and custom ...
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55 views

### MinimalBy with argument and value

I need to find element of some list arr which is minimal by some function f. But I need to get result in form ...
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31 views

### MapApply not converting numbers as strings to numbers

I have large vectors that were imported and came in as strings. I try to convert these to numbers using MapApply of ToExpression (and the "@@@" form of this). There must be some subtle ...
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1 vote
33 views

### Can symbolic sums of indexed arrays be simplified?

As a simple example, is it possible to simplify say Sum[Indexed[x, i], {i, 1, n}] == Indexed[x, n] + Sum[Indexed[x, i], {i, 1, n - 1}] If not, please explain ...
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### Function[0], Function[,0], and Function[{},0]: Is there any inherent distinction in the "academic" sense?

Note that Function[,0] is by default interpreted as Function[Null,0]. The following three calls all give ...
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### Problem with Association in DynamicModule

How can I understand the success of the first append but the failure of the second, here? (Mma 13.3.) Is there a ready work around? ...
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### How to test if the input is a positive fraction?

I would like to check if a fraction is positive. The difficulty arises when there are symbols. I would like to make the assumption that all symbols, variables, and indeterminates are positive real ...
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### How can I list the heads of an expression?

How can I check that a fraction contains only multiplication and power? I would like to check if it contains only the heads of Power and Times. I am wondering how to get a list of heads for a fraction....
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129 views

### Condition inside pure function

Why condition /; not work inside pure function? Suppose we have: ...
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1 vote
53 views

### Why do rules not default to local scope? [closed]

Consider the following: 80 //. a_?EvenQ -> a/2 a = 3 80 //. a_?EvenQ -> a/2 which outputs: 5 3 3/2 I think I understand ...
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### Using Cases to select expressions from a list

I am using v12.2.0 on Win7-x64. I want to use Cases to select the Times and Plus cases from ...
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### Why does using a variable name as pattern name determine its context?

Checking the context of a fresh variable inside Begin-End, it gives the enclosing context. ...
1k views

### What is a function?

Regarding: Map[#[{2, b}] &, {Reverse}] The above works, but it makes my head spin. The documentation for Map says that the ...
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### With[{a=1},{b=a},b] in 13.2 does evaluate to 1 [duplicate]

This isn't documented, and the front end highlights the second comma and third argument in red, but it's used in DownValues[Once][[3]] and is very convenient. Anyone know more?
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1 vote
130 views

### How to convert a function with named arguments to a pure function?

A function is defined with named arguments. How can this function be converted to a pure function that uses slots (#). As a simple example, how can the following: <...
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1 vote
119 views

### Where does the result of thing["Properties"] come from?

Question I'll focus on the example stream=AudioStream@First@\$AudioInputDevices I can do stream@"Properties" to get a ...
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### Do not understand evaluation order of ReplaceAll [duplicate]

{x, x^2, Length@x, Subsets[x]} /. x -> {1, 2, 3} (* {{1, 2, 3}, {1, 4, 9}, 0, {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}} *) with error What ...
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330 views

### Delete first case

How to delete just first occurrence of given value from a list? Without sorting etc. Something like this: ...
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76 views

I am interested in the most efficient way to impose assumptions on indexed variables. In the following stylized problem, the following code ...
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### Using Unevaluated to get a list of symbol names

The official documentation of Unevaluated contains the following example: ...
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### Slots inside nested pure functions

I'd like /@ instead of Table or Map. But let we have it inside pure function: ...
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1 vote
59 views

### Get FullForm content

For this challenge I need to get FullForm as array, string or nested function. Especially for number expressions. The best I have achieved is: ...
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243 views

### How to implement Newton's Identities

I need to produce identities related to Newton's Identities of arbitrary order. More specifically, I need the identities in the following image for an arbitrary n: What I can't quite wrap my head ...
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