Skip to main content

list manipulation - Delete redundant {x,y} pairs


Working through the problems from Hazrat's Mathematica book and there's a simple exercise to find all the square numbers where n2+m2=h2 yields h as an integer (I think they're also called Pythagorean triples?) for n and m 1-100.



Anyway, I'm still learning so I did a brute force attack on every {n,m} pair:


squareNumberQ[{n_Integer,m_Integer}]:= IntegerQ[Sqrt[n^2+m^2]] ;
allPossiblePairs = Flatten[Table[{n,m},{n,1,10},{m,1,10}],1] ;
squareNumbers = Select[allPossiblePairs, squareNumberQ]
(* {{3,4},{4,3},{6,8},{8,6}} *)

I understand I could wrap all that into one line but I'm at the stage where I'm still wrestling with #& syntax so doing it piece by piece helps me debug the individual steps.


My question is how do I delete one of the pairs as {3,4} is the same as {4,3} for this exercise. I can do it by changing the Table command and re-running:


Flatten[Table[{n,m},{n,1,10},{m,n,10}],1]


and there are already a few comments on alternate ways to eliminate duplicates from the candidate {x,y} pairs but I'm wondering how you would delete them if this wasn't an option.


There should be a way to DeleteCases based on a pattern {x_,y_} == {y_,x_} in the results? but my attempt is failing miserably ie:


DeleteCases[squareNumbers,#1[[_,1]]==#2[[_,2]]&]

I've hunted for variations of 'delete duplicate pairs' but most DeleteCases examples I've found are simple T/F statements on a single element of the list.


Trivial example but I'm still wrapping my head around this pattern matching business.



Answer



DeleteDuplicatesBy[Sort][squareNumbers]
DeleteDuplicatesBy[ReverseSort][squareNumbers] (* thanks: @Sascha *)
DeleteDuplicatesBy[squareNumbers, Sort]

DeleteCases[squareNumbers, {x_, y_} /; x > y]
DeleteCases[squareNumbers, _?(Not[OrderedQ@#] &)]
Select[squareNumbers, OrderedQ]
Select[allPossiblePairs, OrderedQ @ # && squareNumberQ @ # &]
Cases[allPossiblePairs, _?(OrderedQ@# && squareNumberQ@# &)]
Cases[allPossiblePairs, x : {_, _} /; OrderedQ@x && squareNumberQ@x]

all give



{{3, 4}, {6, 8}}




Comments

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...

How to remap graph properties?

Graph objects support both custom properties, which do not have special meanings, and standard properties, which may be used by some functions. When importing from formats such as GraphML, we usually get a result with custom properties. What is the simplest way to remap one property to another, e.g. to remap a custom property to a standard one so it can be used with various functions? Example: Let's get Zachary's karate club network with edge weights and vertex names from here: http://nexus.igraph.org/api/dataset_info?id=1&format=html g = Import[ "http://nexus.igraph.org/api/dataset?id=1&format=GraphML", {"ZIP", "karate.GraphML"}] I can remap "name" to VertexLabels and "weights" to EdgeWeight like this: sp[prop_][g_] := SetProperty[g, prop] g2 = g // sp[EdgeWeight -> (PropertyValue[{g, #}, "weight"] & /@ EdgeList[g])] // sp[VertexLabels -> (# -> PropertyValue[{g, #}, "name"]...