# Question:How to categorize the output

## Question:How to categorize the output

Maple

Hello,

I need help to classify my output. If somebody can help me to do that. I want to write the procedure MipEq where
I am interested to extract the first entries for every lists and categorize them. If the second entries are the same, then I want to classify the first entries into one output. Say, I have this output:

>MipEq(10);
{[0,[1,4,2,1]],[1,[2,1,4,2]],[2,[3,6,4,3]],[3,[3,6,4,3]],[4,[4,2,1,4]],[5,[4,3,6,4]],[6,[4,3,6,4]],[7,[5,8,6,5]],[8,[5,8,6,5]],[9,[5,8,6,5]],[10,[6,4,3,6]]}.

The bold output, its second entries are the same. Therefore I want to classify all the first entries so that it doesnt repeat.

I would like to have the new output:

{[0,[1,4,2,1]],[1,[2,1,4,2]],[[2,3],[3,6,4,3]],[4,[4,2,1,4]],[[5,6],[4,3,6,4]],[[7,8,9],[5,8,6,5]],[[10,[6,4,3,6]]}.

If the output is quite complicated to obtain, I can provide the procedures that involved in MipEq.
There are:
for parameter a,b:=3,1;

The function F:

> Fp := proc (x) local Up, up; global a, b; Up := simplify((1/2)*(2*b-a+sqrt((2*b-a)^2+8*a*x))/a); if type(Up, integer) then up := Up+1 else up := ceil(Up) end if; return x+2*up*b-a*up^2 end proc;
> Fm := proc (x) local Um, um; global a, b; Um := simplify((1/2)*(-2*b-a+sqrt((2*b+a)^2-8*a*x))/a); um := ceil(Um); return x+2*um*b+a*um^2 end proc;
> F := proc (x) global Fp, Fm; Fm(Fp(x)); return % end proc;

The orbitPeriodic:

>OrbitPeriodic := proc (Map, ic) local orbit, t, z; z := ic; orbit := z; for t while z <> ic or t = 1 do orbit[t] := z; z := Map(z); orbit[t] := z end do; return [seq(orbit[t], t = 0 .. t-1)] end proc;

The code:

>C := proc (x, Intvl) local i, n; n := nops(Intvl); if x = 0 then return 1 else for i from 2 to n do if x < Intvl[i] and Intvl[i-1] < x then return i-1 end if; if x = Intvl[i] then return i end if end do end if; "ERROR! YOU HAVE TO ADD THE INTERVALS" end proc;

Intervals:

> X := proc (m::integer) local D; D := (1/2)*a*m^2-b*m+(1/2)*a*m; return % end proc;
> Xp := proc (m::integer) local d; if 2*b < a then d := (1/2)*a*m^2-3*b*m+(3/2)*a*m-2*b+a else d := (1/2)*a*m^2+(7/2)*a*m-3*b*m+4*a-4*b end if; return % end proc;
>E := {seq(X(m), m = 0 .. 200)}; H := {seq(Xp(m), m = 0 .. 200)}; Intvl := `union`(E, H);

Equivalence Classes:

MipEq := proc (N) local Used, MinPts, IcCode, AllCodes, Codes, AC, q, ic, x, z, RT, AllPoints, Extract, EqClasses, EqClasses1; global F, C, OrbitPeriodic; Used := array(0 .. N); MinPts := array(0 .. N); IcCode := array(0 .. N); for ic from 0 to N do MinPts[ic] := true; for x in OrbitPeriodic(F, ic) do if x <= N then Used[x] := true end if end do end do; for ic from 0 to N do OrbitPeriodic(F, ic); IcCode[ic] := [ic, map(C, %, Intvl)] end do; Codes := {seq(IcCode[ic], ic = 0 .. N)}; AC := {seq(IcCode[ic], ic = 0 .. N)}; AllCodes := convert(AC, 'list'); RT := select(proc (x) options operator, arrow; `in`(x, AllCodes) end proc, Codes); return Codes, AllCodes end proc;

I hope somebody can help me.
Thank you very much for the help! ﻿