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orbit

orbit (x,ay [x, y]);

orbit (2*x + x^2, [x...

Calculate

orbit

orbit (a*x + b*y, [x,...

orbit (2*x + x^2, [x...

Calculate

orbit

orbit (x,ay [x, y]);

orbit (2*x + x^2, [x...

Calculate

orbit

orbit (a*x + b*y, [x,...

orbit (2*x + x^2, [x...

Calculate

orbit

Run Example
(%i1)? multi_orbit;

 -- Function: multi_orbit (<P>, [<lvar_1>, <lvar_2>,..., <lvar_p>])
     <P> is a polynomial in the set of variables contained in the lists
     <lvar_1>, <lvar_2>, ..., <lvar_p>. This function returns the orbit
     of the polynomial <P> under the action of the product of the
     symmetric groups of the sets of variables represented in these <p>
     lists.

          (%i1) multi_orbit (a*x + b*y, [[x, y], [a, b]]);
          (%o1)                [b y + a x, a y + b x]
          (%i2) multi_orbit (x + y + 2*a, [[x, y], [a, b, c]]);
          (%o2)        [y + x + 2 c, y + x + 2 b, y + x + 2 a]
     Also see: `orbit' for the action of a single symmetric group.


(%o1)                                true
(%i2) 
Run Example
? orbit;

 -- Function: orbit (<P>, <lvar>)
     computes the orbit of the polynomial <P> in the variables in the
     list <lvar> under the action of the symmetric group of the set of
     variables in the list <lvar>.

          (%i1) orbit (a*x + b*y, [x, y]);
          (%o1)                [a y + b x, b y + a x]
          (%i2) orbit (2*x + x^2, [x, y]);
                                  2         2
          (%o2)                 [y  + 2 y, x  + 2 x]
     See also `multi_orbit' for the action of a product of symmetric
     groups on a polynomial.


  There are also some inexact matches for `orbit'.
  Try `?? orbit' to see them.

(%o1)                                true
(%i2) 
Run Example
orbit(x0,r,N):=(  x:x0, xorbit:[[0,x]],  for k thru N do (x:x*%e^(r*(1-x)), xorbit:append(xorbit,[[k,x]])),xorbit);
define: warning: redefining the built-in function orbit
(%o1) orbit(x0, r, N) := (x : x0, xorbit : [[0, x]], 
                         r (1 - x)
for k thru N do (x : x %e         , xorbit : append(xorbit, [[k, x]])), xorbit)
(%i2) orb:orbit(0.2,1.5,40);
(%o2) [[0, 0.2], [1, 0.66402338454731], [2, 1.0991388512912], 
[3, 0.94726038465596], [4, 1.025241461275966], [5, 0.9871492500843], 
[6, 1.006362243418079], [7, 0.99680384327511], [8, 1.001594229178363], 
[9, 0.99920193460021], [10, 1.000398793573195], [11, 0.99980054361045], 
[12, 1.000099713271741], [13, 0.99995013963616], [14, 1.000024929249579], 
[15, 0.99998753514217], [16, 1.00000623237065], [17, 0.99999688380011], 
[18, 1.000001558096304], [19, 0.99999922095094], [20, 1.000000389524304], 
[21, 0.99999980523779], [22, 1.00000009738109], [23, 0.99999995130945], 
[24, 1.000000024345273], [25, 0.99999998782736], [26, 1.000000006086318], 
[27, 0.99999999695684], [28, 1.00000000152158], [29, 0.99999999923921], 
[30, 1.000000000380395], [31, 0.9999999998098], [32, 1.000000000095099], 
[33, 0.99999999995245], [34, 1.000000000023775], [35, 0.99999999998811], 
[36, 1.000000000005944], [37, 0.99999999999703], [38, 1.000000000001486], 
[39, 0.99999999999926], [40, 1.000000000000372]]
(%i3) plot2d([discrete,orb],[style,[linespoints,1,2]],[xlabel,"n"],[ylabel,"x_n"]);
plotplot2d([discrete,orb],[style,[linespoints,1,2]],[xlabel,"n"],[ylabel,"x_n"]);orb1:orbit(0.2,3.98,60);
(%o4) [[0, 0.2], [1, 4.828626639411317], [2, 1.1643216242933109E-6], 
[3, 6.2310751470417825E-5], [4, 0.0033338597301401], [5, 0.17606653250026], 
[6, 4.675620451537547], [7, 2.0728055580549139E-6], 
[8, 1.1092949085122839E-4], [9, 0.0059339969243809], [10, 0.31015764355044], 
[11, 4.830248885819307], [12, 1.1572170037620782E-6], 
[13, 6.1930536763373669E-5], [14, 0.0033135218264516], [15, 0.17500662017581], 
[16, 4.66711998327287], [17, 2.1402340667541333E-6], 
[18, 1.1453800415137725E-4], [19, 0.0061269406169546], [20, 0.31999658312895], 
[21, 4.792099566173335], [22, 1.3363244838713373E-6], 
[23, 7.1515742779777839E-5], [24, 0.0038262212316304], [25, 0.20167335458859], 
[26, 4.836706925261305], [27, 1.1293599962141548E-6], 
[28, 6.0439725904271373E-5], [29, 0.003233776900965], [30, 0.17084903686496], 
[31, 4.632264750713387], [32, 2.4403531090345026E-6], 
[33, 1.3059919239878602E-4], [34, 0.0069856494715329], [35, 0.36360026254794], 
[36, 4.577581310363213], [37, 2.9978869880154502E-6], 
[38, 1.6043610627847777E-4], [39, 0.0085805838322575], [40, 0.4437898915723], 
[41, 4.060524635412123], [42, 2.0820429555331034E-5], 
[43, 0.0011141553124934], [44, 0.059362470231111], [45, 2.508397998824591], 
[46, 0.0061964437920159], [47, 0.32353707047611], [48, 4.777325541572136], 
[49, 1.4128879232964314E-6], [50, 7.5613146154522359E-5], 
[51, 0.0040453737315246], [52, 0.21303859622869], [53, 4.883315819184552], 
[54, 9.4718396663084269E-7], [55, 5.0690285669710595E-5], 
[56, 0.0027122465094761], [57, 0.14359294425094], [58, 4.339361960362271], 
[59, 7.3344122530611896E-6], [60, 3.9250453383392754E-4]]
(%i5) orb2:orbit(0.20000001,3.98,60);
(%o5) [[0, 0.20000001], [1, 4.828626688663302], [2, 1.1643214079357053E-6], 
[3, 6.2310739891707789E-5], [4, 0.0033338591107892], [5, 0.17606650022534], 
[6, 4.675620195048142], [7, 2.0728075603260761E-6], 
[8, 1.1092959800507473E-4], [9, 0.005934002653875], [10, 0.3101579359465], 
[11, 4.83024781831959], [12, 1.1572216646316739E-6], 
[13, 6.1930786196993709E-5], [14, 0.0033135351688198], [15, 0.17500731557158], 
[16, 4.667125611154313], [17, 2.1401887090157399E-6], 
[18, 1.1453557678109251E-4], [19, 0.0061268108296921], [20, 0.31998996991857], 
[21, 4.792126660113076], [22, 1.3361879451853687E-6], 
[23, 7.1508435711970349E-5], [24, 0.0038258304015863], [25, 0.20165306829995], 
[26, 4.836610891165948], [27, 1.1297693055252783E-6], 
[28, 6.0461630727729664E-5], [29, 0.0032349486181666], [30, 0.17091014477186], 
[31, 4.632794705274831], [32, 2.4354898945391083E-6], 
[33, 1.3033893263280491E-4], [34, 0.0069717356001382], [35, 0.36289614672281], 
[36, 4.581538016468197], [37, 2.9535977561640486E-6], 
[38, 1.5806593408446192E-4], [39, 0.0084538999624433], [40, 0.437458282542], 
[41, 4.104738768812528], [42, 1.7650998634773472E-5], 
[43, 9.4456273930273906E-4], [44, 0.050360516838131], [45, 2.205639161366976], 
[46, 0.018180121151702], [47, 0.90503341941938], [48, 1.320728637331805], 
[49, 0.3684993267711], [50, 4.549677198914051], [51, 3.3295980514574762E-6], 
[52, 1.7818785155817679E-4], [53, 0.0095293248743161], [54, 0.49100148881883], 
[55, 3.722911247105146], [56, 7.3173237779471621E-5], 
[57, 0.0039148743778907], [58, 0.20627331093012], [59, 4.857281819437017], 
[60, 1.0449906119960996E-6]]
(%i6) plot2d([[discrete,orb1],[discrete,orb2]],[style,[linespoints,1,1,1,14],[linespoints,1,1,2,14]],[xlabel,"n"],[ylabel,"x_n"]);
plotplot2d([[discrete,orb1],[discrete,orb2]],[style,[linespoints,1,1,1,14],[linespoints,1,1,2,14]],[xlabel,"n"],[ylabel,"x_n"]);

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