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The Maxima on-line user's manual

Algebra Calculator

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Orbit Calculator

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>.

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);
orb:orbit(0.2,1.5,40);
plot2d([discrete,orb],[style,[linespoints,1,2]],[xlabel,"n"],[ylabel,"x_n"]);

          (%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) 

Orbit Example

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orbit

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

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

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