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pui_direct

Maxima Function

Calling Sequence

pui_direct (orbite, [lvar_1, ..., lvar_n], [d_1, d_2, ..., d_n])

Description

Let f be a polynomial in n blocks of variables lvar_1, ..., lvar_n. Let c_i be the number of variables in lvar_i, and SC be the product of n symmetric groups of degree c_1, ..., c_n. This group acts naturally on f. The list orbite is the orbit, denoted SC(f), of the function f under the action of SC. (This list may be obtained by the function multi_orbit.) The di are integers s.t. c_1 \le d_1, c_2 \le d_2, \ldots, c_n \le d_n.

Let SD be the product of the symmetric groups S_[d_1] xS_[d_2] x ... x S_[d_n]. The function pui_direct returns the first n power functions of SD(f) deduced from the power functions of SC(f), where n is the size of SD(f).

The result is in multi-contracted form w.r.t. SD, i.e. only one element is kept per orbit, under the action of SD.

(%i1) l: [[x, y], [a, b]];
(%o1)                   [[x, y], [a, b]]
(%i2) pui_direct (multi_orbit (a*x + b*y, l), l, [2, 2]);
                                       2  2
(%o2)               [a x, 4 a b x y + a  x ]
(%i3) pui_direct (multi_orbit (a*x + b*y, l), l, [3, 2]);
                             2  2     2    2        3  3
(%o3) [2 a x, 4 a b x y + 2 a  x , 3 a  b x  y + 2 a  x ,
    2  2  2  2      3    3        4  4
12 a  b  x  y  + 4 a  b x  y + 2 a  x ,
    3  2  3  2      4    4        5  5
10 a  b  x  y  + 5 a  b x  y + 2 a  x ,
    3  3  3  3       4  2  4  2      5    5        6  6
40 a  b  x  y  + 15 a  b  x  y  + 6 a  b x  y + 2 a  x ]
(%i4) pui_direct ([y + x + 2*c, y + x + 2*b, y + x + 2*a],
      [[x, y], [a, b, c]], [2, 3]);
                             2              2
(%o4) [3 x + 2 a, 6 x y + 3 x  + 4 a x + 4 a ,
                 2                   3        2       2        3
              9 x  y + 12 a x y + 3 x  + 6 a x  + 12 a  x + 8 a ]
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