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