The following returns the formal group law over the Lazard ring (seen as a polynomial ring in the {a_i}'s up to degree n.
i1 : universalFGL(3,"a","x","y") 2 2 o1 = FormalGroupLaw{a x y + a x*y + a x*y + x + y, 3} 2 2 1 o1 : FormalGroupLaw |
i2 : universalFGL(4,"a","x","y") 3 2 2 3 2 2 o2 = FormalGroupLaw{(- 2a a + 2a )x y + (- 2a a + 3a )x y + (- 2a a + 2a )x*y + a x y + a x*y + a x*y + x + y, 4} 1 2 3 1 2 3 1 2 3 2 2 1 o2 : FormalGroupLaw |
The decomposition of the Lazard as a polynomial ring in an infinite number of variables is not canonical, we have made a choice, here, which amounts to choosing, for every d at most n, of Bezout coefficients for the set of binomial coefficients (d,i), 1<i<d. Variables with names equal to the strings (like x, y or a, here) should not have been assigned values (like 3) beforehand otherwise an error will occur.