# universalFGLQ(ZZ,String,String,String) -- universal formal group law in the Lazard ring tensor Q

## Synopsis

• Function: universalFGLQ
• Usage:
universalFGLQ(n,s,t,u)
• Inputs:
• n, an integer, the degree of precision
• s, , the name (such as "b") to be used for the variables of the Lazard ring
• t, , the name (such as "x") of the first variable of the formal group law
• u, , the name (such as "y") of the second variable of the formal group law
• Outputs:

## Description

The following returns a formal group law over the Lazard ring tensor Q (seen as a polynomial ring in the classes of the projective spaces {b_i}'s, up to degree n.

 i1 : universalFGLQ(3,"b","x","y") 2 2 2 2 o1 = FormalGroupLaw{(4b - 3b )x y + (4b - 3b )x*y - 2b x*y + x + y, 3} 1 2 1 2 1 o1 : FormalGroupLaw i2 : universalFGLQ(4,"b","x","y") 3 3 3 2 2 3 3 2 2 2 2 o2 = FormalGroupLaw{(- 8b + 12b b - 4b )x y + (- 20b + 24b b - 6b )x y + (- 8b + 12b b - 4b )x*y + (4b - 3b )x y + (4b - 3b )x*y - 2b x*y + x + y, 4} 1 1 2 3 1 1 2 3 1 1 2 3 1 2 1 2 1 o2 : FormalGroupLaw

## Caveat

Variables with names equal to the strings (like x, y or b, here) should not have been assigned values (like 3) beforehand otherwise an error will occur.