next | previous | forward | backward | up | top | index | toc | Macaulay2 website
FormalGroupLaws :: universalFGLQ(ZZ,String,String,String)

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

Synopsis

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.