Degeneracy locus |
This section briefly describes how to use the implementation of the
main algorithm designed by
Let , be polynomials of satisfying the following conditions:
form a reduced regular sequence outside of , and
is a smooth quasi-affine variety.
Let , and let for and , be a matrix of polynomials in , with .
For , we denote by the rank of the complex -matrix , and we let . For any matrix
with , we write
and define
The function
Mmx] |
use "geomsolvex"; type_mode? := true; |
Mmx] |
X == coordinate ('x); Y == coordinate ('y); Z == coordinate ('z); |
Mmx] |
x == polynomial_dag (1 :> Rational, X); y == polynomial_dag (1 :> Rational, Y); z == polynomial_dag (1 :> Rational, Z); |
Mmx] |
P == x^2 + y^2 + z^2 - 1 |
:
Mmx] |
G == [ P ] |
:
Mmx] |
H == [] :> Vector(Polynomial_dag(Rational)) |
:
Mmx] |
F == matrix (derive (P, X), derive (P, Y), derive (P, Z)) |
:
Mmx] |
a == [1 :> Rational, 2, 3; 3, 5, 2 ] |
:
Mmx] |
degeneracy_locus% (G, H, F, a) |
: