This computes the trace quadratic form of an element f in an Artinian ring
i1 : R = QQ[x,y] o1 = R o1 : PolynomialRing |
i2 : F = {y^2 - x^2 - 1, x-y^2+4*y-2}
2 2 2
o2 = {- x + y - 1, - y + x + 4y - 2}
o2 : List
|
i3 : I = ideal F
2 2 2
o3 = ideal (- x + y - 1, - y + x + 4y - 2)
o3 : Ideal of R
|
i4 : S = R/I o4 = S o4 : QuotientRing |
i5 : f = y^2 - x^2 - x*y + 4 o5 = - x*y + 5 o5 : S |
i6 : traceForm(f)
o6 = | 4 -86 -340 -42 |
| -86 -266 -1262 -340 |
| -340 -1262 -5884 -1454 |
| -42 -340 -1454 -262 |
4 4
o6 : Matrix QQ <--- QQ
|