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 |