i1 : R = QQ[a..i]; |
i2 : I = permanents(2,genericMatrix(R,a,3,3)) o2 = ideal (b*d + a*e, c*d + a*f, c*e + b*f, b*g + a*h, c*g + a*i, c*h + b*i, ------------------------------------------------------------------------ e*g + d*h, f*g + d*i, f*h + e*i) o2 : Ideal of R |
i3 : C = primaryDecomposition I; |
i4 : I == intersect C o4 = true |
i5 : #C o5 = 16 |
i6 : C/toString/print; ideal (i,h,g,f,c,b*d+a*e) ideal (f,e,d,c,b,a) ideal (i,h,f,e,c,b) ideal (i,f,e,d,c,b*g+a*h) ideal (i,f,c,b,a,e*g+d*h) ideal (i,g,f,d,c,a) ideal (g,d,c,b,a,f*h+e*i) ideal (i,h,g,c,b,a) ideal (h,e,c,b,a,f*g+d*i) ideal (g,f,e,d,a,c*h+b*i) ideal (h,g,e,d,b,a) ideal (i,h,g,e,b,c*d+a*f) ideal (h,f,e,d,b,c*g+a*i) ideal (i,h,g,f,e,d) ideal (i,h,g,d,a,c*e+b*f) ideal (i^2,f*h+e*i,c*h+b*i,f*g+d*i,e*g+d*h,c*g+a*i,b*g+a*h,c*e+b*f,c*d+a*f,b*d+a*e,h^2*i,g*h*i,g^2*i,f^2*i,c*f*i,e^2*i,d^2*i,c^2*i,b^2*i,a^2*i,h^3,g*h^2,e^2*h,d*e*h,b*e*h,b^2*h,a*b*h,g^3,d^2*g,a*d*g,a^2*g,f^3,e^2*f,d*e*f,d^2*f,c^2*f,b^2*f,a^2*f,e^3,d*e^2,a*e^2,d^3,c^3,b^2*c,a*b*c,a^2*c,b^3,a*b^2,a^3,b^2*e^2,a^2*d^2) |
i7 : C/codim o7 = {6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9} o7 : List |
i8 : C/degree o8 = {2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 86} o8 : List |
i9 : associatedPrimes I / print; ideal (i, h, g, f, c, b*d + a*e) ideal (f, e, d, c, b, a) ideal (i, h, f, e, c, b) ideal (i, f, e, d, c, b*g + a*h) ideal (i, f, c, b, a, e*g + d*h) ideal (i, g, f, d, c, a) ideal (g, d, c, b, a, f*h + e*i) ideal (i, h, g, c, b, a) ideal (h, e, c, b, a, f*g + d*i) ideal (g, f, e, d, a, c*h + b*i) ideal (h, g, e, d, b, a) ideal (i, h, g, e, b, c*d + a*f) ideal (h, f, e, d, b, c*g + a*i) ideal (i, h, g, f, e, d) ideal (i, h, g, d, a, c*e + b*f) ideal (i, h, g, f, e, d, c, b, a) |