# component example

The following simple example illustrates the use of removeLowestDimension,topComponents,radical, and minimalPrimes.
 i1 : R = ZZ/32003[a..d]; i2 : I = monomialCurveIdeal(R,{1,3,4}) 3 2 2 2 3 2 o2 = ideal (b*c - a*d, c - b*d , a*c - b d, b - a c) o2 : Ideal of R i3 : J = ideal(a^3,b^3,c^3-d^3) 3 3 3 3 o3 = ideal (a , b , c - d ) o3 : Ideal of R i4 : I = intersect(I,J) 4 3 3 3 4 3 3 4 6 3 2 o4 = ideal (b - a d, a*b - a c, b*c - a*c d - b*c*d + a*d , c - b*c d - ------------------------------------------------------------------------ 3 3 5 5 2 3 2 3 2 4 2 4 3 3 3 3 2 3 c d + b*d , a*c - b c d - a*c d + b d , a c - a d + b d - a c*d , ------------------------------------------------------------------------ 3 3 3 3 2 3 3 2 3 2 2 3 2 3 3 2 3 2 b c - a d , a*b c - a c*d + b c*d - a*b d , a b*c - a c d + b c d - ------------------------------------------------------------------------ 2 3 3 3 3 2 4 2 3 2 a b*d , a c - a b*d , a c - a b d) o4 : Ideal of R i5 : removeLowestDimension I 3 2 2 2 3 2 o5 = ideal (b*c - a*d, c - b*d , a*c - b d, b - a c) o5 : Ideal of R i6 : topComponents I 3 2 2 2 3 2 o6 = ideal (b*c - a*d, c - b*d , a*c - b d, b - a c) o6 : Ideal of R i7 : radical I 2 2 3 2 6 3 3 2 4 5 o7 = ideal (b*c - a*d, a*c - b d, b - a c, c - c d - b d + b*d ) o7 : Ideal of R i8 : minimalPrimes I 3 2 2 2 3 2 o8 = {ideal (- b*c + a*d, - c + b*d , a*c - b d, - b + a c), ideal (- c + ------------------------------------------------------------------------ 2 2 d, b, a), ideal (c + c*d + d , b, a)} o8 : List