i1 : R = QQ[a..d]; |
i2 : I = monomialIdeal(a*b*c,b*c*d,a^2*d,b^3*c) 3 2 o2 = monomialIdeal (a*b*c, b c, a d, b*c*d) o2 : MonomialIdeal of R |
i3 : I^2 2 2 2 4 2 6 2 3 2 3 2 2 4 2 o3 = monomialIdeal (a b c , a*b c , b c , a b*c*d, a b c*d, a*b c d, b c d, ------------------------------------------------------------------------ 4 2 2 2 2 2 2 a d , a b*c*d , b c d ) o3 : MonomialIdeal of R |
i4 : I + monomialIdeal(b*c) 2 o4 = monomialIdeal (b*c, a d) o4 : MonomialIdeal of R |
i5 : I : monomialIdeal(b*c) 2 o5 = monomialIdeal (a, b , d) o5 : MonomialIdeal of R |
i6 : radical I o6 = monomialIdeal (b*c, a*d) o6 : MonomialIdeal of R |
i7 : associatedPrimes I o7 = {monomialIdeal (a, b), monomialIdeal (a, c), monomialIdeal (b, d), ------------------------------------------------------------------------ monomialIdeal (c, d), monomialIdeal (a, b, d)} o7 : List |
i8 : primaryDecomposition I 2 2 o8 = {monomialIdeal (a , b), monomialIdeal (a , c), monomialIdeal (b, d), ------------------------------------------------------------------------ 3 monomialIdeal (c, d), monomialIdeal (a, b , d)} o8 : List |
i9 : borel I 3 2 2 3 2 2 2 2 2 o9 = monomialIdeal (a , a b, a*b , b , a c, a*b*c, b c, a*c , b*c , a d, ------------------------------------------------------------------------ 2 a*b*d, b d, a*c*d, b*c*d) o9 : MonomialIdeal of R |
i10 : isBorel I o10 = false |
i11 : I - monomialIdeal(b^3*c,b^4) 2 o11 = monomialIdeal (a*b*c, a d, b*c*d) o11 : MonomialIdeal of R |
i12 : standardPairs I o12 = {{1, {c, d}}, {a, {c, d}}, {1, {b, d}}, {a, {b, d}}, {1, {c, a}}, {1, ----------------------------------------------------------------------- 2 {b, a}}, {b, {c}}, {b , {c}}} o12 : List |
i13 : independentSets I o13 = {a*b, a*c, b*d, c*d} o13 : List |
i14 : dual I 3 2 3 o14 = monomialIdeal (a*b , a*c, a b*d, b d, c*d) o14 : MonomialIdeal of R |
The object MonomialIdeal is a type, with ancestor classes Ideal < HashTable < Thing.