i1 : R = ZZ/32003[symbol a..symbol 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 : time (M,L) = gfan I; LP algorithm being used: "cddgmp". -- used 0.023258 seconds |
i4 : M/toString/print; {b*d^2, a*d, a*c^2, a^2*c} {c^3, a*d, a*c^2, a^2*c} {c^3, b*c, a*c^2, a^2*c, a^3*d} {c^3, b*c, b^4, a*c^2, a^2*c} {c^3, b*c, b^3, a*c^2} {c^3, b*c, b^2*d, b^3} {b*d^2, b^2*d, a*d, a^2*c} {b*d^2, b^2*d, b^3, a*d} {b*d^2, b*c, b^2*d, b^3, a*d^3} {c^4, b*d^2, b*c, b^2*d, b^3} |
i5 : L/toString/print; {-c^3+b*d^2, -b*c+a*d, a*c^2-b^2*d, -b^3+a^2*c} {c^3-b*d^2, -b*c+a*d, a*c^2-b^2*d, -b^3+a^2*c} {c^3-b*d^2, b*c-a*d, a*c^2-b^2*d, -b^3+a^2*c, -b^4+a^3*d} {c^3-b*d^2, b*c-a*d, b^4-a^3*d, a*c^2-b^2*d, -b^3+a^2*c} {c^3-b*d^2, b*c-a*d, b^3-a^2*c, a*c^2-b^2*d} {c^3-b*d^2, b*c-a*d, -a*c^2+b^2*d, b^3-a^2*c} {-c^3+b*d^2, -a*c^2+b^2*d, -b*c+a*d, -b^3+a^2*c} {-c^3+b*d^2, -a*c^2+b^2*d, b^3-a^2*c, -b*c+a*d} {-c^3+b*d^2, b*c-a*d, -a*c^2+b^2*d, b^3-a^2*c, -c^4+a*d^3} {c^4-a*d^3, -c^3+b*d^2, b*c-a*d, -a*c^2+b^2*d, b^3-a^2*c} |
We can see that the leading terms of -c3+b*d2, -b*c+a*d, a*c2-b2*d, -b3+a2*c (which is the first Groebner basis listed in L) are b*d2, a*d, a*c2, a2*c.
i6 : S = ZZ/32003[a..e]; |
i7 : I = ideal"a+b+c+d,ab+bc+cd+da,abc+bcd+cda+dab,abcd-e4" o7 = ideal (a + b + c + d, a*b + b*c + a*d + c*d, a*b*c + a*b*d + a*c*d + ------------------------------------------------------------------------ 4 b*c*d, a*b*c*d - e ) o7 : Ideal of S |
i8 : (inL,L) = gfan I; LP algorithm being used: "cddgmp". |
i9 : #inL o9 = 96 |
i10 : (inL1, L1) = gfan(I, Symmetries=>{(b,c,d,a,e)}); LP algorithm being used: "cddgmp". |
i11 : #inL1 o11 = 24 |
i12 : QQ[f,g,h] o12 = QQ[f, g, h] o12 : PolynomialRing |
i13 : I = ideal"fg + gh"; o13 : Ideal of QQ[f, g, h] |
i14 : gfan I; LP algorithm being used: "cddgmp". --warning: clearing value of symbol g to allow access to subscripted variables based on it |
i15 : R = ring I; |