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; This is the Gfan program for computing Groebner fans and tropical varieties. Use the command "gfan list" to view all subcommands. The command "gfan" is deprecate for computing all Groebner bases of an ideal. Please use subcommand "gfan _bases" instead. Awaiting input. <Ctrl>-D to end. LP algorithm being used: "cddgmp". -- used 0.0196891 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; This is the Gfan program for computing Groebner fans and tropical varieties. Use the command "gfan list" to view all subcommands. The command "gfan" is deprecate for computing all Groebner bases of an ideal. Please use subcommand "gfan _bases" instead. Awaiting input. <Ctrl>-D to end. LP algorithm being used: "cddgmp". |
i9 : #inL o9 = 96 |
i10 : (inL1, L1) = gfan(I, Symmetries=>{(b,c,d,a,e)}); This is the Gfan program for computing Groebner fans and tropical varieties. Use the command "gfan list" to view all subcommands. The command "gfan" is deprecate for computing all Groebner bases of an ideal. Please use subcommand "gfan _bases" instead. Awaiting input. <Ctrl>-D to end. 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; This is the Gfan program for computing Groebner fans and tropical varieties. Use the command "gfan list" to view all subcommands. The command "gfan" is deprecate for computing all Groebner bases of an ideal. Please use subcommand "gfan _bases" instead. Awaiting input. <Ctrl>-D to end. LP algorithm being used: "cddgmp". warning: clearing value of symbol g to allow access to subscripted variables based on it : debug with expression debug 2909 or with command line option --debug 2909 |
i15 : R = ring I; |