From: "Dr. Yang-Hui He" <yang-hui.he@merton.ox.ac.uk>
Date: March 21, 2008 7:36:38 PM EDT
To: Michael Stillman <mike@math.cornell.edu>
Cc: Dan Grayson <dan@math.uiuc.edu>
Subject: Re: gb examples

Dear Mike and Dan,

Here are 2 files of identical Groebner basis calculations for M2 and for Singular.
Of course, these are not typed in, but, rather, generated by Mathematica (would it help if I gave you the mathematica code as well?)
These are supposed to be lists of the gauge invariant operators GIOS I was talking about.
I can generate many these depending on 2 parameters of the physical theory.

the M2 file is "inmod.m2"
and the Singular file is "Sing"

the GB ccomputation is about twice as fast for singular.. and this goes on for more complicated examples..


thanks a lot!

Yang

Michael Stillman wrote:
Dear Yang,

It was great seeing you this week.  Your talk was excellent!

I would like to improve the Groebner basis facility in M2 (I've been working on it...!)  Could you email me some GB examples where singular is much faster (and gives an answer) than M2?  Also, if there are other specific example computations in M2 that you would like to be made faster, please send some of those too.  We can't promise to speed them up, but it is easier to work on speeding things up when there are specific examples that someone is really interested in.

Thanks, and let's stay in touch so that we can provide what you need!

Best,

Mike


LIB "sing.lib" ;
LIB "primdec.lib" ;
ring S = 0,(X_1, X_2, X_3, X_4, X_5, X_6, X_7, X_8, X_9, X_10, X_11, X_12,
X_13, X_14, X_15, X_16, X_17, X_18, X_19, X_20, X_21, X_22, X_23, X_24, X_25,
X_26, X_27, X_28, X_29, X_30, X_31, X_32, X_33, X_34, X_35, X_36, X_37, X_38,
X_39, X_40, X_41, X_42, X_43, X_44, X_45, X_46, X_47, X_48),dp; 
ideal dterms = X_2*X_8*X_11*X_13 - X_2*X_7*X_12*X_13 - X_1*X_8*X_11*X_14 + X_1*X_7*X_12*X_14 - X_2*X_8*X_9*X_15 + X_1*X_8*X_10*X_15 + X_2*X_5*X_12*X_15 - X_1*X_6*X_12*X_15 + X_4*(X_7*(X_10*X_13 - X_9*X_14) + X_6*(-(X_11*X_13) + X_9*X_15) + X_5*(X_11*X_14 - X_10*X_15)) + X_2*X_7*X_9*X_16 - X_1*X_7*X_10*X_16 - X_2*X_5*X_11*X_16 + X_1*X_6*X_11*X_16 + X_3*(X_8*(-(X_10*X_13) + X_9*X_14) + X_6*(X_12*X_13 - X_9*X_16) + X_5*(-(X_12*X_14) + X_10*X_16)), X_2*X_8*X_11*X_17 - X_2*X_7*X_12*X_17 - X_1*X_8*X_11*X_18 + X_1*X_7*X_12*X_18 - X_2*X_8*X_9*X_19 + X_1*X_8*X_10*X_19 + X_2*X_5*X_12*X_19 - X_1*X_6*X_12*X_19 + X_4*(X_7*(X_10*X_17 - X_9*X_18) + X_6*(-(X_11*X_17) + X_9*X_19) + X_5*(X_11*X_18 - X_10*X_19)) + X_2*X_7*X_9*X_20 - X_1*X_7*X_10*X_20 - X_2*X_5*X_11*X_20 + X_1*X_6*X_11*X_20 + X_3*(X_8*(-(X_10*X_17) + X_9*X_18) + X_6*(X_12*X_17 - X_9*X_20) + X_5*(-(X_12*X_18) + X_10*X_20)), X_2*X_8*X_15*X_17 - X_2*X_7*X_16*X_17 - X_1*X_8*X_15*X_18 + X_1*X_7*X_16*X_18 - X_2*X_8*X_13*X_19 + X_1*X_8*X_14*X_19 + X_2*X_5*X_16*X_19 - X_1*X_6*X_16*X_19 + X_4*(X_7*(X_14*X_17 - X_13*X_18) + X_6*(-(X_15*X_17) + X_13*X_19) + X_5*(X_15*X_18 - X_14*X_19)) + X_2*X_7*X_13*X_20 - X_1*X_7*X_14*X_20 - X_2*X_5*X_15*X_20 + X_1*X_6*X_15*X_20 + X_3*(X_8*(-(X_14*X_17) + X_13*X_18) + X_6*(X_16*X_17 - X_13*X_20) + X_5*(-(X_16*X_18) + X_14*X_20)), X_2*X_12*X_15*X_17 - X_2*X_11*X_16*X_17 - X_1*X_12*X_15*X_18 + X_1*X_11*X_16*X_18 - X_2*X_12*X_13*X_19 + X_1*X_12*X_14*X_19 + X_2*X_9*X_16*X_19 - X_1*X_10*X_16*X_19 + X_4*(X_11*(X_14*X_17 - X_13*X_18) + X_10*(-(X_15*X_17) + X_13*X_19) + X_9*(X_15*X_18 - X_14*X_19)) + X_2*X_11*X_13*X_20 - X_1*X_11*X_14*X_20 - X_2*X_9*X_15*X_20 + X_1*X_10*X_15*X_20 + X_3*(X_12*(-(X_14*X_17) + X_13*X_18) + X_10*(X_16*X_17 - X_13*X_20) + X_9*(-(X_16*X_18) + X_14*X_20)), X_6*X_12*X_15*X_17 - X_6*X_11*X_16*X_17 - X_5*X_12*X_15*X_18 + X_5*X_11*X_16*X_18 - X_6*X_12*X_13*X_19 + X_5*X_12*X_14*X_19 + X_6*X_9*X_16*X_19 - X_5*X_10*X_16*X_19 + X_8*(X_11*(X_14*X_17 - X_13*X_18) + X_10*(-(X_15*X_17) + X_13*X_19) + X_9*(X_15*X_18 - X_14*X_19)) + X_6*X_11*X_13*X_20 - X_5*X_11*X_14*X_20 - X_6*X_9*X_15*X_20 + X_5*X_10*X_15*X_20 + X_7*(X_12*(-(X_14*X_17) + X_13*X_18) + X_10*(X_16*X_17 - X_13*X_20) + X_9*(-(X_16*X_18) + X_14*X_20)), X_2*X_8*X_11*X_21 - X_2*X_7*X_12*X_21 - X_1*X_8*X_11*X_22 + X_1*X_7*X_12*X_22 - X_2*X_8*X_9*X_23 + X_1*X_8*X_10*X_23 + X_2*X_5*X_12*X_23 - X_1*X_6*X_12*X_23 + X_4*(X_7*(X_10*X_21 - X_9*X_22) + X_6*(-(X_11*X_21) + X_9*X_23) + X_5*(X_11*X_22 - X_10*X_23)) + X_2*X_7*X_9*X_24 - X_1*X_7*X_10*X_24 - X_2*X_5*X_11*X_24 + X_1*X_6*X_11*X_24 + X_3*(X_8*(-(X_10*X_21) + X_9*X_22) + X_6*(X_12*X_21 - X_9*X_24) + X_5*(-(X_12*X_22) + X_10*X_24)), X_2*X_8*X_15*X_21 - X_2*X_7*X_16*X_21 - X_1*X_8*X_15*X_22 + X_1*X_7*X_16*X_22 - X_2*X_8*X_13*X_23 + X_1*X_8*X_14*X_23 + X_2*X_5*X_16*X_23 - X_1*X_6*X_16*X_23 + X_4*(X_7*(X_14*X_21 - X_13*X_22) + X_6*(-(X_15*X_21) + X_13*X_23) + X_5*(X_15*X_22 - X_14*X_23)) + X_2*X_7*X_13*X_24 - X_1*X_7*X_14*X_24 - X_2*X_5*X_15*X_24 + X_1*X_6*X_15*X_24 + X_3*(X_8*(-(X_14*X_21) + X_13*X_22) + X_6*(X_16*X_21 - X_13*X_24) + X_5*(-(X_16*X_22) + X_14*X_24)), X_2*X_12*X_15*X_21 - X_2*X_11*X_16*X_21 - X_1*X_12*X_15*X_22 + X_1*X_11*X_16*X_22 - X_2*X_12*X_13*X_23 + X_1*X_12*X_14*X_23 + X_2*X_9*X_16*X_23 - X_1*X_10*X_16*X_23 + X_4*(X_11*(X_14*X_21 - X_13*X_22) + X_10*(-(X_15*X_21) + X_13*X_23) + X_9*(X_15*X_22 - X_14*X_23)) + X_2*X_11*X_13*X_24 - X_1*X_11*X_14*X_24 - X_2*X_9*X_15*X_24 + X_1*X_10*X_15*X_24 + X_3*(X_12*(-(X_14*X_21) + X_13*X_22) + X_10*(X_16*X_21 - X_13*X_24) + X_9*(-(X_16*X_22) + X_14*X_24)), X_6*X_12*X_15*X_21 - X_6*X_11*X_16*X_21 - X_5*X_12*X_15*X_22 + X_5*X_11*X_16*X_22 - X_6*X_12*X_13*X_23 + X_5*X_12*X_14*X_23 + X_6*X_9*X_16*X_23 - X_5*X_10*X_16*X_23 + X_8*(X_11*(X_14*X_21 - X_13*X_22) + X_10*(-(X_15*X_21) + X_13*X_23) + X_9*(X_15*X_22 - X_14*X_23)) + X_6*X_11*X_13*X_24 - X_5*X_11*X_14*X_24 - X_6*X_9*X_15*X_24 + X_5*X_10*X_15*X_24 + X_7*(X_12*(-(X_14*X_21) + X_13*X_22) + X_10*(X_16*X_21 - X_13*X_24) + X_9*(-(X_16*X_22) + X_14*X_24)), X_2*X_8*X_19*X_21 - X_2*X_7*X_20*X_21 - X_1*X_8*X_19*X_22 + X_1*X_7*X_20*X_22 - X_2*X_8*X_17*X_23 + X_1*X_8*X_18*X_23 + X_2*X_5*X_20*X_23 - X_1*X_6*X_20*X_23 + X_4*(X_7*(X_18*X_21 - X_17*X_22) + X_6*(-(X_19*X_21) + X_17*X_23) + X_5*(X_19*X_22 - X_18*X_23)) + X_2*X_7*X_17*X_24 - X_1*X_7*X_18*X_24 - X_2*X_5*X_19*X_24 + X_1*X_6*X_19*X_24 + X_3*(X_8*(-(X_18*X_21) + X_17*X_22) + X_6*(X_20*X_21 - X_17*X_24) + X_5*(-(X_20*X_22) + X_18*X_24)), X_2*X_12*X_19*X_21 - X_2*X_11*X_20*X_21 - X_1*X_12*X_19*X_22 + X_1*X_11*X_20*X_22 - X_2*X_12*X_17*X_23 + X_1*X_12*X_18*X_23 + X_2*X_9*X_20*X_23 - X_1*X_10*X_20*X_23 + X_4*(X_11*(X_18*X_21 - X_17*X_22) + X_10*(-(X_19*X_21) + X_17*X_23) + X_9*(X_19*X_22 - X_18*X_23)) + X_2*X_11*X_17*X_24 - X_1*X_11*X_18*X_24 - X_2*X_9*X_19*X_24 + X_1*X_10*X_19*X_24 + X_3*(X_12*(-(X_18*X_21) + X_17*X_22) + X_10*(X_20*X_21 - X_17*X_24) + X_9*(-(X_20*X_22) + X_18*X_24)), X_6*X_12*X_19*X_21 - X_6*X_11*X_20*X_21 - X_5*X_12*X_19*X_22 + X_5*X_11*X_20*X_22 - X_6*X_12*X_17*X_23 + X_5*X_12*X_18*X_23 + X_6*X_9*X_20*X_23 - X_5*X_10*X_20*X_23 + X_8*(X_11*(X_18*X_21 - X_17*X_22) + X_10*(-(X_19*X_21) + X_17*X_23) + X_9*(X_19*X_22 - X_18*X_23)) + X_6*X_11*X_17*X_24 - X_5*X_11*X_18*X_24 - X_6*X_9*X_19*X_24 + X_5*X_10*X_19*X_24 + X_7*(X_12*(-(X_18*X_21) + X_17*X_22) + X_10*(X_20*X_21 - X_17*X_24) + X_9*(-(X_20*X_22) + X_18*X_24)), X_2*X_16*X_19*X_21 - X_2*X_15*X_20*X_21 - X_1*X_16*X_19*X_22 + X_1*X_15*X_20*X_22 - X_2*X_16*X_17*X_23 + X_1*X_16*X_18*X_23 + X_2*X_13*X_20*X_23 - X_1*X_14*X_20*X_23 + X_4*(X_15*(X_18*X_21 - X_17*X_22) + X_14*(-(X_19*X_21) + X_17*X_23) + X_13*(X_19*X_22 - X_18*X_23)) + X_2*X_15*X_17*X_24 - X_1*X_15*X_18*X_24 - X_2*X_13*X_19*X_24 + X_1*X_14*X_19*X_24 + X_3*(X_16*(-(X_18*X_21) + X_17*X_22) + X_14*(X_20*X_21 - X_17*X_24) + X_13*(-(X_20*X_22) + X_18*X_24)), X_6*X_16*X_19*X_21 - X_6*X_15*X_20*X_21 - X_5*X_16*X_19*X_22 + X_5*X_15*X_20*X_22 - X_6*X_16*X_17*X_23 + X_5*X_16*X_18*X_23 + X_6*X_13*X_20*X_23 - X_5*X_14*X_20*X_23 + X_8*(X_15*(X_18*X_21 - X_17*X_22) + X_14*(-(X_19*X_21) + X_17*X_23) + X_13*(X_19*X_22 - X_18*X_23)) + X_6*X_15*X_17*X_24 - X_5*X_15*X_18*X_24 - X_6*X_13*X_19*X_24 + X_5*X_14*X_19*X_24 + X_7*(X_16*(-(X_18*X_21) + X_17*X_22) + X_14*(X_20*X_21 - X_17*X_24) + X_13*(-(X_20*X_22) + X_18*X_24)), X_10*X_16*X_19*X_21 - X_10*X_15*X_20*X_21 - X_9*X_16*X_19*X_22 + X_9*X_15*X_20*X_22 - X_10*X_16*X_17*X_23 + X_9*X_16*X_18*X_23 + X_10*X_13*X_20*X_23 - X_9*X_14*X_20*X_23 + X_12*(X_15*(X_18*X_21 - X_17*X_22) + X_14*(-(X_19*X_21) + X_17*X_23) + X_13*(X_19*X_22 - X_18*X_23)) + X_10*X_15*X_17*X_24 - X_9*X_15*X_18*X_24 - X_10*X_13*X_19*X_24 + X_9*X_14*X_19*X_24 + X_11*(X_16*(-(X_18*X_21) + X_17*X_22) + X_14*(X_20*X_21 - X_17*X_24) + X_13*(-(X_20*X_22) + X_18*X_24)), X_1*X_25 + X_2*X_26 + X_3*X_27 + X_4*X_28, X_5*X_25 + X_6*X_26 + X_7*X_27 + X_8*X_28, X_9*X_25 + X_10*X_26 + X_11*X_27 + X_12*X_28, X_13*X_25 + X_14*X_26 + X_15*X_27 + X_16*X_28, X_17*X_25 + X_18*X_26 + X_19*X_27 + X_20*X_28, X_21*X_25 + X_22*X_26 + X_23*X_27 + X_24*X_28, X_1*X_29 + X_2*X_30 + X_3*X_31 + X_4*X_32, X_5*X_29 + X_6*X_30 + X_7*X_31 + X_8*X_32, X_9*X_29 + X_10*X_30 + X_11*X_31 + X_12*X_32, X_13*X_29 + X_14*X_30 + X_15*X_31 + X_16*X_32, X_17*X_29 + X_18*X_30 + X_19*X_31 + X_20*X_32, X_21*X_29 + X_22*X_30 + X_23*X_31 + X_24*X_32, X_1*X_33 + X_2*X_34 + X_3*X_35 + X_4*X_36, X_5*X_33 + X_6*X_34 + X_7*X_35 + X_8*X_36, X_9*X_33 + X_10*X_34 + X_11*X_35 + X_12*X_36, X_13*X_33 + X_14*X_34 + X_15*X_35 + X_16*X_36, X_17*X_33 + X_18*X_34 + X_19*X_35 + X_20*X_36, X_21*X_33 + X_22*X_34 + X_23*X_35 + X_24*X_36, X_1*X_37 + X_2*X_38 + X_3*X_39 + X_4*X_40, X_5*X_37 + X_6*X_38 + X_7*X_39 + X_8*X_40, X_9*X_37 + X_10*X_38 + X_11*X_39 + X_12*X_40, X_13*X_37 + X_14*X_38 + X_15*X_39 + X_16*X_40, X_17*X_37 + X_18*X_38 + X_19*X_39 + X_20*X_40, X_21*X_37 + X_22*X_38 + X_23*X_39 + X_24*X_40, X_26*X_32*X_35*X_37 - X_26*X_31*X_36*X_37 - X_25*X_32*X_35*X_38 + X_25*X_31*X_36*X_38 - X_26*X_32*X_33*X_39 + X_25*X_32*X_34*X_39 + X_26*X_29*X_36*X_39 - X_25*X_30*X_36*X_39 + X_28*(X_31*(X_34*X_37 - X_33*X_38) + X_30*(-(X_35*X_37) + X_33*X_39) + X_29*(X_35*X_38 - X_34*X_39)) + X_26*X_31*X_33*X_40 - X_25*X_31*X_34*X_40 - X_26*X_29*X_35*X_40 + X_25*X_30*X_35*X_40 + X_27*(X_32*(-(X_34*X_37) + X_33*X_38) + X_30*(X_36*X_37 - X_33*X_40) + X_29*(-(X_36*X_38) + X_34*X_40)), X_1*X_41 + X_2*X_42 + X_3*X_43 + X_4*X_44, X_5*X_41 + X_6*X_42 + X_7*X_43 + X_8*X_44, X_9*X_41 + X_10*X_42 + X_11*X_43 + X_12*X_44, X_13*X_41 + X_14*X_42 + X_15*X_43 + X_16*X_44, X_17*X_41 + X_18*X_42 + X_19*X_43 + X_20*X_44, X_21*X_41 + X_22*X_42 + X_23*X_43 + X_24*X_44, X_26*X_32*X_35*X_41 - X_26*X_31*X_36*X_41 - X_25*X_32*X_35*X_42 + X_25*X_31*X_36*X_42 - X_26*X_32*X_33*X_43 + X_25*X_32*X_34*X_43 + X_26*X_29*X_36*X_43 - X_25*X_30*X_36*X_43 + X_28*(X_31*(X_34*X_41 - X_33*X_42) + X_30*(-(X_35*X_41) + X_33*X_43) + X_29*(X_35*X_42 - X_34*X_43)) + X_26*X_31*X_33*X_44 - X_25*X_31*X_34*X_44 - X_26*X_29*X_35*X_44 + X_25*X_30*X_35*X_44 + X_27*(X_32*(-(X_34*X_41) + X_33*X_42) + X_30*(X_36*X_41 - X_33*X_44) + X_29*(-(X_36*X_42) + X_34*X_44)), X_26*X_32*X_39*X_41 - X_26*X_31*X_40*X_41 - X_25*X_32*X_39*X_42 + X_25*X_31*X_40*X_42 - X_26*X_32*X_37*X_43 + X_25*X_32*X_38*X_43 + X_26*X_29*X_40*X_43 - X_25*X_30*X_40*X_43 + X_28*(X_31*(X_38*X_41 - X_37*X_42) + X_30*(-(X_39*X_41) + X_37*X_43) + X_29*(X_39*X_42 - X_38*X_43)) + X_26*X_31*X_37*X_44 - X_25*X_31*X_38*X_44 - X_26*X_29*X_39*X_44 + X_25*X_30*X_39*X_44 + X_27*(X_32*(-(X_38*X_41) + X_37*X_42) + X_30*(X_40*X_41 - X_37*X_44) + X_29*(-(X_40*X_42) + X_38*X_44)), X_26*X_36*X_39*X_41 - X_26*X_35*X_40*X_41 - X_25*X_36*X_39*X_42 + X_25*X_35*X_40*X_42 - X_26*X_36*X_37*X_43 + X_25*X_36*X_38*X_43 + X_26*X_33*X_40*X_43 - X_25*X_34*X_40*X_43 + X_28*(X_35*(X_38*X_41 - X_37*X_42) + X_34*(-(X_39*X_41) + X_37*X_43) + X_33*(X_39*X_42 - X_38*X_43)) + X_26*X_35*X_37*X_44 - X_25*X_35*X_38*X_44 - X_26*X_33*X_39*X_44 + X_25*X_34*X_39*X_44 + X_27*(X_36*(-(X_38*X_41) + X_37*X_42) + X_34*(X_40*X_41 - X_37*X_44) + X_33*(-(X_40*X_42) + X_38*X_44)), X_30*X_36*X_39*X_41 - X_30*X_35*X_40*X_41 - X_29*X_36*X_39*X_42 + X_29*X_35*X_40*X_42 - X_30*X_36*X_37*X_43 + X_29*X_36*X_38*X_43 + X_30*X_33*X_40*X_43 - X_29*X_34*X_40*X_43 + X_32*(X_35*(X_38*X_41 - X_37*X_42) + X_34*(-(X_39*X_41) + X_37*X_43) + X_33*(X_39*X_42 - X_38*X_43)) + X_30*X_35*X_37*X_44 - X_29*X_35*X_38*X_44 - X_30*X_33*X_39*X_44 + X_29*X_34*X_39*X_44 + X_31*(X_36*(-(X_38*X_41) + X_37*X_42) + X_34*(X_40*X_41 - X_37*X_44) + X_33*(-(X_40*X_42) + X_38*X_44)), X_1*X_45 + X_2*X_46 + X_3*X_47 + X_4*X_48, X_5*X_45 + X_6*X_46 + X_7*X_47 + X_8*X_48, X_9*X_45 + X_10*X_46 + X_11*X_47 + X_12*X_48, X_13*X_45 + X_14*X_46 + X_15*X_47 + X_16*X_48, X_17*X_45 + X_18*X_46 + X_19*X_47 + X_20*X_48, X_21*X_45 + X_22*X_46 + X_23*X_47 + X_24*X_48, X_26*X_32*X_35*X_45 - X_26*X_31*X_36*X_45 - X_25*X_32*X_35*X_46 + X_25*X_31*X_36*X_46 - X_26*X_32*X_33*X_47 + X_25*X_32*X_34*X_47 + X_26*X_29*X_36*X_47 - X_25*X_30*X_36*X_47 + X_28*(X_31*(X_34*X_45 - X_33*X_46) + X_30*(-(X_35*X_45) + X_33*X_47) + X_29*(X_35*X_46 - X_34*X_47)) + X_26*X_31*X_33*X_48 - X_25*X_31*X_34*X_48 - X_26*X_29*X_35*X_48 + X_25*X_30*X_35*X_48 + X_27*(X_32*(-(X_34*X_45) + X_33*X_46) + X_30*(X_36*X_45 - X_33*X_48) + X_29*(-(X_36*X_46) + X_34*X_48)), X_26*X_32*X_39*X_45 - X_26*X_31*X_40*X_45 - X_25*X_32*X_39*X_46 + X_25*X_31*X_40*X_46 - X_26*X_32*X_37*X_47 + X_25*X_32*X_38*X_47 + X_26*X_29*X_40*X_47 - X_25*X_30*X_40*X_47 + X_28*(X_31*(X_38*X_45 - X_37*X_46) + X_30*(-(X_39*X_45) + X_37*X_47) + X_29*(X_39*X_46 - X_38*X_47)) + X_26*X_31*X_37*X_48 - X_25*X_31*X_38*X_48 - X_26*X_29*X_39*X_48 + X_25*X_30*X_39*X_48 + X_27*(X_32*(-(X_38*X_45) + X_37*X_46) + X_30*(X_40*X_45 - X_37*X_48) + X_29*(-(X_40*X_46) + X_38*X_48)), X_26*X_36*X_39*X_45 - X_26*X_35*X_40*X_45 - X_25*X_36*X_39*X_46 + X_25*X_35*X_40*X_46 - X_26*X_36*X_37*X_47 + X_25*X_36*X_38*X_47 + X_26*X_33*X_40*X_47 - X_25*X_34*X_40*X_47 + X_28*(X_35*(X_38*X_45 - X_37*X_46) + X_34*(-(X_39*X_45) + X_37*X_47) + X_33*(X_39*X_46 - X_38*X_47)) + X_26*X_35*X_37*X_48 - X_25*X_35*X_38*X_48 - X_26*X_33*X_39*X_48 + X_25*X_34*X_39*X_48 + X_27*(X_36*(-(X_38*X_45) + X_37*X_46) + X_34*(X_40*X_45 - X_37*X_48) + X_33*(-(X_40*X_46) + X_38*X_48)), X_30*X_36*X_39*X_45 - X_30*X_35*X_40*X_45 - X_29*X_36*X_39*X_46 + X_29*X_35*X_40*X_46 - X_30*X_36*X_37*X_47 + X_29*X_36*X_38*X_47 + X_30*X_33*X_40*X_47 - X_29*X_34*X_40*X_47 + X_32*(X_35*(X_38*X_45 - X_37*X_46) + X_34*(-(X_39*X_45) + X_37*X_47) + X_33*(X_39*X_46 - X_38*X_47)) + X_30*X_35*X_37*X_48 - X_29*X_35*X_38*X_48 - X_30*X_33*X_39*X_48 + X_29*X_34*X_39*X_48 + X_31*(X_36*(-(X_38*X_45) + X_37*X_46) + X_34*(X_40*X_45 - X_37*X_48) + X_33*(-(X_40*X_46) + X_38*X_48)), X_26*X_32*X_43*X_45 - X_26*X_31*X_44*X_45 - X_25*X_32*X_43*X_46 + X_25*X_31*X_44*X_46 - X_26*X_32*X_41*X_47 + X_25*X_32*X_42*X_47 + X_26*X_29*X_44*X_47 - X_25*X_30*X_44*X_47 + X_28*(X_31*(X_42*X_45 - X_41*X_46) + X_30*(-(X_43*X_45) + X_41*X_47) + X_29*(X_43*X_46 - X_42*X_47)) + X_26*X_31*X_41*X_48 - X_25*X_31*X_42*X_48 - X_26*X_29*X_43*X_48 + X_25*X_30*X_43*X_48 + X_27*(X_32*(-(X_42*X_45) + X_41*X_46) + X_30*(X_44*X_45 - X_41*X_48) + X_29*(-(X_44*X_46) + X_42*X_48)), X_26*X_36*X_43*X_45 - X_26*X_35*X_44*X_45 - X_25*X_36*X_43*X_46 + X_25*X_35*X_44*X_46 - X_26*X_36*X_41*X_47 + X_25*X_36*X_42*X_47 + X_26*X_33*X_44*X_47 - X_25*X_34*X_44*X_47 + X_28*(X_35*(X_42*X_45 - X_41*X_46) + X_34*(-(X_43*X_45) + X_41*X_47) + X_33*(X_43*X_46 - X_42*X_47)) + X_26*X_35*X_41*X_48 - X_25*X_35*X_42*X_48 - X_26*X_33*X_43*X_48 + X_25*X_34*X_43*X_48 + X_27*(X_36*(-(X_42*X_45) + X_41*X_46) + X_34*(X_44*X_45 - X_41*X_48) + X_33*(-(X_44*X_46) + X_42*X_48)), X_30*X_36*X_43*X_45 - X_30*X_35*X_44*X_45 - X_29*X_36*X_43*X_46 + X_29*X_35*X_44*X_46 - X_30*X_36*X_41*X_47 + X_29*X_36*X_42*X_47 + X_30*X_33*X_44*X_47 - X_29*X_34*X_44*X_47 + X_32*(X_35*(X_42*X_45 - X_41*X_46) + X_34*(-(X_43*X_45) + X_41*X_47) + X_33*(X_43*X_46 - X_42*X_47)) + X_30*X_35*X_41*X_48 - X_29*X_35*X_42*X_48 - X_30*X_33*X_43*X_48 + X_29*X_34*X_43*X_48 + X_31*(X_36*(-(X_42*X_45) + X_41*X_46) + X_34*(X_44*X_45 - X_41*X_48) + X_33*(-(X_44*X_46) + X_42*X_48)), X_26*X_40*X_43*X_45 - X_26*X_39*X_44*X_45 - X_25*X_40*X_43*X_46 + X_25*X_39*X_44*X_46 - X_26*X_40*X_41*X_47 + X_25*X_40*X_42*X_47 + X_26*X_37*X_44*X_47 - X_25*X_38*X_44*X_47 + X_28*(X_39*(X_42*X_45 - X_41*X_46) + X_38*(-(X_43*X_45) + X_41*X_47) + X_37*(X_43*X_46 - X_42*X_47)) + X_26*X_39*X_41*X_48 - X_25*X_39*X_42*X_48 - X_26*X_37*X_43*X_48 + X_25*X_38*X_43*X_48 + X_27*(X_40*(-(X_42*X_45) + X_41*X_46) + X_38*(X_44*X_45 - X_41*X_48) + X_37*(-(X_44*X_46) + X_42*X_48)), X_30*X_40*X_43*X_45 - X_30*X_39*X_44*X_45 - X_29*X_40*X_43*X_46 + X_29*X_39*X_44*X_46 - X_30*X_40*X_41*X_47 + X_29*X_40*X_42*X_47 + X_30*X_37*X_44*X_47 - X_29*X_38*X_44*X_47 + X_32*(X_39*(X_42*X_45 - X_41*X_46) + X_38*(-(X_43*X_45) + X_41*X_47) + X_37*(X_43*X_46 - X_42*X_47)) + X_30*X_39*X_41*X_48 - X_29*X_39*X_42*X_48 - X_30*X_37*X_43*X_48 + X_29*X_38*X_43*X_48 + X_31*(X_40*(-(X_42*X_45) + X_41*X_46) + X_38*(X_44*X_45 - X_41*X_48) + X_37*(-(X_44*X_46) + X_42*X_48)), X_34*X_40*X_43*X_45 - X_34*X_39*X_44*X_45 - X_33*X_40*X_43*X_46 + X_33*X_39*X_44*X_46 - X_34*X_40*X_41*X_47 + X_33*X_40*X_42*X_47 + X_34*X_37*X_44*X_47 - X_33*X_38*X_44*X_47 + X_36*(X_39*(X_42*X_45 - X_41*X_46) + X_38*(-(X_43*X_45) + X_41*X_47) + X_37*(X_43*X_46 - X_42*X_47)) + X_34*X_39*X_41*X_48 - X_33*X_39*X_42*X_48 - X_34*X_37*X_43*X_48 + X_33*X_38*X_43*X_48 + X_35*(X_40*(-(X_42*X_45) + X_41*X_46) + X_38*(X_44*X_45 - X_41*X_48) + X_37*(-(X_44*X_46) + X_42*X_48)); 
rtimer=1 ;  int t=rtimer; 
groebner(dterms);; 
t=rtimer-t; int tps=system("--ticks-per-sec");
print(t/tps); 

R=ZZ/101[X_{1}..X_{48}];
dterms = {X_{2}*X_{8}*X_{11}*X_{13} - X_{2}*X_{7}*X_{12}*X_{13} - X_{1}*X_{8}*X_{11}*X_{14} + X_{1}*X_{7}*X_{12}*X_{14} - X_{2}*X_{8}*X_{9}*X_{15} + X_{1}*X_{8}*X_{10}*X_{15} + X_{2}*X_{5}*X_{12}*X_{15} - X_{1}*X_{6}*X_{12}*X_{15} + X_{4}*(X_{7}*(X_{10}*X_{13} - X_{9}*X_{14}) + X_{6}*(-(X_{11}*X_{13}) + X_{9}*X_{15}) + X_{5}*(X_{11}*X_{14} - X_{10}*X_{15})) + X_{2}*X_{7}*X_{9}*X_{16} - X_{1}*X_{7}*X_{10}*X_{16} - X_{2}*X_{5}*X_{11}*X_{16} + X_{1}*X_{6}*X_{11}*X_{16} + X_{3}*(X_{8}*(-(X_{10}*X_{13}) + X_{9}*X_{14}) + X_{6}*(X_{12}*X_{13} - X_{9}*X_{16}) + X_{5}*(-(X_{12}*X_{14}) + X_{10}*X_{16})), X_{2}*X_{8}*X_{11}*X_{17} - X_{2}*X_{7}*X_{12}*X_{17} - X_{1}*X_{8}*X_{11}*X_{18} + X_{1}*X_{7}*X_{12}*X_{18} - X_{2}*X_{8}*X_{9}*X_{19} + X_{1}*X_{8}*X_{10}*X_{19} + X_{2}*X_{5}*X_{12}*X_{19} - X_{1}*X_{6}*X_{12}*X_{19} + X_{4}*(X_{7}*(X_{10}*X_{17} - X_{9}*X_{18}) + X_{6}*(-(X_{11}*X_{17}) + X_{9}*X_{19}) + X_{5}*(X_{11}*X_{18} - X_{10}*X_{19})) + X_{2}*X_{7}*X_{9}*X_{20} - X_{1}*X_{7}*X_{10}*X_{20} - X_{2}*X_{5}*X_{11}*X_{20} + X_{1}*X_{6}*X_{11}*X_{20} + X_{3}*(X_{8}*(-(X_{10}*X_{17}) + X_{9}*X_{18}) + X_{6}*(X_{12}*X_{17} - X_{9}*X_{20}) + X_{5}*(-(X_{12}*X_{18}) + X_{10}*X_{20})), X_{2}*X_{8}*X_{15}*X_{17} - X_{2}*X_{7}*X_{16}*X_{17} - X_{1}*X_{8}*X_{15}*X_{18} + X_{1}*X_{7}*X_{16}*X_{18} - X_{2}*X_{8}*X_{13}*X_{19} + X_{1}*X_{8}*X_{14}*X_{19} + X_{2}*X_{5}*X_{16}*X_{19} - X_{1}*X_{6}*X_{16}*X_{19} + X_{4}*(X_{7}*(X_{14}*X_{17} - X_{13}*X_{18}) + X_{6}*(-(X_{15}*X_{17}) + X_{13}*X_{19}) + X_{5}*(X_{15}*X_{18} - X_{14}*X_{19})) + X_{2}*X_{7}*X_{13}*X_{20} - X_{1}*X_{7}*X_{14}*X_{20} - X_{2}*X_{5}*X_{15}*X_{20} + X_{1}*X_{6}*X_{15}*X_{20} + X_{3}*(X_{8}*(-(X_{14}*X_{17}) + X_{13}*X_{18}) + X_{6}*(X_{16}*X_{17} - X_{13}*X_{20}) + X_{5}*(-(X_{16}*X_{18}) + X_{14}*X_{20})), X_{2}*X_{12}*X_{15}*X_{17} - X_{2}*X_{11}*X_{16}*X_{17} - X_{1}*X_{12}*X_{15}*X_{18} + X_{1}*X_{11}*X_{16}*X_{18} - X_{2}*X_{12}*X_{13}*X_{19} + X_{1}*X_{12}*X_{14}*X_{19} + X_{2}*X_{9}*X_{16}*X_{19} - X_{1}*X_{10}*X_{16}*X_{19} + X_{4}*(X_{11}*(X_{14}*X_{17} - X_{13}*X_{18}) + X_{10}*(-(X_{15}*X_{17}) + X_{13}*X_{19}) + X_{9}*(X_{15}*X_{18} - X_{14}*X_{19})) + X_{2}*X_{11}*X_{13}*X_{20} - X_{1}*X_{11}*X_{14}*X_{20} - X_{2}*X_{9}*X_{15}*X_{20} + X_{1}*X_{10}*X_{15}*X_{20} + X_{3}*(X_{12}*(-(X_{14}*X_{17}) + X_{13}*X_{18}) + X_{10}*(X_{16}*X_{17} - X_{13}*X_{20}) + X_{9}*(-(X_{16}*X_{18}) + X_{14}*X_{20})), X_{6}*X_{12}*X_{15}*X_{17} - X_{6}*X_{11}*X_{16}*X_{17} - X_{5}*X_{12}*X_{15}*X_{18} + X_{5}*X_{11}*X_{16}*X_{18} - X_{6}*X_{12}*X_{13}*X_{19} + X_{5}*X_{12}*X_{14}*X_{19} + X_{6}*X_{9}*X_{16}*X_{19} - X_{5}*X_{10}*X_{16}*X_{19} + X_{8}*(X_{11}*(X_{14}*X_{17} - X_{13}*X_{18}) + X_{10}*(-(X_{15}*X_{17}) + X_{13}*X_{19}) + X_{9}*(X_{15}*X_{18} - X_{14}*X_{19})) + X_{6}*X_{11}*X_{13}*X_{20} - X_{5}*X_{11}*X_{14}*X_{20} - X_{6}*X_{9}*X_{15}*X_{20} + X_{5}*X_{10}*X_{15}*X_{20} + X_{7}*(X_{12}*(-(X_{14}*X_{17}) + X_{13}*X_{18}) + X_{10}*(X_{16}*X_{17} - X_{13}*X_{20}) + X_{9}*(-(X_{16}*X_{18}) + X_{14}*X_{20})), X_{2}*X_{8}*X_{11}*X_{21} - X_{2}*X_{7}*X_{12}*X_{21} - X_{1}*X_{8}*X_{11}*X_{22} + X_{1}*X_{7}*X_{12}*X_{22} - X_{2}*X_{8}*X_{9}*X_{23} + X_{1}*X_{8}*X_{10}*X_{23} + X_{2}*X_{5}*X_{12}*X_{23} - X_{1}*X_{6}*X_{12}*X_{23} + X_{4}*(X_{7}*(X_{10}*X_{21} - X_{9}*X_{22}) + X_{6}*(-(X_{11}*X_{21}) + X_{9}*X_{23}) + X_{5}*(X_{11}*X_{22} - X_{10}*X_{23})) + X_{2}*X_{7}*X_{9}*X_{24} - X_{1}*X_{7}*X_{10}*X_{24} - X_{2}*X_{5}*X_{11}*X_{24} + X_{1}*X_{6}*X_{11}*X_{24} + X_{3}*(X_{8}*(-(X_{10}*X_{21}) + X_{9}*X_{22}) + X_{6}*(X_{12}*X_{21} - X_{9}*X_{24}) + X_{5}*(-(X_{12}*X_{22}) + X_{10}*X_{24})), X_{2}*X_{8}*X_{15}*X_{21} - X_{2}*X_{7}*X_{16}*X_{21} - X_{1}*X_{8}*X_{15}*X_{22} + X_{1}*X_{7}*X_{16}*X_{22} - X_{2}*X_{8}*X_{13}*X_{23} + X_{1}*X_{8}*X_{14}*X_{23} + X_{2}*X_{5}*X_{16}*X_{23} - X_{1}*X_{6}*X_{16}*X_{23} + X_{4}*(X_{7}*(X_{14}*X_{21} - X_{13}*X_{22}) + X_{6}*(-(X_{15}*X_{21}) + X_{13}*X_{23}) + X_{5}*(X_{15}*X_{22} - X_{14}*X_{23})) + X_{2}*X_{7}*X_{13}*X_{24} - X_{1}*X_{7}*X_{14}*X_{24} - X_{2}*X_{5}*X_{15}*X_{24} + X_{1}*X_{6}*X_{15}*X_{24} + X_{3}*(X_{8}*(-(X_{14}*X_{21}) + X_{13}*X_{22}) + X_{6}*(X_{16}*X_{21} - X_{13}*X_{24}) + X_{5}*(-(X_{16}*X_{22}) + X_{14}*X_{24})), X_{2}*X_{12}*X_{15}*X_{21} - X_{2}*X_{11}*X_{16}*X_{21} - X_{1}*X_{12}*X_{15}*X_{22} + X_{1}*X_{11}*X_{16}*X_{22} - X_{2}*X_{12}*X_{13}*X_{23} + X_{1}*X_{12}*X_{14}*X_{23} + X_{2}*X_{9}*X_{16}*X_{23} - X_{1}*X_{10}*X_{16}*X_{23} + X_{4}*(X_{11}*(X_{14}*X_{21} - X_{13}*X_{22}) + X_{10}*(-(X_{15}*X_{21}) + X_{13}*X_{23}) + X_{9}*(X_{15}*X_{22} - X_{14}*X_{23})) + X_{2}*X_{11}*X_{13}*X_{24} - X_{1}*X_{11}*X_{14}*X_{24} - X_{2}*X_{9}*X_{15}*X_{24} + X_{1}*X_{10}*X_{15}*X_{24} + X_{3}*(X_{12}*(-(X_{14}*X_{21}) + X_{13}*X_{22}) + X_{10}*(X_{16}*X_{21} - X_{13}*X_{24}) + X_{9}*(-(X_{16}*X_{22}) + X_{14}*X_{24})), X_{6}*X_{12}*X_{15}*X_{21} - X_{6}*X_{11}*X_{16}*X_{21} - X_{5}*X_{12}*X_{15}*X_{22} + X_{5}*X_{11}*X_{16}*X_{22} - X_{6}*X_{12}*X_{13}*X_{23} + X_{5}*X_{12}*X_{14}*X_{23} + X_{6}*X_{9}*X_{16}*X_{23} - X_{5}*X_{10}*X_{16}*X_{23} + X_{8}*(X_{11}*(X_{14}*X_{21} - X_{13}*X_{22}) + X_{10}*(-(X_{15}*X_{21}) + X_{13}*X_{23}) + X_{9}*(X_{15}*X_{22} - X_{14}*X_{23})) + X_{6}*X_{11}*X_{13}*X_{24} - X_{5}*X_{11}*X_{14}*X_{24} - X_{6}*X_{9}*X_{15}*X_{24} + X_{5}*X_{10}*X_{15}*X_{24} + X_{7}*(X_{12}*(-(X_{14}*X_{21}) + X_{13}*X_{22}) + X_{10}*(X_{16}*X_{21} - X_{13}*X_{24}) + X_{9}*(-(X_{16}*X_{22}) + X_{14}*X_{24})), X_{2}*X_{8}*X_{19}*X_{21} - X_{2}*X_{7}*X_{20}*X_{21} - X_{1}*X_{8}*X_{19}*X_{22} + X_{1}*X_{7}*X_{20}*X_{22} - X_{2}*X_{8}*X_{17}*X_{23} + X_{1}*X_{8}*X_{18}*X_{23} + X_{2}*X_{5}*X_{20}*X_{23} - X_{1}*X_{6}*X_{20}*X_{23} + X_{4}*(X_{7}*(X_{18}*X_{21} - X_{17}*X_{22}) + X_{6}*(-(X_{19}*X_{21}) + X_{17}*X_{23}) + X_{5}*(X_{19}*X_{22} - X_{18}*X_{23})) + X_{2}*X_{7}*X_{17}*X_{24} - X_{1}*X_{7}*X_{18}*X_{24} - X_{2}*X_{5}*X_{19}*X_{24} + X_{1}*X_{6}*X_{19}*X_{24} + X_{3}*(X_{8}*(-(X_{18}*X_{21}) + X_{17}*X_{22}) + X_{6}*(X_{20}*X_{21} - X_{17}*X_{24}) + X_{5}*(-(X_{20}*X_{22}) + X_{18}*X_{24})), X_{2}*X_{12}*X_{19}*X_{21} - X_{2}*X_{11}*X_{20}*X_{21} - X_{1}*X_{12}*X_{19}*X_{22} + X_{1}*X_{11}*X_{20}*X_{22} - X_{2}*X_{12}*X_{17}*X_{23} + X_{1}*X_{12}*X_{18}*X_{23} + X_{2}*X_{9}*X_{20}*X_{23} - X_{1}*X_{10}*X_{20}*X_{23} + X_{4}*(X_{11}*(X_{18}*X_{21} - X_{17}*X_{22}) + X_{10}*(-(X_{19}*X_{21}) + X_{17}*X_{23}) + X_{9}*(X_{19}*X_{22} - X_{18}*X_{23})) + X_{2}*X_{11}*X_{17}*X_{24} - X_{1}*X_{11}*X_{18}*X_{24} - X_{2}*X_{9}*X_{19}*X_{24} + X_{1}*X_{10}*X_{19}*X_{24} + X_{3}*(X_{12}*(-(X_{18}*X_{21}) + X_{17}*X_{22}) + X_{10}*(X_{20}*X_{21} - X_{17}*X_{24}) + X_{9}*(-(X_{20}*X_{22}) + X_{18}*X_{24})), X_{6}*X_{12}*X_{19}*X_{21} - X_{6}*X_{11}*X_{20}*X_{21} - X_{5}*X_{12}*X_{19}*X_{22} + X_{5}*X_{11}*X_{20}*X_{22} - X_{6}*X_{12}*X_{17}*X_{23} + X_{5}*X_{12}*X_{18}*X_{23} + X_{6}*X_{9}*X_{20}*X_{23} - X_{5}*X_{10}*X_{20}*X_{23} + X_{8}*(X_{11}*(X_{18}*X_{21} - X_{17}*X_{22}) + X_{10}*(-(X_{19}*X_{21}) + X_{17}*X_{23}) + X_{9}*(X_{19}*X_{22} - X_{18}*X_{23})) + X_{6}*X_{11}*X_{17}*X_{24} - X_{5}*X_{11}*X_{18}*X_{24} - X_{6}*X_{9}*X_{19}*X_{24} + X_{5}*X_{10}*X_{19}*X_{24} + X_{7}*(X_{12}*(-(X_{18}*X_{21}) + X_{17}*X_{22}) + X_{10}*(X_{20}*X_{21} - X_{17}*X_{24}) + X_{9}*(-(X_{20}*X_{22}) + X_{18}*X_{24})), X_{2}*X_{16}*X_{19}*X_{21} - X_{2}*X_{15}*X_{20}*X_{21} - X_{1}*X_{16}*X_{19}*X_{22} + X_{1}*X_{15}*X_{20}*X_{22} - X_{2}*X_{16}*X_{17}*X_{23} + X_{1}*X_{16}*X_{18}*X_{23} + X_{2}*X_{13}*X_{20}*X_{23} - X_{1}*X_{14}*X_{20}*X_{23} + X_{4}*(X_{15}*(X_{18}*X_{21} - X_{17}*X_{22}) + X_{14}*(-(X_{19}*X_{21}) + X_{17}*X_{23}) + X_{13}*(X_{19}*X_{22} - X_{18}*X_{23})) + X_{2}*X_{15}*X_{17}*X_{24} - X_{1}*X_{15}*X_{18}*X_{24} - X_{2}*X_{13}*X_{19}*X_{24} + X_{1}*X_{14}*X_{19}*X_{24} + X_{3}*(X_{16}*(-(X_{18}*X_{21}) + X_{17}*X_{22}) + X_{14}*(X_{20}*X_{21} - X_{17}*X_{24}) + X_{13}*(-(X_{20}*X_{22}) + X_{18}*X_{24})), X_{6}*X_{16}*X_{19}*X_{21} - X_{6}*X_{15}*X_{20}*X_{21} - X_{5}*X_{16}*X_{19}*X_{22} + X_{5}*X_{15}*X_{20}*X_{22} - X_{6}*X_{16}*X_{17}*X_{23} + X_{5}*X_{16}*X_{18}*X_{23} + X_{6}*X_{13}*X_{20}*X_{23} - X_{5}*X_{14}*X_{20}*X_{23} + X_{8}*(X_{15}*(X_{18}*X_{21} - X_{17}*X_{22}) + X_{14}*(-(X_{19}*X_{21}) + X_{17}*X_{23}) + X_{13}*(X_{19}*X_{22} - X_{18}*X_{23})) + X_{6}*X_{15}*X_{17}*X_{24} - X_{5}*X_{15}*X_{18}*X_{24} - X_{6}*X_{13}*X_{19}*X_{24} + X_{5}*X_{14}*X_{19}*X_{24} + X_{7}*(X_{16}*(-(X_{18}*X_{21}) + X_{17}*X_{22}) + X_{14}*(X_{20}*X_{21} - X_{17}*X_{24}) + X_{13}*(-(X_{20}*X_{22}) + X_{18}*X_{24})), X_{10}*X_{16}*X_{19}*X_{21} - X_{10}*X_{15}*X_{20}*X_{21} - X_{9}*X_{16}*X_{19}*X_{22} + X_{9}*X_{15}*X_{20}*X_{22} - X_{10}*X_{16}*X_{17}*X_{23} + X_{9}*X_{16}*X_{18}*X_{23} + X_{10}*X_{13}*X_{20}*X_{23} - X_{9}*X_{14}*X_{20}*X_{23} + X_{12}*(X_{15}*(X_{18}*X_{21} - X_{17}*X_{22}) + X_{14}*(-(X_{19}*X_{21}) + X_{17}*X_{23}) + X_{13}*(X_{19}*X_{22} - X_{18}*X_{23})) + X_{10}*X_{15}*X_{17}*X_{24} - X_{9}*X_{15}*X_{18}*X_{24} - X_{10}*X_{13}*X_{19}*X_{24} + X_{9}*X_{14}*X_{19}*X_{24} + X_{11}*(X_{16}*(-(X_{18}*X_{21}) + X_{17}*X_{22}) + X_{14}*(X_{20}*X_{21} - X_{17}*X_{24}) + X_{13}*(-(X_{20}*X_{22}) + X_{18}*X_{24})), X_{1}*X_{25} + X_{2}*X_{26} + X_{3}*X_{27} + X_{4}*X_{28}, X_{5}*X_{25} + X_{6}*X_{26} + X_{7}*X_{27} + X_{8}*X_{28}, X_{9}*X_{25} + X_{10}*X_{26} + X_{11}*X_{27} + X_{12}*X_{28}, X_{13}*X_{25} + X_{14}*X_{26} + X_{15}*X_{27} + X_{16}*X_{28}, X_{17}*X_{25} + X_{18}*X_{26} + X_{19}*X_{27} + X_{20}*X_{28}, X_{21}*X_{25} + X_{22}*X_{26} + X_{23}*X_{27} + X_{24}*X_{28}, X_{1}*X_{29} + X_{2}*X_{30} + X_{3}*X_{31} + X_{4}*X_{32}, X_{5}*X_{29} + X_{6}*X_{30} + X_{7}*X_{31} + X_{8}*X_{32}, X_{9}*X_{29} + X_{10}*X_{30} + X_{11}*X_{31} + X_{12}*X_{32}, X_{13}*X_{29} + X_{14}*X_{30} + X_{15}*X_{31} + X_{16}*X_{32}, X_{17}*X_{29} + X_{18}*X_{30} + X_{19}*X_{31} + X_{20}*X_{32}, X_{21}*X_{29} + X_{22}*X_{30} + X_{23}*X_{31} + X_{24}*X_{32}, X_{1}*X_{33} + X_{2}*X_{34} + X_{3}*X_{35} + X_{4}*X_{36}, X_{5}*X_{33} + X_{6}*X_{34} + X_{7}*X_{35} + X_{8}*X_{36}, X_{9}*X_{33} + X_{10}*X_{34} + X_{11}*X_{35} + X_{12}*X_{36}, X_{13}*X_{33} + X_{14}*X_{34} + X_{15}*X_{35} + X_{16}*X_{36}, X_{17}*X_{33} + X_{18}*X_{34} + X_{19}*X_{35} + X_{20}*X_{36}, X_{21}*X_{33} + X_{22}*X_{34} + X_{23}*X_{35} + X_{24}*X_{36}, X_{1}*X_{37} + X_{2}*X_{38} + X_{3}*X_{39} + X_{4}*X_{40}, X_{5}*X_{37} + X_{6}*X_{38} + X_{7}*X_{39} + X_{8}*X_{40}, X_{9}*X_{37} + X_{10}*X_{38} + X_{11}*X_{39} + X_{12}*X_{40}, X_{13}*X_{37} + X_{14}*X_{38} + X_{15}*X_{39} + X_{16}*X_{40}, X_{17}*X_{37} + X_{18}*X_{38} + X_{19}*X_{39} + X_{20}*X_{40}, X_{21}*X_{37} + X_{22}*X_{38} + X_{23}*X_{39} + X_{24}*X_{40}, X_{26}*X_{32}*X_{35}*X_{37} - X_{26}*X_{31}*X_{36}*X_{37} - X_{25}*X_{32}*X_{35}*X_{38} + X_{25}*X_{31}*X_{36}*X_{38} - X_{26}*X_{32}*X_{33}*X_{39} + X_{25}*X_{32}*X_{34}*X_{39} + X_{26}*X_{29}*X_{36}*X_{39} - X_{25}*X_{30}*X_{36}*X_{39} + X_{28}*(X_{31}*(X_{34}*X_{37} - X_{33}*X_{38}) + X_{30}*(-(X_{35}*X_{37}) + X_{33}*X_{39}) + X_{29}*(X_{35}*X_{38} - X_{34}*X_{39})) + X_{26}*X_{31}*X_{33}*X_{40} - X_{25}*X_{31}*X_{34}*X_{40} - X_{26}*X_{29}*X_{35}*X_{40} + X_{25}*X_{30}*X_{35}*X_{40} + X_{27}*(X_{32}*(-(X_{34}*X_{37}) + X_{33}*X_{38}) + X_{30}*(X_{36}*X_{37} - X_{33}*X_{40}) + X_{29}*(-(X_{36}*X_{38}) + X_{34}*X_{40})), X_{1}*X_{41} + X_{2}*X_{42} + X_{3}*X_{43} + X_{4}*X_{44}, X_{5}*X_{41} + X_{6}*X_{42} + X_{7}*X_{43} + X_{8}*X_{44}, X_{9}*X_{41} + X_{10}*X_{42} + X_{11}*X_{43} + X_{12}*X_{44}, X_{13}*X_{41} + X_{14}*X_{42} + X_{15}*X_{43} + X_{16}*X_{44}, X_{17}*X_{41} + X_{18}*X_{42} + X_{19}*X_{43} + X_{20}*X_{44}, X_{21}*X_{41} + X_{22}*X_{42} + X_{23}*X_{43} + X_{24}*X_{44}, X_{26}*X_{32}*X_{35}*X_{41} - X_{26}*X_{31}*X_{36}*X_{41} - X_{25}*X_{32}*X_{35}*X_{42} + X_{25}*X_{31}*X_{36}*X_{42} - X_{26}*X_{32}*X_{33}*X_{43} + X_{25}*X_{32}*X_{34}*X_{43} + X_{26}*X_{29}*X_{36}*X_{43} - X_{25}*X_{30}*X_{36}*X_{43} + X_{28}*(X_{31}*(X_{34}*X_{41} - X_{33}*X_{42}) + X_{30}*(-(X_{35}*X_{41}) + X_{33}*X_{43}) + X_{29}*(X_{35}*X_{42} - X_{34}*X_{43})) + X_{26}*X_{31}*X_{33}*X_{44} - X_{25}*X_{31}*X_{34}*X_{44} - X_{26}*X_{29}*X_{35}*X_{44} + X_{25}*X_{30}*X_{35}*X_{44} + X_{27}*(X_{32}*(-(X_{34}*X_{41}) + X_{33}*X_{42}) + X_{30}*(X_{36}*X_{41} - X_{33}*X_{44}) + X_{29}*(-(X_{36}*X_{42}) + X_{34}*X_{44})), X_{26}*X_{32}*X_{39}*X_{41} - X_{26}*X_{31}*X_{40}*X_{41} - X_{25}*X_{32}*X_{39}*X_{42} + X_{25}*X_{31}*X_{40}*X_{42} - X_{26}*X_{32}*X_{37}*X_{43} + X_{25}*X_{32}*X_{38}*X_{43} + X_{26}*X_{29}*X_{40}*X_{43} - X_{25}*X_{30}*X_{40}*X_{43} + X_{28}*(X_{31}*(X_{38}*X_{41} - X_{37}*X_{42}) + X_{30}*(-(X_{39}*X_{41}) + X_{37}*X_{43}) + X_{29}*(X_{39}*X_{42} - X_{38}*X_{43})) + X_{26}*X_{31}*X_{37}*X_{44} - X_{25}*X_{31}*X_{38}*X_{44} - X_{26}*X_{29}*X_{39}*X_{44} + X_{25}*X_{30}*X_{39}*X_{44} + X_{27}*(X_{32}*(-(X_{38}*X_{41}) + X_{37}*X_{42}) + X_{30}*(X_{40}*X_{41} - X_{37}*X_{44}) + X_{29}*(-(X_{40}*X_{42}) + X_{38}*X_{44})), X_{26}*X_{36}*X_{39}*X_{41} - X_{26}*X_{35}*X_{40}*X_{41} - X_{25}*X_{36}*X_{39}*X_{42} + X_{25}*X_{35}*X_{40}*X_{42} - X_{26}*X_{36}*X_{37}*X_{43} + X_{25}*X_{36}*X_{38}*X_{43} + X_{26}*X_{33}*X_{40}*X_{43} - X_{25}*X_{34}*X_{40}*X_{43} + X_{28}*(X_{35}*(X_{38}*X_{41} - X_{37}*X_{42}) + X_{34}*(-(X_{39}*X_{41}) + X_{37}*X_{43}) + X_{33}*(X_{39}*X_{42} - X_{38}*X_{43})) + X_{26}*X_{35}*X_{37}*X_{44} - X_{25}*X_{35}*X_{38}*X_{44} - X_{26}*X_{33}*X_{39}*X_{44} + X_{25}*X_{34}*X_{39}*X_{44} + X_{27}*(X_{36}*(-(X_{38}*X_{41}) + X_{37}*X_{42}) + X_{34}*(X_{40}*X_{41} - X_{37}*X_{44}) + X_{33}*(-(X_{40}*X_{42}) + X_{38}*X_{44})), X_{30}*X_{36}*X_{39}*X_{41} - X_{30}*X_{35}*X_{40}*X_{41} - X_{29}*X_{36}*X_{39}*X_{42} + X_{29}*X_{35}*X_{40}*X_{42} - X_{30}*X_{36}*X_{37}*X_{43} + X_{29}*X_{36}*X_{38}*X_{43} + X_{30}*X_{33}*X_{40}*X_{43} - X_{29}*X_{34}*X_{40}*X_{43} + X_{32}*(X_{35}*(X_{38}*X_{41} - X_{37}*X_{42}) + X_{34}*(-(X_{39}*X_{41}) + X_{37}*X_{43}) + X_{33}*(X_{39}*X_{42} - X_{38}*X_{43})) + X_{30}*X_{35}*X_{37}*X_{44} - X_{29}*X_{35}*X_{38}*X_{44} - X_{30}*X_{33}*X_{39}*X_{44} + X_{29}*X_{34}*X_{39}*X_{44} + X_{31}*(X_{36}*(-(X_{38}*X_{41}) + X_{37}*X_{42}) + X_{34}*(X_{40}*X_{41} - X_{37}*X_{44}) + X_{33}*(-(X_{40}*X_{42}) + X_{38}*X_{44})), X_{1}*X_{45} + X_{2}*X_{46} + X_{3}*X_{47} + X_{4}*X_{48}, X_{5}*X_{45} + X_{6}*X_{46} + X_{7}*X_{47} + X_{8}*X_{48}, X_{9}*X_{45} + X_{10}*X_{46} + X_{11}*X_{47} + X_{12}*X_{48}, X_{13}*X_{45} + X_{14}*X_{46} + X_{15}*X_{47} + X_{16}*X_{48}, X_{17}*X_{45} + X_{18}*X_{46} + X_{19}*X_{47} + X_{20}*X_{48}, X_{21}*X_{45} + X_{22}*X_{46} + X_{23}*X_{47} + X_{24}*X_{48}, X_{26}*X_{32}*X_{35}*X_{45} - X_{26}*X_{31}*X_{36}*X_{45} - X_{25}*X_{32}*X_{35}*X_{46} + X_{25}*X_{31}*X_{36}*X_{46} - X_{26}*X_{32}*X_{33}*X_{47} + X_{25}*X_{32}*X_{34}*X_{47} + X_{26}*X_{29}*X_{36}*X_{47} - X_{25}*X_{30}*X_{36}*X_{47} + X_{28}*(X_{31}*(X_{34}*X_{45} - X_{33}*X_{46}) + X_{30}*(-(X_{35}*X_{45}) + X_{33}*X_{47}) + X_{29}*(X_{35}*X_{46} - X_{34}*X_{47})) + X_{26}*X_{31}*X_{33}*X_{48} - X_{25}*X_{31}*X_{34}*X_{48} - X_{26}*X_{29}*X_{35}*X_{48} + X_{25}*X_{30}*X_{35}*X_{48} + X_{27}*(X_{32}*(-(X_{34}*X_{45}) + X_{33}*X_{46}) + X_{30}*(X_{36}*X_{45} - X_{33}*X_{48}) + X_{29}*(-(X_{36}*X_{46}) + X_{34}*X_{48})), X_{26}*X_{32}*X_{39}*X_{45} - X_{26}*X_{31}*X_{40}*X_{45} - X_{25}*X_{32}*X_{39}*X_{46} + X_{25}*X_{31}*X_{40}*X_{46} - X_{26}*X_{32}*X_{37}*X_{47} + X_{25}*X_{32}*X_{38}*X_{47} + X_{26}*X_{29}*X_{40}*X_{47} - X_{25}*X_{30}*X_{40}*X_{47} + X_{28}*(X_{31}*(X_{38}*X_{45} - X_{37}*X_{46}) + X_{30}*(-(X_{39}*X_{45}) + X_{37}*X_{47}) + X_{29}*(X_{39}*X_{46} - X_{38}*X_{47})) + X_{26}*X_{31}*X_{37}*X_{48} - X_{25}*X_{31}*X_{38}*X_{48} - X_{26}*X_{29}*X_{39}*X_{48} + X_{25}*X_{30}*X_{39}*X_{48} + X_{27}*(X_{32}*(-(X_{38}*X_{45}) + X_{37}*X_{46}) + X_{30}*(X_{40}*X_{45} - X_{37}*X_{48}) + X_{29}*(-(X_{40}*X_{46}) + X_{38}*X_{48})), X_{26}*X_{36}*X_{39}*X_{45} - X_{26}*X_{35}*X_{40}*X_{45} - X_{25}*X_{36}*X_{39}*X_{46} + X_{25}*X_{35}*X_{40}*X_{46} - X_{26}*X_{36}*X_{37}*X_{47} + X_{25}*X_{36}*X_{38}*X_{47} + X_{26}*X_{33}*X_{40}*X_{47} - X_{25}*X_{34}*X_{40}*X_{47} + X_{28}*(X_{35}*(X_{38}*X_{45} - X_{37}*X_{46}) + X_{34}*(-(X_{39}*X_{45}) + X_{37}*X_{47}) + X_{33}*(X_{39}*X_{46} - X_{38}*X_{47})) + X_{26}*X_{35}*X_{37}*X_{48} - X_{25}*X_{35}*X_{38}*X_{48} - X_{26}*X_{33}*X_{39}*X_{48} + X_{25}*X_{34}*X_{39}*X_{48} + X_{27}*(X_{36}*(-(X_{38}*X_{45}) + X_{37}*X_{46}) + X_{34}*(X_{40}*X_{45} - X_{37}*X_{48}) + X_{33}*(-(X_{40}*X_{46}) + X_{38}*X_{48})), X_{30}*X_{36}*X_{39}*X_{45} - X_{30}*X_{35}*X_{40}*X_{45} - X_{29}*X_{36}*X_{39}*X_{46} + X_{29}*X_{35}*X_{40}*X_{46} - X_{30}*X_{36}*X_{37}*X_{47} + X_{29}*X_{36}*X_{38}*X_{47} + X_{30}*X_{33}*X_{40}*X_{47} - X_{29}*X_{34}*X_{40}*X_{47} + X_{32}*(X_{35}*(X_{38}*X_{45} - X_{37}*X_{46}) + X_{34}*(-(X_{39}*X_{45}) + X_{37}*X_{47}) + X_{33}*(X_{39}*X_{46} - X_{38}*X_{47})) + X_{30}*X_{35}*X_{37}*X_{48} - X_{29}*X_{35}*X_{38}*X_{48} - X_{30}*X_{33}*X_{39}*X_{48} + X_{29}*X_{34}*X_{39}*X_{48} + X_{31}*(X_{36}*(-(X_{38}*X_{45}) + X_{37}*X_{46}) + X_{34}*(X_{40}*X_{45} - X_{37}*X_{48}) + X_{33}*(-(X_{40}*X_{46}) + X_{38}*X_{48})), X_{26}*X_{32}*X_{43}*X_{45} - X_{26}*X_{31}*X_{44}*X_{45} - X_{25}*X_{32}*X_{43}*X_{46} + X_{25}*X_{31}*X_{44}*X_{46} - X_{26}*X_{32}*X_{41}*X_{47} + X_{25}*X_{32}*X_{42}*X_{47} + X_{26}*X_{29}*X_{44}*X_{47} - X_{25}*X_{30}*X_{44}*X_{47} + X_{28}*(X_{31}*(X_{42}*X_{45} - X_{41}*X_{46}) + X_{30}*(-(X_{43}*X_{45}) + X_{41}*X_{47}) + X_{29}*(X_{43}*X_{46} - X_{42}*X_{47})) + X_{26}*X_{31}*X_{41}*X_{48} - X_{25}*X_{31}*X_{42}*X_{48} - X_{26}*X_{29}*X_{43}*X_{48} + X_{25}*X_{30}*X_{43}*X_{48} + X_{27}*(X_{32}*(-(X_{42}*X_{45}) + X_{41}*X_{46}) + X_{30}*(X_{44}*X_{45} - X_{41}*X_{48}) + X_{29}*(-(X_{44}*X_{46}) + X_{42}*X_{48})), X_{26}*X_{36}*X_{43}*X_{45} - X_{26}*X_{35}*X_{44}*X_{45} - X_{25}*X_{36}*X_{43}*X_{46} + X_{25}*X_{35}*X_{44}*X_{46} - X_{26}*X_{36}*X_{41}*X_{47} + X_{25}*X_{36}*X_{42}*X_{47} + X_{26}*X_{33}*X_{44}*X_{47} - X_{25}*X_{34}*X_{44}*X_{47} + X_{28}*(X_{35}*(X_{42}*X_{45} - X_{41}*X_{46}) + X_{34}*(-(X_{43}*X_{45}) + X_{41}*X_{47}) + X_{33}*(X_{43}*X_{46} - X_{42}*X_{47})) + X_{26}*X_{35}*X_{41}*X_{48} - X_{25}*X_{35}*X_{42}*X_{48} - X_{26}*X_{33}*X_{43}*X_{48} + X_{25}*X_{34}*X_{43}*X_{48} + X_{27}*(X_{36}*(-(X_{42}*X_{45}) + X_{41}*X_{46}) + X_{34}*(X_{44}*X_{45} - X_{41}*X_{48}) + X_{33}*(-(X_{44}*X_{46}) + X_{42}*X_{48})), X_{30}*X_{36}*X_{43}*X_{45} - X_{30}*X_{35}*X_{44}*X_{45} - X_{29}*X_{36}*X_{43}*X_{46} + X_{29}*X_{35}*X_{44}*X_{46} - X_{30}*X_{36}*X_{41}*X_{47} + X_{29}*X_{36}*X_{42}*X_{47} + X_{30}*X_{33}*X_{44}*X_{47} - X_{29}*X_{34}*X_{44}*X_{47} + X_{32}*(X_{35}*(X_{42}*X_{45} - X_{41}*X_{46}) + X_{34}*(-(X_{43}*X_{45}) + X_{41}*X_{47}) + X_{33}*(X_{43}*X_{46} - X_{42}*X_{47})) + X_{30}*X_{35}*X_{41}*X_{48} - X_{29}*X_{35}*X_{42}*X_{48} - X_{30}*X_{33}*X_{43}*X_{48} + X_{29}*X_{34}*X_{43}*X_{48} + X_{31}*(X_{36}*(-(X_{42}*X_{45}) + X_{41}*X_{46}) + X_{34}*(X_{44}*X_{45} - X_{41}*X_{48}) + X_{33}*(-(X_{44}*X_{46}) + X_{42}*X_{48})), X_{26}*X_{40}*X_{43}*X_{45} - X_{26}*X_{39}*X_{44}*X_{45} - X_{25}*X_{40}*X_{43}*X_{46} + X_{25}*X_{39}*X_{44}*X_{46} - X_{26}*X_{40}*X_{41}*X_{47} + X_{25}*X_{40}*X_{42}*X_{47} + X_{26}*X_{37}*X_{44}*X_{47} - X_{25}*X_{38}*X_{44}*X_{47} + X_{28}*(X_{39}*(X_{42}*X_{45} - X_{41}*X_{46}) + X_{38}*(-(X_{43}*X_{45}) + X_{41}*X_{47}) + X_{37}*(X_{43}*X_{46} - X_{42}*X_{47})) + X_{26}*X_{39}*X_{41}*X_{48} - X_{25}*X_{39}*X_{42}*X_{48} - X_{26}*X_{37}*X_{43}*X_{48} + X_{25}*X_{38}*X_{43}*X_{48} + X_{27}*(X_{40}*(-(X_{42}*X_{45}) + X_{41}*X_{46}) + X_{38}*(X_{44}*X_{45} - X_{41}*X_{48}) + X_{37}*(-(X_{44}*X_{46}) + X_{42}*X_{48})), X_{30}*X_{40}*X_{43}*X_{45} - X_{30}*X_{39}*X_{44}*X_{45} - X_{29}*X_{40}*X_{43}*X_{46} + X_{29}*X_{39}*X_{44}*X_{46} - X_{30}*X_{40}*X_{41}*X_{47} + X_{29}*X_{40}*X_{42}*X_{47} + X_{30}*X_{37}*X_{44}*X_{47} - X_{29}*X_{38}*X_{44}*X_{47} + X_{32}*(X_{39}*(X_{42}*X_{45} - X_{41}*X_{46}) + X_{38}*(-(X_{43}*X_{45}) + X_{41}*X_{47}) + X_{37}*(X_{43}*X_{46} - X_{42}*X_{47})) + X_{30}*X_{39}*X_{41}*X_{48} - X_{29}*X_{39}*X_{42}*X_{48} - X_{30}*X_{37}*X_{43}*X_{48} + X_{29}*X_{38}*X_{43}*X_{48} + X_{31}*(X_{40}*(-(X_{42}*X_{45}) + X_{41}*X_{46}) + X_{38}*(X_{44}*X_{45} - X_{41}*X_{48}) + X_{37}*(-(X_{44}*X_{46}) + X_{42}*X_{48})), X_{34}*X_{40}*X_{43}*X_{45} - X_{34}*X_{39}*X_{44}*X_{45} - X_{33}*X_{40}*X_{43}*X_{46} + X_{33}*X_{39}*X_{44}*X_{46} - X_{34}*X_{40}*X_{41}*X_{47} + X_{33}*X_{40}*X_{42}*X_{47} + X_{34}*X_{37}*X_{44}*X_{47} - X_{33}*X_{38}*X_{44}*X_{47} + X_{36}*(X_{39}*(X_{42}*X_{45} - X_{41}*X_{46}) + X_{38}*(-(X_{43}*X_{45}) + X_{41}*X_{47}) + X_{37}*(X_{43}*X_{46} - X_{42}*X_{47})) + X_{34}*X_{39}*X_{41}*X_{48} - X_{33}*X_{39}*X_{42}*X_{48} - X_{34}*X_{37}*X_{43}*X_{48} + X_{33}*X_{38}*X_{43}*X_{48} + X_{35}*(X_{40}*(-(X_{42}*X_{45}) + X_{41}*X_{46}) + X_{38}*(X_{44}*X_{45} - X_{41}*X_{48}) + X_{37}*(-(X_{44}*X_{46}) + X_{42}*X_{48}))};
print timing gb ideal dterms;
