-- -*- M2-comint -*- {* hash: -1857755625 *}
i1 : R = ZZ/101[a..g];
i2 : I = ideal random(R^1, R^{3:-3});
o2 : Ideal of R
i3 : hf = poincare ideal(a^3,b^3,c^3)
3 6 9
o3 = 1 - 3T + 3T - T
o3 : ZZ[T]
i4 : installHilbertFunction(I, hf)
i5 : gbTrace=3
o5 = 3
i6 : time poincare I
-- used 0. seconds
3 6 9
o6 = 1 - 3T + 3T - T
o6 : ZZ[T]
i7 : time gens gb I;
-- registering gb 3 at 0x912f000
-- [gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(2,6)mm{7}(1,4)m{8}(0,2)
-- number of (nonminimal) gb elements = 11
-- number of monomials = 4179
-- ncalls = 10
-- nloop = 29
-- nsaved = 0
--
removing gb 1 at 0x9349e40
-- used 0.046993 seconds
1 11
o7 : Matrix R <--- R
i8 : R = QQ[a..d];
-- registering polynomial ring 5 at 0x8f69f30
i9 : I = ideal random(R^1, R^{3:-3});
-- registering gb 4 at 0x9490ab0
-- [gb]
-- number of (nonminimal) gb elements = 0
-- number of monomials = 0
-- ncalls = 0
-- nloop = 0
-- nsaved = 0
--
o9 : Ideal of R
i10 : time hf = poincare I
-- registering gb 5 at 0x9490980
-- [gb]{3}(3)mmm{4}(2)mm{5}(3)mmm{6}(6)mmoooo{7}(4)mooo{8}(2)oo
-- number of (nonminimal) gb elements = 11
-- number of monomials = 267
-- ncalls = 10
-- nloop = 20
-- nsaved = 0
-- -- used 0.008999 seconds
3 6 9
o10 = 1 - 3T + 3T - T
o10 : ZZ[T]
i11 : S = QQ[a..d,MonomialOrder=>Eliminate 2]
-- registering polynomial ring 6 at 0x8f69ea0
o11 = S
o11 : PolynomialRing
i12 : J = substitute(I,S)
1 3 7 2 4 2 1 3 4 2 1 2 2 2
o12 = ideal (-a + -a b + -a*b + -b + -a c + -a*b*c + b c + -a d + 2a*b*d +
3 8 3 7 7 4 9
-----------------------------------------------------------------------
1 2 9 2 10 2 1 5 2 7 2 3 3 2
-b d + -a*c + --b*c + -a*c*d + -b*c*d + 10a*d + -b*d + -c + 10c d
7 5 7 3 4 8 8
-----------------------------------------------------------------------
1 2 3 3 2 3 2 3 3 2 9 8 2 7 2
+ -c*d + d , a + 2a b + -a*b + -b + a c + -a*b*c + -b c + --a d +
2 2 2 2 7 10
-----------------------------------------------------------------------
3 5 2 2 2 5 2 9 5 2 2 2 3
-a*b*d + -b d + -a*c + -b*c + -a*c*d + 3b*c*d + -a*d + b*d + -c +
5 3 5 8 5 4 5
-----------------------------------------------------------------------
9 2 2 3 1 3 2 5 2 3 9 2 1 5 2
-c d + c*d + 3d , --a + 4a b + -a*b + 2b + -a c + -a*b*c + -b c +
8 10 6 4 7 3
-----------------------------------------------------------------------
10 2 3 2 2 2 2 5 1 2 9 2
--a d + a*b*d + -b d + 4a*c + -b*c + -a*c*d + -b*c*d + a*d + -b*d +
9 2 3 2 4 8
-----------------------------------------------------------------------
3 7 2 3 2 3
5c + -c d + -c*d + d )
2 2
o12 : Ideal of S
i13 : installHilbertFunction(J, hf)
i14 : gbTrace=3
o14 = 3
i15 : time gens gb J;
-- registering gb 6 at 0x94905f0
-- [gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(3,7)mmm{7}(3,8)mmm{8}(3,9)mmm{9}(3,9)m
-- mm{10}(2,8)mm{11}(1,5)m{12}(1,3)m{13}(1,3)m{14}(1,3)m{15}(1,3)m{16}(1,3)m
-- {17}(1,3)m{18}(1,3)m{19}(1,3)m{20}(1,3)m{21}(1,3)m{22}(1,3)m{23}(1,3)m{24}(1,3)m
-- {25}(1,3)m{26}(1,3)m{27}(1,3)m{28}(0,2)
-- number of (nonminimal) gb elements = 39
-- number of monomials = 1051
-- ncalls = 46
-- nloop = 54
-- nsaved = 0
-- -- used 0.287957 seconds
1 39
o15 : Matrix S <--- S
i16 : selectInSubring(1,gens gb J)
o16 = | 739412929760026489587300972025342941573944541459417029705594323415910
-----------------------------------------------------------------------
1132800c27-411855407446221557734128747048632866529110478240091846586444
-----------------------------------------------------------------------
22156518306944000c26d+8774023133267410734751057402152074136774027763791
-----------------------------------------------------------------------
59260032052060564012984281600c25d2-
-----------------------------------------------------------------------
33251504605433573286890242546005434672753097081943041498586542996229008
-----------------------------------------------------------------------
39509760c24d3+173339297061843998455902038429842063738816474775692735689
-----------------------------------------------------------------------
78080470584857188430400c23d4-
-----------------------------------------------------------------------
86733106046835537707079947012151647240671189464973001906836110935364998
-----------------------------------------------------------------------
152041600c22d5+24490191621809724100947748452140403918778202731520163180
-----------------------------------------------------------------------
0744938236715766910498848c21d6-
-----------------------------------------------------------------------
36329970498504192792445164134482202337392862391956984783024009043858133
-----------------------------------------------------------------------
2096293600c20d7+3029572571013681703166050581540361494530007898561746257
-----------------------------------------------------------------------
88469757577307060636291140c19d8-
-----------------------------------------------------------------------
11434072053964259447211514708716377188869333656092516193167302151812018
-----------------------------------------------------------------------
9544408560c18d9-8197006746314878454973566342512111569826323502510032528
-----------------------------------------------------------------------
1953809190902983202987220c17d10+
-----------------------------------------------------------------------
43246380044428650123442224803033852369309526392596207165235257428343421
-----------------------------------------------------------------------
4321148320c16d11-333491965675567944341038248730586414098582448251158046
-----------------------------------------------------------------------
977479229822449628288923300c15d12-
-----------------------------------------------------------------------
18694574464866135749052747829315777517599755951432292386047513140432008
-----------------------------------------------------------------------
3806496400c14d13+704411051600002301637133770710968465691875754422668979
-----------------------------------------------------------------------
477538695506714176279533100c13d14-
-----------------------------------------------------------------------
14301103932351205496440879867168012931180919117294888207223569807029941
-----------------------------------------------------------------------
520924300c12d15-5959289606861327451299615807358116391406223619830355344
-----------------------------------------------------------------------
11458469299453888522995375c11d16-
-----------------------------------------------------------------------
22550980563460786464498873304780254723425231521149989266259639001327229
-----------------------------------------------------------------------
6542758500c10d17+346888622353995181486770568814942377652201478709574705
-----------------------------------------------------------------------
523037585011833228114838375c9d18+
-----------------------------------------------------------------------
84156733419059162977149439604509145606599041598581356639020759924902856
-----------------------------------------------------------------------
102323000c8d19+96702302590542716326212036076558734371284446291397468375
-----------------------------------------------------------------------
74474692267646091269000c7d20-
-----------------------------------------------------------------------
22240738603655626357644951083034610634684799359508153658568570060945436
-----------------------------------------------------------------------
255744000c6d21-79044370109172847201880141843239409049913534274159059620
-----------------------------------------------------------------------
03805645715968577017500c5d22-
-----------------------------------------------------------------------
33045688473634278086246398900047398158450856659251555753075592705374398
-----------------------------------------------------------------------
728605000c4d23+33879926654728481096333597720518088753961518356718943374
-----------------------------------------------------------------------
88144461118886422075000c3d24+
-----------------------------------------------------------------------
10136825703529029705393067570283677651317433731648159850913396409289557
-----------------------------------------------------------------------
510000000c2d25+26012052882612536122907272491336838464238960366976184856
-----------------------------------------------------------------------
28822229299522432400000cd26-
-----------------------------------------------------------------------
23285136339746181069612076136005800393859844569510052764243876725840985
-----------------------------------------------------------------------
30800000d27 |
1 1
o16 : Matrix S <--- S
i17 :
