-- -*- M2-comint -*- {* hash: -1106702772 *}
i1 : R4 = ZZ/32003[a..d];
i2 : R5 = ZZ/32003[a..e];
i3 : R6 = ZZ/32003[a..f];
i4 : M = coker genericMatrix(R6,a,2,3)
o4 = cokernel | a c e |
| b d f |
2
o4 : R6-module, quotient of R6
i5 : pdim M
o5 = 2
i6 : G = map(R6,R5,{a+b+c+d+e+f,b,c,d,e})
o6 = map(R6,R5,{a + b + c + d + e + f, b, c, d, e})
o6 : RingMap R6 <--- R5
i7 : F = map(R5,R4,random(R5^1, R5^{4:-1}))
o7 = map(R5,R4,{- 2829a - 1435b + 8058c + 9689d + 14723e, 12865a - 3926b - 12267c - 11130d - 15042e, 8553a - 9311b - 13007c - 12446d - 9173e, 2800a + 3068b - 10799c - 7772d - 8215e})
o7 : RingMap R5 <--- R4
i8 : P = pushForward(G,M)
o8 = cokernel | c -de |
| d bc-ad+bd+cd+d2+de |
2
o8 : R5-module, quotient of R5
i9 : pdim P
o9 = 1
i10 : Q = pushForward(F,P)
3
o10 = R4
o10 : R4-module, free, degrees {0, 1, 0}
i11 : pdim Q
o11 = 0
i12 : P3 = QQ[a..d];
i13 : M = comodule monomialCurveIdeal(P3,{1,2,3})
o13 = cokernel | c2-bd bc-ad b2-ac |
1
o13 : P3-module, quotient of P3
i14 : P2 = QQ[a,b,c];
i15 : F = map(P3,P2,random(P3^1, P3^{-1,-1,-1}))
5 10 6 1 3 3 1 5 5 1
o15 = map(P3,P2,{4a + 6b + -c + --d, -a + -b + -c + --d, -a + -b + -c + -d})
7 9 7 2 5 10 2 9 7 6
o15 : RingMap P3 <--- P2
i16 : N = pushForward(F,M)
o16 = cokernel {0} | 30779930429955ab-131800438279650b2-66374160751755ac+158853407152860bc+223880299534440c2 2638279751139a2+182813941470300b2-29957171223834ac-584649608404680bc+535814803151856c2 16254779874687636083792271648927000b3-78707410788008924789026176600237900b2c+279947730366138663179680606940250ac2+127509160069495706614246839452113800bc2-71413271842960346782498089153332400c3 0 |
{1} | -19941099352965a+148580137757380b-136111547698731c -15094700977359a+70556279211950b-25254142964124c 120175710355802816491444299167535a2-1442129616974558298205614904363215ab+1126556210065667747771421622059650b2+2233769573129702969190510834676434ac-2440197088624604283293124623314440bc-2144305087505625664481300960634072c2 37759287645a3-614804300955a2b+5603021144700ab2-26169340550500b3+548063491788a2c-10812992256630abc+90638470295100b2c+3519714763242ac2-105794899065000bc2+48285683500752c3 |
2
o16 : P2-module, quotient of P2
i17 : hilbertPolynomial M
o17 = - 2*P + 3*P
0 1
o17 : ProjectiveHilbertPolynomial
i18 : hilbertPolynomial N
o18 = - 2*P + 3*P
0 1
o18 : ProjectiveHilbertPolynomial
i19 : ann N
3 2 2
o19 = ideal(37759287645a - 614804300955a b + 5603021144700a*b -
-----------------------------------------------------------------------
3 2
26169340550500b + 548063491788a c - 10812992256630a*b*c +
-----------------------------------------------------------------------
2 2 2
90638470295100b c + 3519714763242a*c - 105794899065000b*c +
-----------------------------------------------------------------------
3
48285683500752c )
o19 : Ideal of P2
i20 :
