-- -*- M2-comint -*- {* hash: -1259043627 *}
i1 : R = ZZ/101[a..f];
i2 : m = matrix{{a,b,c,d}};
1 4
o2 : Matrix R <--- R
i3 : m1 = schreyerOrder m
o3 = | a b c d |
1 4
o3 : Matrix R <--- R
i4 : F = source m1
4
o4 = R
o4 : R-module, free, degrees {1, 1, 1, 1}
i5 : g = syz m1
o5 = {1} | -b 0 -c 0 0 -d |
{1} | a -c 0 0 -d 0 |
{1} | 0 b a -d 0 0 |
{1} | 0 0 0 c b a |
4 6
o5 : Matrix R <--- R
i6 : leadTerm g
o6 = {1} | 0 0 0 0 0 0 |
{1} | a 0 0 0 0 0 |
{1} | 0 b a 0 0 0 |
{1} | 0 0 0 c b a |
4 6
o6 : Matrix R <--- R
i7 : schreyerOrder target m
o7 = 0
1
o7 : Matrix 0 <--- R
i8 : schreyerOrder source g
o8 = 0
6
o8 : Matrix 0 <--- R
i9 : R = QQ[a..f];
i10 : I = ideal"abc-def,a2c-d2f,aef-bcd,a3-d3,af2-cd2"
2 2 3 3 2
o10 = ideal (a*b*c - d*e*f, a c - d f, - b*c*d + a*e*f, a - d , - c*d +
-----------------------------------------------------------------------
2
a*f )
o10 : Ideal of R
i11 : F = syz gens I
o11 = {3} | a2+ad+d2 bcd-aef cd2+a2f+d2f a2b+bd2+ade a3-d3 0
{3} | 0 0 aef-def abe-bde 0 a3-d3
{3} | a2+ad+d2 abc-def acd+adf+d2f abd+bd2+d2e 0 0
{3} | -bc-ef 0 -bcf-cef -b2c-bce -abc+def -a2c+d2f
{3} | 0 0 0 0 0 0
-----------------------------------------------------------------------
acd-acf a2c-a2f+acf-d2f -a2f+acf a2d-a2f
-bcd-ace+bcf+aef ace-bcf-aef+def abc+ace-bcf-aef -a2e+ade
d2f-df2 cd2-adf-d2f+df2 cd2-adf-d2f+df2 d3-d2f
c2e-cef -bc2-c2e+bcf+cef -bc2-c2e+bcf+cef -bcd+ace-cde+bcf
-cde+def cde-def cde-def -ade+d2e
-----------------------------------------------------------------------
a2e+bdf+aef d3-d2f 0 0 0 cd2-af2 0 ad2-adf
ae2-bef a2e-d2e -ade+abf 0 a2c-df2 0 cd2-af2 -ade+bdf
ade+d2e+abf ad2-adf -d3+d2f -cd2+af2 0 0 0 0
-bce-ce2 -ace+ef2 cde-bcf 0 -ac2+f3 0 0 cde-bf2
-abe+de2 -a2e+ade bd2-d2e bcd-aef acd-a2f abc-def a2c-d2f a2b-d2e
-----------------------------------------------------------------------
0 abc2-def2 ac2f-df3 ab2c+bdef+ae2f cdef-bcf2 |
0 -b2c2+e2f2 ac2e-bc2f-acef+ef3 -b3c+abe2+ae3-be2f 0 |
0 bcdf-acef cdf2-af3 bd2e+d2e2+b2df -bc2d+ef3 |
cd2-af2 0 -c3e+c2ef -bce2-ce3 0 |
a3-d3 0 c2de-acef-cdef+aef2 -b2de+de3 b2c2-e2f2 |
5 23
o11 : Matrix R <--- R
i12 : betti gens gb syz F
0 1
o12 = total: 23 67
5: 1 .
6: 18 19
7: 4 27
8: . 8
9: . 8
10: . 5
o12 : BettiTally
i13 : G = schreyerOrder F
o13 = {3} | a2+ad+d2 bcd-aef cd2+a2f+d2f a2b+bd2+ade a3-d3 0
{3} | 0 0 aef-def abe-bde 0 a3-d3
{3} | a2+ad+d2 abc-def acd+adf+d2f abd+bd2+d2e 0 0
{3} | -bc-ef 0 -bcf-cef -b2c-bce -abc+def -a2c+d2f
{3} | 0 0 0 0 0 0
-----------------------------------------------------------------------
acd-acf a2c-a2f+acf-d2f -a2f+acf a2d-a2f
-bcd-ace+bcf+aef ace-bcf-aef+def abc+ace-bcf-aef -a2e+ade
d2f-df2 cd2-adf-d2f+df2 cd2-adf-d2f+df2 d3-d2f
c2e-cef -bc2-c2e+bcf+cef -bc2-c2e+bcf+cef -bcd+ace-cde+bcf
-cde+def cde-def cde-def -ade+d2e
-----------------------------------------------------------------------
a2e+bdf+aef d3-d2f 0 0 0 cd2-af2 0 ad2-adf
ae2-bef a2e-d2e -ade+abf 0 a2c-df2 0 cd2-af2 -ade+bdf
ade+d2e+abf ad2-adf -d3+d2f -cd2+af2 0 0 0 0
-bce-ce2 -ace+ef2 cde-bcf 0 -ac2+f3 0 0 cde-bf2
-abe+de2 -a2e+ade bd2-d2e bcd-aef acd-a2f abc-def a2c-d2f a2b-d2e
-----------------------------------------------------------------------
0 abc2-def2 ac2f-df3 ab2c+bdef+ae2f cdef-bcf2 |
0 -b2c2+e2f2 ac2e-bc2f-acef+ef3 -b3c+abe2+ae3-be2f 0 |
0 bcdf-acef cdf2-af3 bd2e+d2e2+b2df -bc2d+ef3 |
cd2-af2 0 -c3e+c2ef -bce2-ce3 0 |
a3-d3 0 c2de-acef-cdef+aef2 -b2de+de3 b2c2-e2f2 |
5 23
o13 : Matrix R <--- R
i14 : betti gens gb syz G
0 1
o14 = total: 23 45
5: 1 .
6: 18 19
7: 4 22
8: . 4
o14 : BettiTally
i15 :
