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Project: Software 22.04
Path: m2.ipynb
Views: 294Image: ubuntu2204-dev
Kernel: M2
Macaulay2 on CoCalc
Examples picked from http://www2.macaulay2.com/Macaulay2/doc/Macaulay2/share/doc/Macaulay2/Macaulay2Doc/html/index.html
In [1]:
o1 = 15511210043330985984000000
In [2]:
o4 = | a b c |
| b c d |
| c d e |
3 3
o4 : Matrix S <--- S
In [3]:
o5 = | a2+b2+c2 ab+bc+cd ac+bd+ce |
| ab+bc+cd b2+c2+d2 bc+cd+de |
| ac+bd+ce bc+cd+de c2+d2+e2 |
3 3
o5 : Matrix S <--- S
In [4]:
3 2 2
o6 = - c + 2b*c*d - a*d - b e + a*c*e
o6 : S
In [2]:
o3 = X
o3 : ProjectiveVariety
In [3]:
o4 = cokernel {2} | c 0 0 d 0 a3 b3 0 |
{2} | a d 0 0 b3 -c3 0 0 |
{2} | -b 0 d 0 a3 0 c3 0 |
{2} | 0 b a 0 -d3 0 0 c3 |
{2} | 0 -c 0 a 0 -d3 0 b3 |
{2} | 0 0 -c -b 0 0 d3 a3 |
6
o4 : coherent sheaf on X, quotient of OO (-2)
X
In [4]:
20
o5 = QQ
o5 : QQ-module, free
In [5]:
o6 = cokernel | a b |
1
o6 : coherent sheaf on X, quotient of OO
X
In [6]:
o7 = cokernel | a b |
1
o7 : R-module, quotient of R
In [10]:
o20 = | x_0 0 0 0 0 |
| 0 x_2 0 0 0 |
| 0 0 x_4 0 0 |
| 0 0 0 x_1 0 |
| 0 0 0 0 x_3 |
5 5
o20 : Matrix R <--- R
In [11]:
o21 = | 0 x_1 0 0 x_4 |
| x_1 0 x_3 0 0 |
| 0 x_3 0 x_0 0 |
| 0 0 x_0 0 x_2 |
| x_4 0 0 x_2 0 |
5 5
o21 : Matrix R <--- R
In [12]:
o22 = | 0 0 x_2 x_3 0 |
| 0 0 0 x_4 x_0 |
| x_2 0 0 0 x_1 |
| x_3 x_4 0 0 0 |
| 0 x_0 x_1 0 0 |
5 5
o22 : Matrix R <--- R
In [13]:
5 15
o23 : Matrix R <--- R
In [21]:
0 1 2 3 4 5
o31 = total: 5 15 29 37 20 2
0: 5 15 10 2 . .
1: . . 4 . . .
2: . . 15 35 20 .
3: . . . . . 2
o31 : BettiTally
In [25]:
35 19
o35 : Matrix R <--- R
In [26]:
0 1 2 3 4 5
o36 = total: 35 19 19 35 20 2
-5: 35 15 . . . .
-4: . 4 . . . .
-3: . . . . . .
-2: . . . . . .
-1: . . . . . .
0: . . 4 . . .
1: . . 15 35 20 .
2: . . . . . 2
o36 : BettiTally
In [27]:
o37 = Pfour
o37 : ProjectiveVariety
In [28]:
In [29]:
o39 = cokernel {-1} | x_4 x_2 0 0 x_0 0 0 0 x_3 0 0 0 0 0 x_1 |
{-1} | 0 -x_3 x_1 0 0 x_4 x_2 0 0 0 0 x_0 0 0 0 |
{-1} | 0 0 0 x_3 -x_2 x_0 0 x_1 0 0 0 0 0 -x_4 0 |
{-1} | 0 0 0 0 0 0 -x_4 -x_2 x_1 x_0 x_3 0 0 0 0 |
{-1} | 0 0 0 0 0 0 0 0 0 0 x_4 -x_3 x_2 x_1 x_0 |
5
o39 : R-module, quotient of R
In [30]:
o40 = (5, 10, 10, 2)
o40 : Sequence
In [0]: