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NumericalGodeaux :: fromLineToStandardResolution

fromLineToStandardResolution -- compute a standard resolution F of an S-module R from a given line

Synopsis

Description

Starting with a line in Q computed from the procedure fromPointInP3xP3xP3xP3ToLine, the function computes an $S$-module $R$ together with a standard resolution $F$. Note that because of size of the coefficients, the computations over the rational numbers are very time consuming.

i1 : kk=ZZ/101

o1 = kk

o1 : QuotientRing
 
i2 : H = precomputedModelInP3xP5(kk);

                                1                          1
o2 : Matrix (kk[w ..w , z ..z ])  <--- (kk[w ..w , z ..z ])
                 0   3   0   5              0   3   0   5
 
i3 : pt=findPointInP3xP5(kk)

o3 = | 2 44 16 22 45 -34 -48 -47 47 19 |

              1        10
o3 : Matrix kk  <--- kk
 
i4 : pt1=fromPointInP3xP5ToPointInP3xP3xP3xP3(pt)

o4 = | 38 13 32 1 32 -17 -24 1 5 27 -27 1 46 2 -36 1 |

              1        16
o4 : Matrix kk  <--- kk
 
i5 : line =fromPointInP3xP3xP3xP3ToLine(pt1)

o5 = | 48 32 -24 38 -33 -25 -11 -31 19 33 0 1 |
     | 10 46 -47 6  23  -44 -6  20  10 -4 1 0 |

              2        12
o5 : Matrix kk  <--- kk
 
i6 : F = fromLineToStandardResolution(line);
 
i7 : betti F

            0  1  2 3
o7 = total: 8 26 26 8
         0: 1  .  . .
         1: .  .  . .
         2: .  .  . .
         3: .  .  . .
         4: 4  .  . .
         5: 3  6  . .
         6: . 12  . .
         7: .  8  8 .
         8: .  . 12 .
         9: .  .  6 3
        10: .  .  . 4
        11: .  .  . .
        12: .  .  . .
        13: .  .  . .
        14: .  .  . 1

o7 : BettiTally

See also

Ways to use fromLineToStandardResolution :

For the programmer

The object fromLineToStandardResolution is a method function.