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ChainComplexExtras :: taylorResolution

taylorResolution -- Gives the Taylor resolution of a monomial ideal I.

Synopsis

Description

i1 : R = ZZ/101[a,b]

o1 = R

o1 : PolynomialRing
i2 : I = monomialIdeal (ideal vars R)^3

                     3   2      2   3
o2 = monomialIdeal (a , a b, a*b , b )

o2 : MonomialIdeal of R
i3 : T = taylorResolution(I)

      1      4      6      4      1
o3 = R  <-- R  <-- R  <-- R  <-- R
                                  
     0      1      2      3      4

o3 : ChainComplex
i4 : T.dd

          1                         4
o4 = 0 : R  <--------------------- R  : 1
               | a3 a2b ab2 b3 |

          4                                    6
     1 : R  <-------------------------------- R  : 2
               {3} | -b -b2 0  -b3 0   0  |
               {3} | a  0   -b 0   -b2 0  |
               {3} | 0  a2  a  0   0   -b |
               {3} | 0  0   0  a3  a2  a  |

          6                           4
     2 : R  <----------------------- R  : 3
               {4} | b  b2 0  0  |
               {5} | -1 0  b  0  |
               {4} | a  0  0  b  |
               {6} | 0  -1 -1 0  |
               {5} | 0  a  0  -1 |
               {4} | 0  0  a2 a  |

          4                  1
     3 : R  <-------------- R  : 4
               {5} | -b |
               {6} | 1  |
               {6} | -1 |
               {5} | a  |

o4 : ChainComplexMap

Ways to use taylorResolution :

For the programmer

The object taylorResolution is a method function with options.