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ChainComplexExtras :: taylor

taylor -- Gives the nth differential in 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 : T2 = taylor(2,I)

o3 = {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  |

             4       6
o3 : Matrix R  <--- R
i4 : T3 = taylor(3,I)

o4 = {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  |

             6       4
o4 : Matrix R  <--- R

Ways to use taylor :

For the programmer

The object taylor is a method function.