next | previous | forward | backward | up | index | toc

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

## Synopsis

• Usage:
taylorResolution(I)
• Inputs:
• I,
• Optional inputs:
• LengthLimit => ..., default value 0, How many steps to compute
• Outputs:
• ChainComplex

## 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 :

• taylorResolution(MonomialIdeal)

## For the programmer

The object taylorResolution is .