Macaulay2 » Documentation
Packages » AInfinity » burkeResolution » Check
next | previous | forward | backward | up | index | toc

# Check -- Option for burkeResolution

- Usage:
    `F := burkeResolution(M, Check => true)`
- Inputs:
  - M, a module,
  - Check, a Boolean value,
- Outputs:
  - F, a complex,

## Description

with Check => true, burkeResolution includes lines that check F.dd^2 == 0 and also that F is acyclic (as far as it has been computed). The default value is true.

    i1 : R = ZZ/101[a,b,c]/(ideal(a,b,c))^2

    o1 = R

    o1 : QuotientRing

    i2 : M = coker vars R

    o2 = cokernel | a b c |

                                1
    o2 : R-module, quotient of R

    i3 : elapsedTime burkeResolution(M, 7, Check => false)
     -- 1.5361s elapsed

          1      3      9      27      81      243      729      2187
    o3 = R  <-- R  <-- R  <-- R   <-- R   <-- R    <-- R    <-- R

         0      1      2      3       4       5        6        7

    o3 : Complex

    i4 : elapsedTime burkeResolution(M, 7, Check => true)
     -- 2.03029s elapsed

          1      3      9      27      81      243      729      2187
    o4 = R  <-- R  <-- R  <-- R   <-- R   <-- R    <-- R    <-- R

         0      1      2      3       4       5        6        7

    o4 : Complex

## Caveat

The Check takes time.

## See also

- burkeResolution -- compute a resolution from A-infinity structures

## Functions with optional argument named Check:

- `aInfinity(...,Check=>...)` -- see aInfinity -- aInfinity algebra and module structures on free resolutions
- `burkeResolution(...,Check=>...)` -- see burkeResolution -- compute a resolution from A-infinity structures

## For the programmer

The object Check is a symbol.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/AInfinity.m2:1282:0.