Check -- Option for burkeResolution

Synopsis

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)
 -- 0.748801 seconds 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)
 -- 1.03895 seconds 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.

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.