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Check -- Option for burkeResolution

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)
 -- 2.80502s 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)
 -- 3.54054s 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

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 AInfinity.m2:1282:0.