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Macaulay2Doc :: max(GradedModule)

max(GradedModule)

Synopsis

Description

i1 : R = QQ[a..e]

o1 = R

o1 : PolynomialRing
i2 : C = res coker vars R

      1      5      10      10      5      1
o2 = R  <-- R  <-- R   <-- R   <-- R  <-- R  <-- 0
                                                  
     0      1      2       3       4      5      6

o2 : ChainComplex
i3 : max C

o3 = 6
i4 : dual C
-- ker (21) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (21) returned CacheFunction: -*a cache function*-
-- ker (21) called with Matrix: 0
--                            1
-- ker (21) returned Module: R
assert( ker(map(R^0,R^1,0)) === (R^1))
-- ker (22) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (22) returned CacheFunction: -*a cache function*-
-- ker (22) called with Matrix: 0
--                            5
-- ker (22) returned Module: R
assert( ker(map(R^0,R^{{1}, {1}, {1}, {1}, {1}},0)) === (R^{{1}, {1}, {1}, {1}, {1}}))
-- ker (23) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (23) returned CacheFunction: -*a cache function*-
-- ker (23) called with Matrix: 0
--                            10
-- ker (23) returned Module: R
assert( ker(map(R^0,R^{{2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}},0)) === (R^{{2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}}))
-- ker (24) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (24) returned CacheFunction: -*a cache function*-
-- ker (24) called with Matrix: 0
--                            10
-- ker (24) returned Module: R
assert( ker(map(R^0,R^{{3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}},0)) === (R^{{3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}}))
-- ker (25) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (25) returned CacheFunction: -*a cache function*-
-- ker (25) called with Matrix: 0
--                            5
-- ker (25) returned Module: R
assert( ker(map(R^0,R^{{4}, {4}, {4}, {4}, {4}},0)) === (R^{{4}, {4}, {4}, {4}, {4}}))
-- ker (26) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (26) returned CacheFunction: -*a cache function*-
-- ker (26) called with Matrix: 0
--                            1
-- ker (26) returned Module: R
assert( ker(map(R^0,R^{{5}},0)) === (R^{{5}}))
-- ker (27) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (27) returned CacheFunction: -*a cache function*-
-- ker (27) called with Matrix: 0
-- ker (27) returned Module: 0
assert( ker(map(R^0,R^0,0)) === (R^0))

             1      5      10      10      5      1
o4 = 0  <-- R  <-- R  <-- R   <-- R   <-- R  <-- R
                                                  
     -6     -5     -4     -3      -2      -1     0

o4 : ChainComplex
i5 : max dual C
-- ker (28) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (28) returned CacheFunction: -*a cache function*-
-- ker (28) called with Matrix: 0
--                            1
-- ker (28) returned Module: R
assert( ker(map(R^0,R^1,0)) === (R^1))
-- ker (29) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (29) returned CacheFunction: -*a cache function*-
-- ker (29) called with Matrix: 0
--                            5
-- ker (29) returned Module: R
assert( ker(map(R^0,R^{{1}, {1}, {1}, {1}, {1}},0)) === (R^{{1}, {1}, {1}, {1}, {1}}))
-- ker (30) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (30) returned CacheFunction: -*a cache function*-
-- ker (30) called with Matrix: 0
--                            10
-- ker (30) returned Module: R
assert( ker(map(R^0,R^{{2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}},0)) === (R^{{2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}}))
-- ker (31) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (31) returned CacheFunction: -*a cache function*-
-- ker (31) called with Matrix: 0
--                            10
-- ker (31) returned Module: R
assert( ker(map(R^0,R^{{3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}},0)) === (R^{{3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}}))
-- ker (32) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (32) returned CacheFunction: -*a cache function*-
-- ker (32) called with Matrix: 0
--                            5
-- ker (32) returned Module: R
assert( ker(map(R^0,R^{{4}, {4}, {4}, {4}, {4}},0)) === (R^{{4}, {4}, {4}, {4}, {4}}))
-- ker (33) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (33) returned CacheFunction: -*a cache function*-
-- ker (33) called with Matrix: 0
--                            1
-- ker (33) returned Module: R
assert( ker(map(R^0,R^{{5}},0)) === (R^{{5}}))
-- ker (34) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (34) returned CacheFunction: -*a cache function*-
-- ker (34) called with Matrix: 0
-- ker (34) returned Module: 0
assert( ker(map(R^0,R^0,0)) === (R^0))

o5 = 0

See also