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

extend(ChainComplex,ChainComplex,Matrix) -- extend a module map to a chain map, if possible

Synopsis

• Function: extend
• Usage:
extend(D,C,f0)
• Inputs:
• D,
• C,
• f0, , a map from C_0 to D_0
• Optional inputs:
• Verify => , default value true, whether to check that the map extends
• Outputs:
• , a chain complex map f: D <--- C of degree 0 extending f0 in the sense that f_0==f0

Description

 i1 : R = ZZ/101[a..c] o1 = R o1 : PolynomialRing i2 : I = image vars R o2 = image | a b c | 1 o2 : R-module, submodule of R i3 : J = image symmetricPower (2,vars R) o3 = image | a2 ab ac b2 bc c2 | 1 o3 : R-module, submodule of R i4 : g = extend( resolution (R^1/I), resolution (R^1/J), id_(R^1)) 1 1 o4 = 0 : R <--------- R : 0 | 1 | 3 6 1 : R <----------------------- R : 1 {1} | a b 0 0 0 0 | {1} | 0 0 b 0 0 0 | {1} | 0 0 0 a b c | 3 8 2 : R <--------------------------- R : 2 {2} | 0 b 0 0 0 0 0 0 | {2} | 0 0 a b 0 0 0 0 | {2} | 0 0 0 0 0 b 0 0 | 1 3 3 : R <----------------- R : 3 {3} | 0 b 0 | 4 : 0 <----- 0 : 4 0 o4 : ChainComplexMap i5 : g_1 o5 = {1} | a b 0 0 0 0 | {1} | 0 0 b 0 0 0 | {1} | 0 0 0 a b c | 3 6 o5 : Matrix R <--- R i6 : g_2 o6 = {2} | 0 b 0 0 0 0 0 0 | {2} | 0 0 a b 0 0 0 0 | {2} | 0 0 0 0 0 b 0 0 | 3 8 o6 : Matrix R <--- R