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substitute(ChainComplex,Ring) -- Substitute a chain complex to a new ring.

Synopsis

Description

Substitute a chain complex cc to a new ring R.

i1 : R=QQ[x_1..x_8];
i2 : Z=QQ[z];
i3 : cc=cycResDef(4,R,Z);
i4 : S= ring cc;
i5 : cc

      1      16      30      16      1
o5 = S  <-- S   <-- S   <-- S   <-- S
                                     
     0      1       2       3       4

o5 : ChainComplex
i6 : print cc.dd_1
| x_1x_3x_5 x_1x_3x_6 x_1x_4x_6 x_2x_4x_6 x_2x_4x_7 x_2x_5x_7 x_3x_5x_7 x_8zx_3-x_1x_3x_7 x_8zx_4-x_1x_4x_7 x_8x_2x_4 x_8zx_5-x_1x_5x_7 x_8x_2x_5 x_8x_3x_5 x_8x_2x_6 x_8x_3x_6 x_8x_4x_6 |
i7 : cs=substitute(cc,R)

      1      16      30      16      1
o7 = R  <-- R   <-- R   <-- R   <-- R
                                     
     0      1       2       3       4

o7 : ChainComplex
i8 : print cs.dd_1
| x_1x_3x_5 x_1x_3x_6 x_1x_4x_6 x_2x_4x_6 x_2x_4x_7 x_2x_5x_7 x_3x_5x_7 -x_1x_3x_7 -x_1x_4x_7 x_2x_4x_8 -x_1x_5x_7 x_2x_5x_8 x_3x_5x_8 x_2x_6x_8 x_3x_6x_8 x_4x_6x_8 |

See also

  • substitute -- substituting values for variables
  • cycResDef -- Compute the minimal resolution of the unprojection deformation of a cyclic polytope