Macaulay2 » Documentation
Packages » OIGroebnerBases > describeFull
next | previous | forward | backward | up | index | toc

describeFull -- describe an OI-resolution and the maps

Synopsis

Description

Displays the free OI-modules and describes the differentials of an OI-resolution.

i1 : P = makePolynomialOIAlgebra(2, x, QQ);
i2 : F = makeFreeOIModule(e, {1,1}, P);
i3 : installGeneratorsInWidth(F, 2);
i4 : b = x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);
i5 : time C = oiRes({b}, 1);
 -- used 0.101617s (cpu); 0.0744935s (thread); 0s (gc)
i6 : describeFull C

o6 = 0: Module: Basis symbol: e0
                Basis element widths: {2}
                Degree shifts: {-2}
                Polynomial OI-algebra: (2, x, QQ, RowUpColUp)
                Monomial order: Lex
     Differential: Source: (e0, {2}, {-2}) Target: (e, {1, 1}, {0, 0})
     1: Module: Basis symbol: e1
                Basis element widths: {4, 4}
                Degree shifts: {-4, -4}
                Polynomial OI-algebra: (2, x, QQ, RowUpColUp)
                Monomial order: Lex
     Differential: Source: (e1, {4, 4}, {-4, -4}) Target: (e0, {2}, {-2})
                   Basis element images: {0, -x   x   e0           + x   x   e0           + x   x   e0           - x   x   e0          }
                                               2,3 1,1  4,{2, 4},1    2,4 1,1  4,{2, 3},1    2,3 1,2  4,{1, 4},1    2,4 1,2  4,{1, 3},1

Ways to use describeFull:

For the programmer

The object describeFull is a method function.