CheckProjective -- optional input which gives the user the option to check whether the given module is projective

Description

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : f = matrix{{x^2*y+1,x+y-2,2*x*y}}

o2 = | x2y+1 x+y-2 2xy |

             1      3
o2 : Matrix R  <-- R

i3 : P = ker f

o3 = image {3} | 0      2x+2y-4          2y2-4y        |
           {1} | 2xy    -2x2y-2xy2+4xy-2 -2xy3+4xy2-2y |
           {2} | -x-y+2 xy+y2-2x-4y+4    y3-4y2+4y+1   |

                             3
o3 : R-module, submodule of R

i4 : phi = qsIsomorphism(P, CheckProjective => true)

o4 = {3} | 0 0 |
     {4} | 1 0 |
     {5} | 0 1 |

                   2
o4 : Matrix P <-- R

i5 : isIsomorphism phi

o5 = true

Functions with optional argument named CheckProjective:

computeFreeBasis(...,CheckProjective=>...) -- see computeFreeBasis -- computes a free basis of a projective module
qsIsomorphism(...,CheckProjective=>...) -- see qsIsomorphism -- computes an isomorphism between a free module and a given projective module

For the programmer

The object CheckProjective is a symbol.

The source of this document is in QuillenSuslin.m2:2528:0.

CheckProjective -- optional input which gives the user the option to check whether the given module is projective

Description

See also

Functions with optional argument named CheckProjective:

For the programmer