bug in map and image

[mahrud]

What is happening here?

i1 : f = vars(QQ[x,y]);

i2 : map(image f, , f)
stdio:2:1:(3): error: expected matrix and new target module to agree

Note: I understand that inducedMap works here, but that method can be computationally expensive (e.g. computes Grobner bases in some cases) which seems unnecessary for what the code above should do.

[mahrud]

Related: say I have the following matrix:

i1 : R = QQ[a..d];

i2 : P = image map(R^{4:-3}, , {{d}, {0}, {-c}, {b}})

o2 = image {3} | d  |
           {3} | 0  |
           {3} | -c |
           {3} | b  |

                             4
o2 : R-module, submodule of R

i3 : f = basis(5, P)

o3 = {4} | a b c d |

                   4
o3 : Matrix P <-- R

Now I take it's image and forget about f:

i4 : F = image f

o4 = image {3} | ad  bd  cd  d2  |
           {3} | 0   0   0   0   |
           {3} | -ac -bc -c2 -cd |
           {3} | ab  b2  bc  bd  |

                             4
o4 : R-module, submodule of R

How do I recover the 1x4 map f again? gens F gives the 4x4 matrix. The only way seems to be inducedMap(P, , gens F), which performs a gb computation, for something we should have cached!