Augment kernel basis functionalities

[vneiger]

• provide a verification function is_kernel (which still lacks some generation check) and make testing more complete for kernel basis functions
• add a function for kernel via approximation at large order (useful for very unbalanced shifts)
• review recent code for ZLS algorithm and provide an "enhanced" version (see below)
• add a profile file to benchmark performance
• add an interface that provides a convenient choice for the orientation (left kernel, right kernel, and conventions for pivots in weak Popov form)

Enhanced because the modified version:

• returns a basis in a stronger form (ordered weak Popov form, rather than reduced)
• is often faster (sometimes marginally), thanks to the use of more aggressive parameters (in particular for the order when calling approximant basis).

[vneiger]

Some timings.
The column flint is for nmod_poly_mat_nullspace: this has a weaker output, by computing a basis of the rational nullspace (which most often does not generate the polynomial kernel via polynomial combinations), and not ensuring any kind of reducedness.

*****************************************************
*  left kernel of rdim x cdim matrix of degree deg  *
*****************************************************

bits rdim cdim deg     approx   zls(now) flint    zls(before)
50   5    1    2       2.94e-06 3.37e-06 1.77e-07 7.31e-06
50   5    1    5       9.05e-06 6.36e-06 1.84e-07 2.13e-05
50   5    1    10      2.36e-05 1.41e-05 2.02e-07 6.02e-05
50   5    1    20      6.84e-05 3.41e-05 2.03e-07 1.62e-04
50   5    1    40      1.66e-04 8.47e-05 2.09e-07 3.35e-04
50   5    1    80      4.77e-04 2.43e-04 2.33e-07 8.44e-04
50   5    1    160     1.24e-03 7.73e-04 4.48e-07 1.95e-03
50   5    1    320     3.18e-03 2.15e-03 6.98e-07 4.65e-03
50   5    1    640     7.68e-03 5.57e-03 1.27e-06 1.06e-02
50   5    1    1280    1.86e-02 1.47e-02 2.45e-06 2.40e-02
50   5    1    2560    4.63e-02 3.99e-02 4.82e-06 5.68e-02
50   5    1    5120    1.12e-01 9.05e-02 1.00e-05 1.31e-01
50   5    1    10240   2.59e-01 2.29e-01 2.21e-05 2.96e-01
50   5    4    2       1.08e-05 1.52e-05 3.25e-06 4.77e-05
50   5    4    5       5.22e-05 4.12e-05 8.20e-06 1.07e-04
50   5    4    10      2.11e-04 1.06e-04 2.38e-05 2.34e-04
50   5    4    20      7.88e-04 2.97e-04 6.20e-05 7.58e-04
50   5    4    40      2.36e-03 1.06e-03 1.59e-04 2.13e-03
50   5    4    80      6.72e-03 2.37e-03 3.91e-04 5.81e-03
50   5    4    160     1.80e-02 5.71e-03 9.51e-04 1.56e-02
50   5    4    320     4.78e-02 1.57e-02 2.43e-03 3.94e-02
50   5    4    640     1.37e-01 3.51e-02 5.11e-03 1.03e-01
50   5    4    1280    3.13e-01 8.79e-02 1.06e-02 2.54e-01
50   5    4    2560    7.71e-01 2.11e-01 2.20e-02 5.96e-01
50   5    4    5120    1.82e+00 5.13e-01 4.45e-02 1.44e+00
50   5    4    10240   4.37e+00 1.19e+00 1.12e-01 3.40e+00
50   100  1    2       4.91e-04 4.01e-04 7.33e-06 1.59e-03
50   100  1    5       1.51e-03 7.70e-04 7.53e-06 4.14e-03
50   100  1    10      4.57e-03 1.42e-03 7.68e-06 1.32e-02
50   100  1    20      3.57e-02 2.70e-03 7.75e-06 7.94e-02
50   100  1    40      1.38e-01 8.03e-03 8.61e-06 3.15e-01
50   100  1    80      4.43e-01 1.87e-02 1.08e-05 9.59e-01
50   100  1    160     1.28e+00 4.43e-02 1.51e-05 2.81e+00
50   100  1    320     3.48e+00 1.16e-01 2.05e-05 7.49e+00
50   100  50   2       2.58e-01 5.30e-03 1.84e-01 1.16e-02
50   100  50   5       2.35e+00 1.85e-02 1.02e+00 3.58e-02
50   100  50   10      7.19e+00 4.89e-02 2.71e+00 1.07e-01
50   100  50   20      2.08e+01 2.24e-01 6.64e+00 4.44e-01
50   100  50   40      5.70e+01 8.21e-01 1.61e+01 1.55e+00
50   100  50   80      xxxxxxxx 2.98e+00 3.58e+01 5.85e+00
50   100  50   160     xxxxxxxx 1.42e+01 xxxxxxxx 2.11e+01
50   100  99   2       8.96e-01 1.79e-02 6.48e-01 6.86e-02
50   100  99   5       1.08e+01 9.50e-02 3.72e+00 3.35e-01
50   100  99   10      4.02e+01 3.10e-01 1.04e+01 1.21e+00
50   100  99   20      1.25e+02 9.74e-01 2.75e+01 4.33e+00
50   100  99   40      xxxxxxxx 3.08e+00 6.71e+01 1.41e+01