error in factoring non-monic polynomial< gf_element >

[benediamond]

There appears to be a bug when attempting to factor a non-monic polynomial< gf_element > f over a finite field F_q. indeed:

#include <LiDIA/galois_field.h>
#include <LiDIA/gf_polynomial.h>
#include <LiDIA/factorization.h>

int main(int argc, const char * argv[]) {
  galois_field F(61, 2);
  polynomial< gf_element > f = randomize(F, 5);
  std::cout << f << std::endl;
  factorization< gf_polynomial > f_fact;
  factor(f_fact, f);
  std::cout << "factored: " << f_fact << std::endl;
}

yields:

(12 * x+ 11) * y^5 + (34) * y^4 + (19 * x+ 27) * y^3 + (19 * x+ 56) * y^2 + (10 * x+ 8) * y + (37 * x+ 2)
libc++abi.dylib: terminating with uncaught exception of type LiDIA::generic_error: common_field::arguments are different fields
Abort trap: 6

However,

#include <LiDIA/galois_field.h>
#include <LiDIA/gf_polynomial.h>
#include <LiDIA/factorization.h>

int main(int argc, const char * argv[]) {
  galois_field F(61, 2);
  polynomial< gf_element > f = randomize(F, 5);
  divide(f, f, f.lead_coeff());
  std::cout << f << std::endl;
  factorization< gf_polynomial > f_fact;
  factor(f_fact, f);
  std::cout << "factored: " << f_fact << std::endl;
}

yields

y^5 + (59 * x+ 37) * y^4 + (15 * x+ 43) * y^3 + (29 * x+ 8) * y^2 + (2 * x+ 3) * y + (25 * x+ 58)
factored: [ [y+ (56 * x+ 13),1],[y^2 + (6 * x+ 36) * y + (43 * x+ 42),1],[y^2 + (58 * x+ 49) * y + (52 * x+ 3),1] ]

I narrowed down the offending function call to lines 493 and 239, respectively, in the following two snippets:
https://github.com/mkoeppe/LiDIA/blob/f10edd172f858b46caf8efb45c79a742cc2407f1/src/finite_fields/factorization/gf_polynomial/gf_berlekamp.cc#L491-L494
https://github.com/mkoeppe/LiDIA/blob/f10edd172f858b46caf8efb45c79a742cc2407f1/src/base/include/LiDIA/factorization.h#L237-L240
In this setting, ff and a wind up as the scalar quantity which originally appeared as f's leading coefficient. Not sure exactly what's going on, but this appears to be a bug. Please let me know if you can help clarify this, and then I can put together a pull request. Thanks for your work!