python - Why doesn't numpy determinant return a Fraction when given a Fraction matrix? -

i want perform operations on rational matrices. use modules numpy , fractions.

here code:

import numpy np fractions import fraction  m=np.matrix([[fraction(1, 6), fraction(8, 7)], [fraction(1, 2), fraction(3, 2)]]) print(np.linalg.det(m)) # gives -0.321428571429  print(m[0,0]*m[1,1] - m[0,1]*m[1,0]) # gives -9/28 

since computing determinant require rational operations gauss' method, determinant of rational matrix rational.

so questions are: why numpy return float , not fraction? how can rational determinant?

note other operations on matrix give rational output (for instance m.trace()).

numpy computes determinant of matrix lower upper decomposition routine in lapack. routine can handle floating point numbers.

before calculating determinant of matrix, linalg.det checks types of values has , establishes type of internal loop should run using call function named _commontype(). function set loop run either double or complex-double values.

here python part of function linalg.det handles checking:

def det(a):     = asarray(a) # convert matrix numpy array     _assertnoempty2d(a)     _assertrankatleast2(a)     _assertndsquareness(a)     t, result_t = _commontype(a) # input/output types established here     signature = 'd->d' if iscomplextype(t) else 'd->d' # signature 'float->float' chosen      return _umath_linalg.det(a, signature=signature).astype(result_t)  

after running checks on shape of matrix , determining types, return line passes values in array lapack implementation of lower-upper decomposition , float returned.

trying bypass type checking type signature of our own raises error saying no such loop defined object types:

>>> np.linalg._umath_linalg.det(a, signature='o->o') # 'o' 'object' typeerror: no loop matching specified signature found ufunc det 

this implies not possible keep fraction type return type when using det.

other functions such trace() not same type checking det , object type may persist. trace sums diagonal calling fraction object's __add__ method, fraction object can kept return type.

if want calculate determinant rational number, investigate sympy. matrix operations such calculating determinants documented here.