python中的矩阵行列式符号

Question

大家好，我想计算下面这个矩阵的行列式" symbolic ">在python

x, y, z, a, b, c = symbols('x,y,z,a,b,c')
arr3 = np.array(([1-a,6,8-x],[2-b,10,12-y],[6-c,3,15-z]))
linalg.det(arr3)

但是我得到这个错误:

ValueError                                Traceback (most recent call last)
<ipython-input-34-fa7fd6eebff6> in <module>
----> 1 linalg.det(arr3)
~anaconda3libsite-packagesscipylinalgbasic.py in det(a, overwrite_a, check_finite)
1030 
1031     """
-> 1032     a1 = _asarray_validated(a, check_finite=check_finite)
1033     if len(a1.shape) != 2 or a1.shape[0] != a1.shape[1]:
1034         raise ValueError('expected square matrix')
~anaconda3libsite-packagesscipy_lib_util.py in _asarray_validated(a, check_finite, sparse_ok, objects_ok, mask_ok, as_inexact)
264     if not objects_ok:
265         if a.dtype is np.dtype('O'):
--> 266             raise ValueError('object arrays are not supported')
267     if as_inexact:
268         if not np.issubdtype(a.dtype, np.inexact):
ValueError: object arrays are not supported

我是新来的，所以你能告诉我我是怎么做错的，我能解决它吗?

Answer 1

不能使用numpy数组进行sympy的符号计算。相反，使用sympy矩阵:

import sympy as sp
x, y, z, a, b, c = sp.symbols('x,y,z,a,b,c')
arr3 = sp.Matrix(([1-a,6,8-x],[2-b,10,12-y],[6-c,3,15-z]))
print(sp.det(arr3))

收益率

-3*a*y + 10*a*z - 114*a + 3*b*x - 6*b*z + 66*b - 10*c*x + 6*c*y + 8*c + 54*x - 33*y + 2*z - 66