Given the picture, i have to guess your construction (tell ):
Your field K
:
sage: K = Qp(5,prec=70)
sage: K
5-adic Field with capped relative precision 70
Your matrix I
(which is the identity) :
sage: I = matrix.identity(K,15)
There is no information about the construction of Matrix2
, hence, i will pick one randomly:
sage: M = I.parent()
sage: M
Full MatrixSpace of 15 by 15 dense matrices over 5-adic Field with capped relative precision 70
sage: Matrix2 = M.random_element()
On my installation,
sage: Matrix2.charpoly()
works well.
The folowing does not work:
sage: x*Matrix2
because, by default x
is a symbol, to be used in symbolic expressions like sin(x)*sqrt(2)
.
What you might want is a polynomial indeterminate. The following non-Pythonic constructions builds both the polynomial ring R
and the indeterminate x
sage: R.<x> = K[]
sage: R
Univariate Polynomial Ring in x over 5-adic Field with capped relative precision 70
WIth such a x
, you can do:
sage: det(I - x*Matrix2)
The difference with the previous charpoly result seem to be some residual things due to bounded precision:
sage: det(I - x*Matrix2) - Matrix2.charpoly()
O(5^-1843)*x^15 + O(5^-1813)*x^14 + O(5^-1585)*x^13 + O(5^-1544)*x^12 + O(5^-1316)*x^11 + O(5^-1275)*x^10 + O(5^-1047)*x^9 + O(5^-1006)*x^8 + O(5^-1006)*x^7 + O(5^-1047)*x^6 + O(5^-1275)*x^5 + O(5^-1316)*x^4 + O(5^-1544)*x^3 + O(5^-1585)*x^2 + O(5^-1813)*x + O(5^-1843)
Could you please provide your code so that we can understand ? The picture does not show the whole construction.