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 | 1 | initial version |
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 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.
Te 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:
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)
| | 2 | No.2 Revision |
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 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.
Te 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
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:
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)
| | 3 | No.3 Revision |
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.
Te 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:
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)
| | 4 | No.4 Revision |
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: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)
