parent, [entries=True], [coerce_entries=True], [copy=0]) |
charpoly,
echelon_form,
entries,
hessenberg_form,
iterates,
list,
minpoly,
pivots
Further documentation:
[bound=None]) |
Return the characteristic polynomial of this matrix, computed using the standard multimodular Hessenberg algorithm.
The multimodular algorithm works by first computing a bound B, then computing the characteristic polynomial (using Hessenberg form) modulo enough primes so that their product is bigger than B. One then uses the Chinese Remainder Theorem to recover the characteristic polynomial. If the optional bound is specified, that bound is used for B instead of a potentially much worse general bound.
) |
Return the Hessenberg form of this matrix.
v, n) |
Let A be this matrix. Return a matrix with rows
Instances of class Matrix_rational_dense also have the following special functions:
__getitem__,
__mul__,
__setitem__
Further documentation:
ij) |
Use A[i,j]
to obtain the the
th entry of
, and
A[i]
to obtain the
-th row of
.
ij, x) |
Use A[i,j]=x
to set the
th entry of
to
,
and
A[i]=v
to set the
th row of
to the entries
of
.
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