parent) |
base_field,
base_ring,
copy,
degree,
denominator,
dict,
dot_product,
entries,
get,
height,
is_dense,
is_sparse,
is_vector,
list,
nonzero_positions,
parent,
rational_reconstruction,
set,
str_latex
Further documentation:
right) |
Return the dot product of self and right, which is the sum of the product of the corresponding entries.
INPUT: right -- vector of the same degree as self. it need not be in the same vector space as self, as long as the coefficients can be multiplied.
sage: V = VectorSpace(RationalField(),3) sage: v = V([1,2,3]) sage: w = V([4,5,6]) sage: v.dot_product(w) 32
sage: W = VectorSpace(GF(3),3) sage: w = W([0,1,2]) sage: w.dot_product(v) 2 sage: w.dot_product(v).parent() Finite field of size 3
Note that in SAGE implicit coercions, when defined, coerce the
element on the right into the parent of the element on the
left. Thus the dot product in the other order results in the
rational number
, since the finite field elements are
lifted up to the rationals.
sage: v.dot_product(w) 8
i) |
get is meant to be more efficient than getitem, because it does not do any error checking.
) |
Returns the sorted list of integers i such that self[i] != 0.
i, x) |
set is meant to be more efficient than setitem, because it does not do any error checking or coercion. Use with care.
) |
Print a latex representation of self. For example, if self is [1,2,3,4], the following latex is generated: (1,2,3,4)
Instances of class Vector also have the following special functions:
__abs__,
__add__,
__cmp__,
__getitem__,
__invert__,
__len__,
__mod__,
__mul__,
__neg__,
__pos__,
__pow__,
__rmul__,
__setitem__,
__str__,
__sub__
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