Definition:Multiplication of Polynomials/Sequence
< Definition:Multiplication of Polynomials(Redirected from Definition:Multiplication of Polynomials over Field as Sequence)
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Definition
Let:
- $f = \sequence {a_k} = \tuple {a_0, a_1, a_2, \ldots}$
and:
- $g = \sequence {b_k} = \tuple {b_0, b_1, b_2, \ldots}$
be polynomials over a field $F$.
Then the operation of (polynomial) multiplication is defined as:
- $f g := \tuple {c_0, c_1, c_2, \ldots}$
where $\ds c_i = \sum_{j \mathop + k \mathop = i} a_j b_k$
Sources
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $6$: Polynomials and Euclidean Rings: $\S 25$. Polynomials