TAOCP 4.6: Polynomial Arithmetic
Section 4.6 exercises: 5/5 solved.
Section 4.6. Polynomial Arithmetic
Exercises from TAOCP Volume 2 Section 4.6: 5/5 solved.
| # | Rating | Category | Status | Time |
|---|---|---|---|---|
| 1 | [10] | simple | verified | 1m54s |
| 2 | [17] | medium | verified | 5m03s |
| 3 | [M20] | math-medium | verified | 1m09s |
| 4 | [21] | medium | verified | 3m48s |
| 5 | ▶ [M21] | math-medium | verified | 1m53s |
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TAOCP
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TAOCP Vol 2: Seminumerical Algorithms
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TAOCP 4.6: Polynomial Arithmetic
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TAOCP 4.6 Exercise 1
In polynomial arithmetic modulo $10$, coefficients are reduced modulo $10$ after each operation.
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Mathematics
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TAOCP
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TAOCP Vol 2: Seminumerical Algorithms
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TAOCP 4.6: Polynomial Arithmetic
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TAOCP 4.6 Exercise 2
(a) Let $u(x)$ and $v(x)$ be monic polynomials, with leading coefficients $\ell(u) = \ell(v) = 1$.
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Mathematics
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TAOCP
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TAOCP Vol 2: Seminumerical Algorithms
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TAOCP 4.6: Polynomial Arithmetic
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TAOCP 4.6 Exercise 3
By equation (4), w_k=u_0v_k+u_1v_{k-1}+\cdots+u_kv_0, where coefficients with indices exceeding $s$ are taken to be $0$.
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Mathematics
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TAOCP
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TAOCP Vol 2: Seminumerical Algorithms
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TAOCP 4.6: Polynomial Arithmetic
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TAOCP 4.6 Exercise 4
Yes, polynomial multiplication modulo $2$ can be facilitated by packing coefficients into machine words, but **ordinary integer multiplication cannot be used directly**, because its carries do not cor...