| 1 |
- polynomial division and gcd
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| 2 |
- polynomial documentation
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| 3 |
7. add combinatorial, linear algebra, factorization, polynomial functions
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| 4 |
as in SAC-2.
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| 5 |
7. finite fields, e.g.
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| 6 |
- gf256_log_2, gf256_antilog_2, gf256_power_of_2, gf256_add, gf256_minus,
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| 7 |
gf256_subtract, gf256_mul, gf256_inv, gf256_div, gf256_product, gf256_exp,
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| 8 |
gf256_term, gfmul, gfadd, gfinv, gfexp.
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| 9 |
more polynomial operations:
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| 10 |
x(), power, >>, <<, division, scalmult, content, primitivepart,
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| 11 |
gcd, xgcd, no_of_real_roots, factorization.
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| 12 |
modular polynomials: powmod etc.
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| 13 |
7. chinese remainder algorithm, maybe Hensel-lifting as in Magnum.
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| 14 |
8. factor and primality testing for small integers
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| 15 |
8. primality test in Z:
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| 16 |
+ polynomials cl_MUP_MI, cl_MUP_I
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| 17 |
use integer FFT for multiplication in cl_UP_MI and cl_MUP_MI
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| 18 |
+ - Pollard rho
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| 19 |
+ - complex values of j()
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| 20 |
- Hilbert polynomial for j() 7.6.1
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| 21 |
+ roots of polynomials mod N 1.6.1
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| 22 |
+ - elliptic curves, Jacobi representation
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| 23 |
- m.P on elliptic curve
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| 24 |
+ Atkin's algorithm
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| 25 |
10. factoring in Z:
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| 26 |
- small prime table,
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| 27 |
- Pollard rho,
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| 28 |
- multiple polynomial quadratic sieve
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| 29 |
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| 30 |
Document the timing class
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| 31 |
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