Lines Matching +refs:factor +refs:if +refs:small
1 Function: factor
5 Help: factor(x,{D}): factorization of x over domain D. If x and D are both
10 (int,small):vec Z_factor_limit($1, $2)
11 (gen):vec factor($1)
12 (gen,):vec factor($1)
14 Doc: factor $x$ over domain $D$; if $D$ is omitted, it is determined from $x$.
15 For instance, if $x$ is an integer, it is factored in $\Z$, if it is a
27 ? factor(-7/106)
43 ? fa = factor(2^2^7 + 1)
53 will perform a rigorous primality proof for each pseudoprime factor but will
66 ? factor(2^2^7 +1, 10^5)
77 guarantee that all small prime factors are found, but it also finds larger
80 ? F = (2^2^7 + 1) * 1009 * (10^5+3); factor(F, 10^5) \\ fast, incomplete
87 ? factor(F, 10^9) \\ slow
96 ? factorint(F, 1+8) \\ much faster and all small primes were found
105 ? factor(F) \\ complete factorization
117 Setting $D = I$ will factor in the Gaussian integers
127 not proven primes; a rational factor is prime if less than $2^{64}$ and an
128 irrational one if its norm is less than $2^{64}$.
130 ? factor(5*I)
138 ? factor(-5, I)
150 PARI can factor univariate polynomials in $K[t]$. The following base fields
163 ? P = t^2 + 5*t/2 + 1; F = factor(P)
202 $p$-adic accuracy \kbd{padicprec}$(D)$, possibly less if $x$ is inexact
207 ? factor(T, 1); \\ over Q
208 ? factor(T, Mod(1,3)) \\ over F_3
209 ? factor(T, ffgen(ffinit(3,2,'t))^0) \\ over F_{3^2}
210 ? factor(T, Mod(Mod(1,3), t^2+t+2)) \\ over F_{3^2}, again
211 ? factor(T, O(3^6)) \\ over Q_3, precision 6
212 ? factor(T, 1.) \\ over R, current precision
213 ? factor(T, I*1.) \\ over C
214 ? factor(T, Mod(1, y^3-2)) \\ over Q(2^{1/3})
229 \typ{INTMOD}s and \typ{POLMOD}s (e.g.~if a coefficient in $\Z/n\Z$ is known,
234 ? factor(T); \\ over Q
235 ? factor(T*Mod(1,3)) \\ over F_3
236 ? factor(T*ffgen(ffinit(3,2,'t))^0) \\ over F_{3^2}
237 ? factor(T*Mod(Mod(1,3), t^2+t+2)) \\ over F_{3^2}, again
238 ? factor(T*(1 + O(3^6)) \\ over Q_3, precision 6
239 ? factor(T*1.) \\ over R, current precision
240 ? factor(T*(1.+0.*I)) \\ over C
241 ? factor(T*Mod(1, y^3-2)) \\ over Q(2^{1/3})
252 virtual factorization. To avoid pitfalls, we advise to only factor
255 ? factor(x^2-1+O(2^2)) \\ rounded to x^2 + 3, irreducible in Q_2
259 ? factor(x^2-1+O(2^3)) \\ rounded to x^2 + 7, reducible !
265 ? factor(x^2-1, O(2^2)) \\ no ambiguity now
281 ? factor(z^2 + O(5^2)))
286 ? factor(z^2, O(5^2))
298 ? factor(x^2 + y^2, Mod(1,5))
304 ? factor(x^2 + y^2, O(5^2))
316 real fields ($\R$ or $\C$) and usually misses factors even if the input
319 ? factor(x^2 + y^2, I) \\ over Q(i)
325 ? factor(x^2 + y^2, I*1.) \\ over C
330 \fun{GEN}{factor}{GEN x}
337 Help: _factor_Aurifeuille(a,d): return an algebraic factor of Phi_d(a), a != 0
343 Help: _factor_Aurifeuille_prime(p,d): return an algebraic factor of Phi_d(p), p prime