def test_dup_add_mul():
assert dup_add_mul([ZZ(1), ZZ(2), ZZ(3)],
[ZZ(3), ZZ(2), ZZ(1)], [ZZ(1), ZZ(2)],
ZZ) == [ZZ(3), ZZ(9), ZZ(7), ZZ(5)]
assert dmp_add_mul([[ZZ(1), ZZ(2)], [ZZ(3)]],
[[ZZ(3)], [ZZ(2), ZZ(1)]], [[ZZ(1)], [ZZ(2)]], 1,
ZZ) == [[ZZ(3)], [ZZ(3), ZZ(9)], [ZZ(4), ZZ(5)]]
def add(f, g):
"""Add two multivariate fractions `f` and `g`. """
if isinstance(g, DMP):
lev, dom, per, (F_num, F_den), G = f.poly_unify(g)
num, den = dmp_add_mul(F_num, F_den, G, lev, dom), F_den
else:
lev, dom, per, F, G = f.frac_unify(g)
(F_num, F_den), (G_num, G_den) = F, G
num = dmp_add(dmp_mul(F_num, G_den, lev, dom), dmp_mul(F_den, G_num, lev, dom), lev, dom)
den = dmp_mul(F_den, G_den, lev, dom)
return per(num, den)
def dmp_zz_wang_hensel_lifting(f, H, LC, A, p, u, K):
"""Wang/EEZ: Parallel Hensel lifting algorithm. """
S, n, v = [f], len(A), u - 1
H = list(H)
for i, a in enumerate(reversed(A[1:])):
s = dmp_eval_in(S[0], a, n - i, u - i, K)
S.insert(0, dmp_ground_trunc(s, p, v - i, K))
d = max(dmp_degree_list(f, u)[1:])
for j, s, a in zip(xrange(2, n + 2), S, A):
G, w = list(H), j - 1
I, J = A[:j - 2], A[j - 1:]
for i, (h, lc) in enumerate(zip(H, LC)):
lc = dmp_ground_trunc(dmp_eval_tail(lc, J, v, K), p, w - 1, K)
H[i] = [lc] + dmp_raise(h[1:], 1, w - 1, K)
m = dmp_nest([K.one, -a], w, K)
M = dmp_one(w, K)
c = dmp_sub(s, dmp_expand(H, w, K), w, K)
dj = dmp_degree_in(s, w, w)
for k in xrange(0, dj):
if dmp_zero_p(c, w):
break
M = dmp_mul(M, m, w, K)
C = dmp_diff_eval_in(c, k + 1, a, w, w, K)
if not dmp_zero_p(C, w - 1):
C = dmp_quo_ground(C, K.factorial(k + 1), w - 1, K)
T = dmp_zz_diophantine(G, C, I, d, p, w - 1, K)
for i, (h, t) in enumerate(zip(H, T)):
h = dmp_add_mul(h, dmp_raise(t, 1, w - 1, K), M, w, K)
H[i] = dmp_ground_trunc(h, p, w, K)
h = dmp_sub(s, dmp_expand(H, w, K), w, K)
c = dmp_ground_trunc(h, p, w, K)
if dmp_expand(H, u, K) != f:
raise ExtraneousFactors # pragma: no cover
else:
return H
def dmp_zz_wang_hensel_lifting(f, H, LC, A, p, u, K):
"""Wang/EEZ: Parallel Hensel lifting algorithm. """
S, n, v = [f], len(A), u-1
H = list(H)
for i, a in enumerate(reversed(A[1:])):
s = dmp_eval_in(S[0], a, n-i, u-i, K)
S.insert(0, dmp_ground_trunc(s, p, v-i, K))
d = max(dmp_degree_list(f, u)[1:])
for j, s, a in zip(xrange(2, n+2), S, A):
G, w = list(H), j-1
I, J = A[:j-2], A[j-1:]
for i, (h, lc) in enumerate(zip(H, LC)):
lc = dmp_ground_trunc(dmp_eval_tail(lc, J, v, K), p, w-1, K)
H[i] = [lc] + dmp_raise(h[1:], 1, w-1, K)
m = dmp_nest([K.one, -a], w, K)
M = dmp_one(w, K)
c = dmp_sub(s, dmp_expand(H, w, K), w, K)
dj = dmp_degree_in(s, w, w)
for k in xrange(0, dj):
if dmp_zero_p(c, w):
break
M = dmp_mul(M, m, w, K)
C = dmp_diff_eval_in(c, k+1, a, w, w, K)
if not dmp_zero_p(C, w-1):
C = dmp_quo_ground(C, K.factorial(k+1), w-1, K)
T = dmp_zz_diophantine(G, C, I, d, p, w-1, K)
for i, (h, t) in enumerate(zip(H, T)):
h = dmp_add_mul(h, dmp_raise(t, 1, w-1, K), M, w, K)
H[i] = dmp_ground_trunc(h, p, w, K)
h = dmp_sub(s, dmp_expand(H, w, K), w, K)
c = dmp_ground_trunc(h, p, w, K)
if dmp_expand(H, u, K) != f:
raise ExtraneousFactors # pragma: no cover
else:
return H
def add(f, g):
"""Add two multivariate fractions `f` and `g`. """
if isinstance(g, DMP):
lev, dom, per, (F_num, F_den), G = f.poly_unify(g)
num, den = dmp_add_mul(F_num, F_den, G, lev, dom), F_den
else:
lev, dom, per, F, G = f.frac_unify(g)
(F_num, F_den), (G_num, G_den) = F, G
num = dmp_add(dmp_mul(F_num, G_den, lev, dom),
dmp_mul(F_den, G_num, lev, dom), lev, dom)
den = dmp_mul(F_den, G_den, lev, dom)
return per(num, den)
def test_dup_add_mul():
assert dmp_add_mul([[ZZ(1),ZZ(2)],[ZZ(3)]], [[ZZ(3)],[ZZ(2),ZZ(1)]],
[[ZZ(1)],[ZZ(2)]], 1, ZZ) == [[ZZ(3)], [ZZ(3), ZZ(9)], [ZZ(4), ZZ(5)]]
