def test_dmp_sqr():
assert dmp_sqr([ZZ(1), ZZ(2)], 0, ZZ) == dup_sqr([ZZ(1), ZZ(2)], ZZ)
assert dmp_sqr([[[]]], 2, ZZ) == [[[]]]
assert dmp_sqr([[[ZZ(2)]]], 2, ZZ) == [[[ZZ(4)]]]
assert dmp_sqr([[[]]], 2, QQ) == [[[]]]
assert dmp_sqr([[[QQ(2, 3)]]], 2, QQ) == [[[QQ(4, 9)]]]
def test_dmp_sqr():
assert dmp_sqr([ZZ(1),ZZ(2)], 0, ZZ) == \
dup_sqr([ZZ(1),ZZ(2)], ZZ)
assert dmp_sqr([[[]]], 2, ZZ) == [[[]]]
assert dmp_sqr([[[ZZ(2)]]], 2, ZZ) == [[[ZZ(4)]]]
assert dmp_sqr([[[]]], 2, QQ) == [[[]]]
assert dmp_sqr([[[QQ(2,3)]]], 2, QQ) == [[[QQ(4,9)]]]
def test_dmp_sqf():
assert dmp_sqf_part([[]], 1, ZZ) == [[]]
assert dmp_sqf_p([[]], 1, ZZ) == True
assert dmp_sqf_part([[7]], 1, ZZ) == [[1]]
assert dmp_sqf_p([[7]], 1, ZZ) == True
assert dmp_sqf_p(f_0, 2, ZZ) == True
assert dmp_sqf_p(dmp_sqr(f_0, 2, ZZ), 2, ZZ) == False
assert dmp_sqf_p(f_1, 2, ZZ) == True
assert dmp_sqf_p(dmp_sqr(f_1, 2, ZZ), 2, ZZ) == False
assert dmp_sqf_p(f_2, 2, ZZ) == True
assert dmp_sqf_p(dmp_sqr(f_2, 2, ZZ), 2, ZZ) == False
assert dmp_sqf_p(f_3, 2, ZZ) == True
assert dmp_sqf_p(dmp_sqr(f_3, 2, ZZ), 2, ZZ) == False
assert dmp_sqf_p(f_5, 2, ZZ) == False
assert dmp_sqf_p(dmp_sqr(f_5, 2, ZZ), 2, ZZ) == False
assert dmp_sqf_p(f_4, 2, ZZ) == True
assert dmp_sqf_part(f_4, 2, ZZ) == dmp_neg(f_4, 2, ZZ)
assert dmp_sqf_p(f_6, 3, ZZ) == True
assert dmp_sqf_part(f_6, 3, ZZ) == f_6
assert dmp_sqf_part(f_5, 2, ZZ) == [[[1]], [[1], [-1, 0]]]
assert dup_sqf_list([], ZZ) == (ZZ(0), [])
assert dup_sqf_list_include([], ZZ) == [([], 1)]
assert dmp_sqf_list([[ZZ(3)]], 1, ZZ) == (ZZ(3), [])
assert dmp_sqf_list_include([[ZZ(3)]], 1, ZZ) == [([[ZZ(3)]], 1)]
f = [-1,1,0,0,1,-1]
assert dmp_sqf_list(f, 0, ZZ) == \
(-1, [([1,1,1,1], 1), ([1,-1], 2)])
assert dmp_sqf_list_include(f, 0, ZZ) == \
[([-1,-1,-1,-1], 1), ([1,-1], 2)]
f = [[-1],[1],[],[],[1],[-1]]
assert dmp_sqf_list(f, 1, ZZ) == \
(-1, [([[1],[1],[1],[1]], 1), ([[1],[-1]], 2)])
assert dmp_sqf_list_include(f, 1, ZZ) == \
[([[-1],[-1],[-1],[-1]], 1), ([[1],[-1]], 2)]
K = FF(2)
f = [[-1], [2], [-1]]
assert dmp_sqf_list_include(f, 1, ZZ) == \
[([[-1]], 1), ([[1], [-1]], 2)]
raises(DomainError, "dmp_sqf_list([[K(1), K(0), K(1)]], 1, K)")
def dmp_fateman_poly_F_3(n, K):
"""Fateman's GCD benchmark: sparse inputs (deg f ~ vars f) """
u = dup_from_raw_dict({n+1: K.one}, K)
for i in xrange(0, n-1):
u = dmp_add_term([u], dmp_one(i, K), n+1, i+1, K)
v = dmp_add_term(u, dmp_ground(K(2), n-2), 0, n, K)
f = dmp_sqr(dmp_add_term([dmp_neg(v, n-1, K)], dmp_one(n-1, K), n+1, n, K), n, K)
g = dmp_sqr(dmp_add_term([v], dmp_one(n-1, K), n+1, n, K), n, K)
v = dmp_add_term(u, dmp_one(n-2, K), 0, n-1, K)
h = dmp_sqr(dmp_add_term([v], dmp_one(n-1, K), n+1, n, K), n, K)
return dmp_mul(f, h, n, K), dmp_mul(g, h, n, K), h
def dmp_fateman_poly_F_3(n, K):
"""Fateman's GCD benchmark: sparse inputs (deg f ~ vars f) """
u = dup_from_raw_dict({n+1: K.one}, K)
for i in xrange(0, n-1):
u = dmp_add_term([u], dmp_one(i, K), n+1, i+1, K)
v = dmp_add_term(u, dmp_ground(K(2), n-2), 0, n, K)
f = dmp_sqr(dmp_add_term([dmp_neg(v, n-1, K)], dmp_one(n-1, K), n+1, n, K), n, K)
g = dmp_sqr(dmp_add_term([v], dmp_one(n-1, K), n+1, n, K), n, K)
v = dmp_add_term(u, dmp_one(n-2, K), 0, n-1, K)
h = dmp_sqr(dmp_add_term([v], dmp_one(n-1, K), n+1, n, K), n, K)
return dmp_mul(f, h, n, K), dmp_mul(g, h, n, K), h
def dmp_fateman_poly_F_2(n, K):
"""Fateman's GCD benchmark: linearly dense quartic inputs """
u = [K(1), K(0)]
for i in range(0, n - 1):
u = [dmp_one(i, K), u]
m = n - 1
v = dmp_add_term(u, dmp_ground(K(2), m - 1), 0, n, K)
f = dmp_sqr([dmp_one(m, K), dmp_neg(v, m, K)], n, K)
g = dmp_sqr([dmp_one(m, K), v], n, K)
v = dmp_add_term(u, dmp_one(m - 1, K), 0, n, K)
h = dmp_sqr([dmp_one(m, K), v], n, K)
return dmp_mul(f, h, n, K), dmp_mul(g, h, n, K), h
def dmp_fateman_poly_F_2(n, K):
"""Fateman's GCD benchmark: linearly dense quartic inputs """
u = [K(1), K(0)]
for i in xrange(0, n - 1):
u = [dmp_one(i, K), u]
m = n - 1
v = dmp_add_term(u, dmp_ground(K(2), m - 1), 0, n, K)
f = dmp_sqr([dmp_one(m, K), dmp_neg(v, m, K)], n, K)
g = dmp_sqr([dmp_one(m, K), v], n, K)
v = dmp_add_term(u, dmp_one(m - 1, K), 0, n, K)
h = dmp_sqr([dmp_one(m, K), v], n, K)
return dmp_mul(f, h, n, K), dmp_mul(g, h, n, K), h
def test_dmp_sqr():
assert dmp_sqr([ZZ(1),ZZ(2)], 0, ZZ) == \
dup_sqr([ZZ(1),ZZ(2)], ZZ)
assert dmp_sqr([[[]]], 2, ZZ) == [[[]]]
assert dmp_sqr([[[ZZ(2)]]], 2, ZZ) == [[[ZZ(4)]]]
assert dmp_sqr([[[]]], 2, QQ) == [[[]]]
assert dmp_sqr([[[QQ(2,3)]]], 2, QQ) == [[[QQ(4,9)]]]
K = FF(9)
assert dmp_sqr([[K(3)],[K(4)]], 1, K) == [[K(6)],[K(7)]]
def sqr(f):
"""Square a multivariate polynomial `f`. """
return f.per(dmp_sqr(f.rep, f.lev, f.dom))
def sqr(f):
"""Square a multivariate polynomial `f`. """
return f.per(dmp_sqr(f.rep, f.lev, f.dom))