def test_dup_pow():
assert dup_pow([], 0, ZZ) == [ZZ(1)]
assert dup_pow([], 0, QQ) == [QQ(1)]
assert dup_pow([], 1, ZZ) == []
assert dup_pow([], 7, ZZ) == []
assert dup_pow([ZZ(1)], 0, ZZ) == [ZZ(1)]
assert dup_pow([ZZ(1)], 1, ZZ) == [ZZ(1)]
assert dup_pow([ZZ(1)], 7, ZZ) == [ZZ(1)]
assert dup_pow([ZZ(3)], 0, ZZ) == [ZZ(1)]
assert dup_pow([ZZ(3)], 1, ZZ) == [ZZ(3)]
assert dup_pow([ZZ(3)], 7, ZZ) == [ZZ(2187)]
assert dup_pow([QQ(1,1)], 0, QQ) == [QQ(1,1)]
assert dup_pow([QQ(1,1)], 1, QQ) == [QQ(1,1)]
assert dup_pow([QQ(1,1)], 7, QQ) == [QQ(1,1)]
assert dup_pow([QQ(3,7)], 0, QQ) == [QQ(1,1)]
assert dup_pow([QQ(3,7)], 1, QQ) == [QQ(3,7)]
assert dup_pow([QQ(3,7)], 7, QQ) == [QQ(2187,823543)]
f = dup_normal([2,0,0,1,7], ZZ)
assert dup_pow(f, 0, ZZ) == dup_normal([1], ZZ)
assert dup_pow(f, 1, ZZ) == dup_normal([2,0,0,1,7], ZZ)
assert dup_pow(f, 2, ZZ) == dup_normal([4,0,0,4,28,0,1,14,49], ZZ)
assert dup_pow(f, 3, ZZ) == dup_normal([8,0,0,12,84,0,6,84,294,1,21,147,343], ZZ)
def test_dup_diff():
assert dup_diff([], 1, ZZ) == []
assert dup_diff([7], 1, ZZ) == []
assert dup_diff([2, 7], 1, ZZ) == [2]
assert dup_diff([1, 2, 1], 1, ZZ) == [2, 2]
assert dup_diff([1, 2, 3, 4], 1, ZZ) == [3, 4, 3]
assert dup_diff([1, -1, 0, 0, 2], 1, ZZ) == [4, -3, 0, 0]
f = dup_normal([17, 34, 56, -345, 23, 76, 0, 0, 12, 3, 7], ZZ)
assert dup_diff(f, 0, ZZ) == f
assert dup_diff(f, 1, ZZ) == dup_diff(f, 1, ZZ)
assert dup_diff(f, 2, ZZ) == dup_diff(dup_diff(f, 1, ZZ), 1, ZZ)
assert dup_diff(
f, 3, ZZ) == dup_diff(dup_diff(dup_diff(f, 1, ZZ), 1, ZZ), 1, ZZ)
K = FF(3)
f = dup_normal([17, 34, 56, -345, 23, 76, 0, 0, 12, 3, 7], K)
assert dup_diff(f, 1, K) == dup_normal([2, 0, 1, 0, 0, 2, 0, 0, 0, 0], K)
assert dup_diff(f, 2, K) == dup_normal([1, 0, 0, 2, 0, 0, 0], K)
assert dup_diff(f, 3, K) == dup_normal([], K)
assert dup_diff(f, 0, K) == f
assert dup_diff(f, 1, K) == dup_diff(f, 1, K)
assert dup_diff(f, 2, K) == dup_diff(dup_diff(f, 1, K), 1, K)
assert dup_diff(
f, 3, K) == dup_diff(dup_diff(dup_diff(f, 1, K), 1, K), 1, K)
def test_dup_mul():
assert dup_mul([], [], ZZ) == []
assert dup_mul([], [ZZ(1)], ZZ) == []
assert dup_mul([ZZ(1)], [], ZZ) == []
assert dup_mul([ZZ(1)], [ZZ(1)], ZZ) == [ZZ(1)]
assert dup_mul([ZZ(5)], [ZZ(7)], ZZ) == [ZZ(35)]
assert dup_mul([], [], QQ) == []
assert dup_mul([], [QQ(1,2)], QQ) == []
assert dup_mul([QQ(1,2)], [], QQ) == []
assert dup_mul([QQ(1,2)], [QQ(4,7)], QQ) == [QQ(2,7)]
assert dup_mul([QQ(5,7)], [QQ(3,7)], QQ) == [QQ(15,49)]
f = dup_normal([3,0,0,6,1,2], ZZ)
g = dup_normal([4,0,1,0], ZZ)
h = dup_normal([12,0,3,24,4,14,1,2,0], ZZ)
assert dup_mul(f, g, ZZ) == h
assert dup_mul(g, f, ZZ) == h
f = dup_normal([2,0,0,1,7], ZZ)
h = dup_normal([4,0,0,4,28,0,1,14,49], ZZ)
assert dup_mul(f, f, ZZ) == h
K = FF(6)
assert dup_mul([K(2),K(1)], [K(3),K(4)], K) == [K(5),K(4)]
def test_dup_extract():
f = dup_normal([2930944, 0, 2198208, 0, 549552, 0, 45796], ZZ)
g = dup_normal([17585664, 0, 8792832, 0, 1099104, 0], ZZ)
F = dup_normal([64, 0, 48, 0, 12, 0, 1], ZZ)
G = dup_normal([384, 0, 192, 0, 24, 0], ZZ)
assert dup_extract(f, g, ZZ) == (45796, F, G)
def test_dup_extract():
f = dup_normal([2930944, 0, 2198208, 0, 549552, 0, 45796], ZZ)
g = dup_normal([17585664, 0, 8792832, 0, 1099104, 0], ZZ)
F = dup_normal([64, 0, 48, 0, 12, 0, 1], ZZ)
G = dup_normal([384, 0, 192, 0, 24, 0], ZZ)
assert dup_extract(f, g, ZZ) == (45796, F, G)
def test_dup_rr_div():
raises(ZeroDivisionError, lambda: dup_rr_div([1,2,3], [], ZZ))
f = dup_normal([3,1,1,5], ZZ)
g = dup_normal([5,-3,1], ZZ)
q, r = [], f
assert dup_rr_div(f, g, ZZ) == (q, r)
def test_dup_mul_ground():
f = dup_normal([], ZZ)
assert dup_mul_ground(f, ZZ(2), ZZ) == dup_normal([], ZZ)
f = dup_normal([1,2,3], ZZ)
assert dup_mul_ground(f, ZZ(0), ZZ) == dup_normal([], ZZ)
assert dup_mul_ground(f, ZZ(2), ZZ) == dup_normal([2,4,6], ZZ)
def test_dup_ff_div():
raises(ZeroDivisionError, lambda: dup_ff_div([1,2,3], [], QQ))
f = dup_normal([3,1,1,5], QQ)
g = dup_normal([5,-3,1], QQ)
q = [QQ(3,5), QQ(14,25)]
r = [QQ(52,25), QQ(111,25)]
assert dup_ff_div(f, g, QQ) == (q, r)
def test_dup_sqr():
assert dup_sqr([], ZZ) == []
assert dup_sqr([ZZ(2)], ZZ) == [ZZ(4)]
assert dup_sqr([ZZ(1),ZZ(2)], ZZ) == [ZZ(1),ZZ(4),ZZ(4)]
assert dup_sqr([], QQ) == []
assert dup_sqr([QQ(2,3)], QQ) == [QQ(4,9)]
assert dup_sqr([QQ(1,3),QQ(2,3)], QQ) == [QQ(1,9),QQ(4,9),QQ(4,9)]
f = dup_normal([2,0,0,1,7], ZZ)
assert dup_sqr(f, ZZ) == dup_normal([4,0,0,4,28,0,1,14,49], ZZ)
def test_dup_sqr():
assert dup_sqr([], ZZ) == []
assert dup_sqr([ZZ(2)], ZZ) == [ZZ(4)]
assert dup_sqr([ZZ(1),ZZ(2)], ZZ) == [ZZ(1),ZZ(4),ZZ(4)]
assert dup_sqr([], QQ) == []
assert dup_sqr([QQ(2,3)], QQ) == [QQ(4,9)]
assert dup_sqr([QQ(1,3),QQ(2,3)], QQ) == [QQ(1,9),QQ(4,9),QQ(4,9)]
f = dup_normal([2,0,0,1,7], ZZ)
assert dup_sqr(f, ZZ) == dup_normal([4,0,0,4,28,0,1,14,49], ZZ)
def dup_ff_div(f, g, K):
"""Polynomial division with remainder over a field. """
df = dup_degree(f)
dg = dup_degree(g)
q, r = [], f
if not g:
raise ZeroDivisionError("polynomial division")
elif df < dg:
return q, r
lc_g = dup_LC(g, K)
while True:
dr = dup_degree(r)
if dr < dg:
break
lc_r = dup_LC(r, K)
c = K.exquo(lc_r, lc_g)
j = dr - dg
q = dup_add_term(q, c, j, K)
h = dup_mul_term(g, c, j, K)
r = dup_sub(r, h, K)
if not K.is_Exact:
r = dup_normal(r, K)
return q, r
def dup_ff_div(f, g, K):
"""Polynomial division with remainder over a field. """
df = dup_degree(f)
dg = dup_degree(g)
q, r = [], f
if not g:
raise ZeroDivisionError("polynomial division")
elif df < dg:
return q, r
lc_g = dup_LC(g, K)
while True:
dr = dup_degree(r)
if dr < dg:
break
lc_r = dup_LC(r, K)
c = K.exquo(lc_r, lc_g)
j = dr - dg
q = dup_add_term(q, c, j, K)
h = dup_mul_term(g, c, j, K)
r = dup_sub(r, h, K)
if not K.is_Exact:
r = dup_normal(r, K)
return q, r
def test_dup_normal():
assert dup_normal([0, 0, 2, 1, 0, 11, 0], ZZ) == [
ZZ(2),
ZZ(1),
ZZ(0),
ZZ(11),
ZZ(0),
]
def test_dup_quo_ground():
raises(ZeroDivisionError, 'dup_quo_ground(dup_normal([1,2,3], ZZ), ZZ(0), ZZ)')
raises(ExactQuotientFailed, 'dup_quo_ground(dup_normal([1,2,3], ZZ), ZZ(3), ZZ)')
f = dup_normal([], ZZ)
assert dup_quo_ground(f, ZZ(3), ZZ) == dup_normal([], ZZ)
f = dup_normal([6,2,8], ZZ)
assert dup_quo_ground(f, ZZ(1), ZZ) == f
assert dup_quo_ground(f, ZZ(2), ZZ) == dup_normal([3,1,4], ZZ)
f = dup_normal([6,2,8], QQ)
assert dup_quo_ground(f, QQ(1), QQ) == f
assert dup_quo_ground(f, QQ(2), QQ) == [QQ(3),QQ(1),QQ(4)]
assert dup_quo_ground(f, QQ(7), QQ) == [QQ(6,7),QQ(2,7),QQ(8,7)]
def test_dup_quo_ground():
raises(ZeroDivisionError, 'dup_quo_ground(dup_normal([1,2,3], ZZ), ZZ(0), ZZ)')
raises(ExactQuotientFailed, 'dup_quo_ground(dup_normal([1,2,3], ZZ), ZZ(3), ZZ)')
f = dup_normal([], ZZ)
assert dup_quo_ground(f, ZZ(3), ZZ) == dup_normal([], ZZ)
f = dup_normal([6,2,8], ZZ)
assert dup_quo_ground(f, ZZ(1), ZZ) == f
assert dup_quo_ground(f, ZZ(2), ZZ) == dup_normal([3,1,4], ZZ)
f = dup_normal([6,2,8], QQ)
assert dup_quo_ground(f, QQ(1), QQ) == f
assert dup_quo_ground(f, QQ(2), QQ) == [QQ(3),QQ(1),QQ(4)]
assert dup_quo_ground(f, QQ(7), QQ) == [QQ(6,7),QQ(2,7),QQ(8,7)]
def test_dup_mul_term():
f = dup_normal([], ZZ)
assert dup_mul_term(f, ZZ(2), 3, ZZ) == dup_normal([], ZZ)
f = dup_normal([1,1], ZZ)
assert dup_mul_term(f, ZZ(0), 3, ZZ) == dup_normal([], ZZ)
f = dup_normal([1,2,3], ZZ)
assert dup_mul_term(f, ZZ(2), 0, ZZ) == dup_normal([2,4,6], ZZ)
assert dup_mul_term(f, ZZ(2), 1, ZZ) == dup_normal([2,4,6,0], ZZ)
assert dup_mul_term(f, ZZ(2), 2, ZZ) == dup_normal([2,4,6,0,0], ZZ)
assert dup_mul_term(f, ZZ(2), 3, ZZ) == dup_normal([2,4,6,0,0,0], ZZ)
def test_dup_gcdex():
f = dup_normal([1, -2, -6, 12, 15], QQ)
g = dup_normal([1, 1, -4, -4], QQ)
s = [QQ(-1, 5), QQ(3, 5)]
t = [QQ(1, 5), QQ(-6, 5), QQ(2)]
h = [QQ(1), QQ(1)]
assert dup_half_gcdex(f, g, QQ) == (s, h)
assert dup_gcdex(f, g, QQ) == (s, t, h)
f = dup_normal([1, 4, 0, -1, 1], QQ)
g = dup_normal([1, 0, -1, 1], QQ)
s, t, h = dup_gcdex(f, g, QQ)
S, T, H = dup_gcdex(g, f, QQ)
assert dup_add(dup_mul(s, f, QQ), dup_mul(t, g, QQ), QQ) == h
assert dup_add(dup_mul(S, g, QQ), dup_mul(T, f, QQ), QQ) == H
f = dup_normal([2, 0], QQ)
g = dup_normal([1, 0, -16], QQ)
s = [QQ(1, 32), QQ(0)]
t = [QQ(-1, 16)]
h = [QQ(1)]
assert dup_half_gcdex(f, g, QQ) == (s, h)
assert dup_gcdex(f, g, QQ) == (s, t, h)
def test_dup_gcdex():
f = dup_normal([1,-2,-6,12,15], QQ)
g = dup_normal([1,1,-4,-4], QQ)
s = [QQ(-1,5),QQ(3,5)]
t = [QQ(1,5),QQ(-6,5),QQ(2)]
h = [QQ(1),QQ(1)]
assert dup_half_gcdex(f, g, QQ) == (s, h)
assert dup_gcdex(f, g, QQ) == (s, t, h)
f = dup_normal([1,4,0,-1,1], QQ)
g = dup_normal([1,0,-1,1], QQ)
s, t, h = dup_gcdex(f, g, QQ)
S, T, H = dup_gcdex(g, f, QQ)
assert dup_add(dup_mul(s, f, QQ),
dup_mul(t, g, QQ), QQ) == h
assert dup_add(dup_mul(S, g, QQ),
dup_mul(T, f, QQ), QQ) == H
f = dup_normal([2,0], QQ)
g = dup_normal([1,0,-16], QQ)
s = [QQ(1,32),QQ(0)]
t = [QQ(-1,16)]
h = [QQ(1)]
assert dup_half_gcdex(f, g, QQ) == (s, h)
assert dup_gcdex(f, g, QQ) == (s, t, h)
def dup_ff_div(f, g, K):
"""
Polynomial division with remainder over a field.
Examples
========
>>> from sympy.polys.domains import QQ
>>> from sympy.polys.densearith import dup_ff_div
>>> f = QQ.map([1, 0, 1])
>>> g = QQ.map([2, -4])
>>> dup_ff_div(f, g, QQ)
([1/2, 1/1], [5/1])
"""
df = dup_degree(f)
dg = dup_degree(g)
q, r = [], f
if not g:
raise ZeroDivisionError("polynomial division")
elif df < dg:
return q, r
lc_g = dup_LC(g, K)
while True:
dr = dup_degree(r)
if dr < dg:
break
lc_r = dup_LC(r, K)
c = K.exquo(lc_r, lc_g)
j = dr - dg
q = dup_add_term(q, c, j, K)
h = dup_mul_term(g, c, j, K)
r = dup_sub(r, h, K)
if not K.is_Exact:
r = dup_normal(r, K)
return q, r
def dup_ff_div(f, g, K):
"""
Polynomial division with remainder over a field.
Examples
========
>>> from sympy.polys.domains import QQ
>>> from sympy.polys.densearith import dup_ff_div
>>> f = QQ.map([1, 0, 1])
>>> g = QQ.map([2, -4])
>>> dup_ff_div(f, g, QQ)
([1/2, 1/1], [5/1])
"""
df = dup_degree(f)
dg = dup_degree(g)
q, r = [], f
if not g:
raise ZeroDivisionError("polynomial division")
elif df < dg:
return q, r
lc_g = dup_LC(g, K)
while True:
dr = dup_degree(r)
if dr < dg:
break
lc_r = dup_LC(r, K)
c = K.exquo(lc_r, lc_g)
j = dr - dg
q = dup_add_term(q, c, j, K)
h = dup_mul_term(g, c, j, K)
r = dup_sub(r, h, K)
if not K.is_Exact:
r = dup_normal(r, K)
return q, r
def test_dup_mul():
assert dup_mul([], [], ZZ) == []
assert dup_mul([], [ZZ(1)], ZZ) == []
assert dup_mul([ZZ(1)], [], ZZ) == []
assert dup_mul([ZZ(1)], [ZZ(1)], ZZ) == [ZZ(1)]
assert dup_mul([ZZ(5)], [ZZ(7)], ZZ) == [ZZ(35)]
assert dup_mul([], [], QQ) == []
assert dup_mul([], [QQ(1,2)], QQ) == []
assert dup_mul([QQ(1,2)], [], QQ) == []
assert dup_mul([QQ(1,2)], [QQ(4,7)], QQ) == [QQ(2,7)]
assert dup_mul([QQ(5,7)], [QQ(3,7)], QQ) == [QQ(15,49)]
f = dup_normal([3,0,0,6,1,2], ZZ)
g = dup_normal([4,0,1,0], ZZ)
h = dup_normal([12,0,3,24,4,14,1,2,0], ZZ)
assert dup_mul(f, g, ZZ) == h
assert dup_mul(g, f, ZZ) == h
f = dup_normal([2,0,0,1,7], ZZ)
h = dup_normal([4,0,0,4,28,0,1,14,49], ZZ)
assert dup_mul(f, f, ZZ) == h
def dup_ff_div(f, g, K):
"""
Polynomial division with remainder over a field.
Examples
========
>>> from sympy.polys import ring, QQ
>>> R, x = ring("x", QQ)
>>> R.dup_ff_div(x**2 + 1, 2*x - 4)
(1/2*x + 1, 5)
"""
df = dup_degree(f)
dg = dup_degree(g)
q, r = [], f
if not g:
raise ZeroDivisionError("polynomial division")
elif df < dg:
return q, r
lc_g = dup_LC(g, K)
while True:
dr = dup_degree(r)
if dr < dg:
break
lc_r = dup_LC(r, K)
c = K.exquo(lc_r, lc_g)
j = dr - dg
q = dup_add_term(q, c, j, K)
h = dup_mul_term(g, c, j, K)
r = dup_sub(r, h, K)
if not K.is_Exact:
r = dup_normal(r, K)
return q, r
def dup_ff_div(f, g, K):
"""
Polynomial division with remainder over a field.
Examples
========
>>> from sympy.polys import ring, QQ
>>> R, x = ring("x", QQ)
>>> R.dup_ff_div(x**2 + 1, 2*x - 4)
(1/2*x + 1, 5)
"""
df = dup_degree(f)
dg = dup_degree(g)
q, r = [], f
if not g:
raise ZeroDivisionError("polynomial division")
elif df < dg:
return q, r
lc_g = dup_LC(g, K)
while True:
dr = dup_degree(r)
if dr < dg:
break
lc_r = dup_LC(r, K)
c = K.exquo(lc_r, lc_g)
j = dr - dg
q = dup_add_term(q, c, j, K)
h = dup_mul_term(g, c, j, K)
r = dup_sub(r, h, K)
if not K.is_Exact:
r = dup_normal(r, K)
return q, r
def test_dmp_pow():
assert dmp_pow([[]], 0, 1, ZZ) == [[ZZ(1)]]
assert dmp_pow([[]], 0, 1, QQ) == [[QQ(1)]]
assert dmp_pow([[]], 1, 1, ZZ) == [[]]
assert dmp_pow([[]], 7, 1, ZZ) == [[]]
assert dmp_pow([[ZZ(1)]], 0, 1, ZZ) == [[ZZ(1)]]
assert dmp_pow([[ZZ(1)]], 1, 1, ZZ) == [[ZZ(1)]]
assert dmp_pow([[ZZ(1)]], 7, 1, ZZ) == [[ZZ(1)]]
assert dmp_pow([[QQ(3,7)]], 0, 1, QQ) == [[QQ(1,1)]]
assert dmp_pow([[QQ(3,7)]], 1, 1, QQ) == [[QQ(3,7)]]
assert dmp_pow([[QQ(3,7)]], 7, 1, QQ) == [[QQ(2187,823543)]]
f = dup_normal([2,0,0,1,7], ZZ)
assert dmp_pow(f, 2, 0, ZZ) == dup_pow(f, 2, ZZ)
def test_dup_quo_ground():
raises(ZeroDivisionError, lambda: dup_quo_ground(dup_normal([1,2,3], ZZ), ZZ(0), ZZ))
f = dup_normal([], ZZ)
assert dup_quo_ground(f, ZZ(3), ZZ) == dup_normal([], ZZ)
f = dup_normal([6,2,8], ZZ)
assert dup_quo_ground(f, ZZ(1), ZZ) == f
assert dup_quo_ground(f, ZZ(2), ZZ) == dup_normal([3,1,4], ZZ)
assert dup_quo_ground(f, ZZ(3), ZZ) == dup_normal([2,0,2], ZZ)
f = dup_normal([6,2,8], QQ)
assert dup_quo_ground(f, QQ(1), QQ) == f
assert dup_quo_ground(f, QQ(2), QQ) == [QQ(3),QQ(1),QQ(4)]
assert dup_quo_ground(f, QQ(7), QQ) == [QQ(6,7),QQ(2,7),QQ(8,7)]
def test_dup_pdiv():
f = dup_normal([3,1,1,5], ZZ)
g = dup_normal([5,-3,1], ZZ)
q = dup_normal([15, 14], ZZ)
r = dup_normal([52, 111], ZZ)
assert dup_pdiv(f, g, ZZ) == (q, r)
assert dup_pquo(f, g, ZZ) == q
assert dup_prem(f, g, ZZ) == r
raises(ExactQuotientFailed, lambda: dup_pexquo(f, g, ZZ))
f = dup_normal([3,1,1,5], QQ)
g = dup_normal([5,-3,1], QQ)
q = dup_normal([15, 14], QQ)
r = dup_normal([52, 111], QQ)
assert dup_pdiv(f, g, QQ) == (q, r)
assert dup_pquo(f, g, QQ) == q
assert dup_prem(f, g, QQ) == r
raises(ExactQuotientFailed, lambda: dup_pexquo(f, g, QQ))
def test_dup_mul():
assert dup_mul([], [], ZZ) == []
assert dup_mul([], [ZZ(1)], ZZ) == []
assert dup_mul([ZZ(1)], [], ZZ) == []
assert dup_mul([ZZ(1)], [ZZ(1)], ZZ) == [ZZ(1)]
assert dup_mul([ZZ(5)], [ZZ(7)], ZZ) == [ZZ(35)]
assert dup_mul([], [], QQ) == []
assert dup_mul([], [QQ(1, 2)], QQ) == []
assert dup_mul([QQ(1, 2)], [], QQ) == []
assert dup_mul([QQ(1, 2)], [QQ(4, 7)], QQ) == [QQ(2, 7)]
assert dup_mul([QQ(5, 7)], [QQ(3, 7)], QQ) == [QQ(15, 49)]
f = dup_normal([3, 0, 0, 6, 1, 2], ZZ)
g = dup_normal([4, 0, 1, 0], ZZ)
h = dup_normal([12, 0, 3, 24, 4, 14, 1, 2, 0], ZZ)
assert dup_mul(f, g, ZZ) == h
assert dup_mul(g, f, ZZ) == h
f = dup_normal([2, 0, 0, 1, 7], ZZ)
h = dup_normal([4, 0, 0, 4, 28, 0, 1, 14, 49], ZZ)
assert dup_mul(f, f, ZZ) == h
K = FF(6)
assert dup_mul([K(2), K(1)], [K(3), K(4)], K) == [K(5), K(4)]
p1 = dup_normal([79, -1, 78, -94, -10, 11, 32, -19, 78, 2, -89, 30, 73, 42,
85, 77, 83, -30, -34, -2, 95, -81, 37, -49, -46, -58, -16, 37, 35, -11,
-57, -15, -31, 67, -20, 27, 76, 2, 70, 67, -65, 65, -26, -93, -44, -12,
-92, 57, -90, -57, -11, -67, -98, -69, 97, -41, 89, 33, 89, -50, 81,
-31, 60, -27, 43, 29, -77, 44, 21, -91, 32, -57, 33, 3, 53, -51, -38,
-99, -84, 23, -50, 66, -100, 1, -75, -25, 27, -60, 98, -51, -87, 6, 8,
78, -28, -95, -88, 12, -35, 26, -9, 16, -92, 55, -7, -86, 68, -39, -46,
84, 94, 45, 60, 92, 68, -75, -74, -19, 8, 75, 78, 91, 57, 34, 14, -3,
-49, 65, 78, -18, 6, -29, -80, -98, 17, 13, 58, 21, 20, 9, 37, 7, -30,
-53, -20, 34, 67, -42, 89, -22, 73, 43, -6, 5, 51, -8, -15, -52, -22,
-58, -72, -3, 43, -92, 82, 83, -2, -13, -23, -60, 16, -94, -8, -28,
-95, -72, 63, -90, 76, 6, -43, -100, -59, 76, 3, 3, 46, -85, 75, 62,
-71, -76, 88, 97, -72, -1, 30, -64, 72, -48, 14, -78, 58, 63, -91, 24,
-87, -27, -80, -100, -44, 98, 70, 100, -29, -38, 11, 77, 100, 52, 86,
65, -5, -42, -81, -38, -42, 43, -2, -70, -63, -52], ZZ)
p2 = dup_normal([65, -19, -47, 1, 90, 81, -15, -34, 25, -75, 9, -83, 50, -5,
-44, 31, 1, 70, -7, 78, 74, 80, 85, 65, 21, 41, 66, 19, -40, 63, -21,
-27, 32, 69, 83, 34, -35, 14, 81, 57, -75, 32, -67, -89, -100, -61, 46,
84, -78, -29, -50, -94, -24, -32, -68, -16, 100, -7, -72, -89, 35, 82,
58, 81, -92, 62, 5, -47, -39, -58, -72, -13, 84, 44, 55, -25, 48, -54,
-31, -56, -11, -50, -84, 10, 67, 17, 13, -14, 61, 76, -64, -44, -40,
-96, 11, -11, -94, 2, 6, 27, -6, 68, -54, 66, -74, -14, -1, -24, -73,
96, 89, -11, -89, 56, -53, 72, -43, 96, 25, 63, -31, 29, 68, 83, 91,
-93, -19, -38, -40, 40, -12, -19, -79, 44, 100, -66, -29, -77, 62, 39,
-8, 11, -97, 14, 87, 64, 21, -18, 13, 15, -59, -75, -99, -88, 57, 54,
56, -67, 6, -63, -59, -14, 28, 87, -20, -39, 84, -91, -2, 49, -75, 11,
-24, -95, 36, 66, 5, 25, -72, -40, 86, 90, 37, -33, 57, -35, 29, -18,
4, -79, 64, -17, -27, 21, 29, -5, -44, -87, -24, 52, 78, 11, -23, -53,
36, 42, 21, -68, 94, -91, -51, -21, 51, -76, 72, 31, 24, -48, -80, -9,
37, -47, -6, -8, -63, -91, 79, -79, -100, 38, -20, 38, 100, 83, -90,
87, 63, -36, 82, -19, 18, -98, -38, 26, 98, -70, 79, 92, 12, 12, 70,
74, 36, 48, -13, 31, 31, -47, -71, -12, -64, 36, -42, 32, -86, 60, 83,
70, 55, 0, 1, 29, -35, 8, -82, 8, -73, -46, -50, 43, 48, -5, -86, -72,
44, -90, 19, 19, 5, -20, 97, -13, -66, -5, 5, -69, 64, -30, 41, 51, 36,
13, -99, -61, 94, -12, 74, 98, 68, 24, 46, -97, -87, -6, -27, 82, 62,
-11, -77, 86, 66, -47, -49, -50, 13, 18, 89, -89, 46, -80, 13, 98, -35,
-36, -25, 12, 20, 26, -52, 79, 27, 79, 100, 8, 62, -58, -28, 37], ZZ)
res = dup_normal([5135, -1566, 1376, -7466, 4579, 11710, 8001, -7183,
-3737, -7439, 345, -10084, 24522, -1201, 1070, -10245, 9582, 9264,
1903, 23312, 18953, 10037, -15268, -5450, 6442, -6243, -3777, 5110,
10936, -16649, -6022, 16255, 31300, 24818, 31922, 32760, 7854, 27080,
15766, 29596, 7139, 31945, -19810, 465, -38026, -3971, 9641, 465,
-19375, 5524, -30112, -11960, -12813, 13535, 30670, 5925, -43725,
-14089, 11503, -22782, 6371, 43881, 37465, -33529, -33590, -39798,
-37854, -18466, -7908, -35825, -26020, -36923, -11332, -5699, 25166,
-3147, 19885, 12962, -20659, -1642, 27723, -56331, -24580, -11010,
-20206, 20087, -23772, -16038, 38580, 20901, -50731, 32037, -4299,
26508, 18038, -28357, 31846, -7405, -20172, -15894, 2096, 25110,
-45786, 45918, -55333, -31928, -49428, -29824, -58796, -24609, -15408,
69, -35415, -18439, 10123, -20360, -65949, 33356, -20333, 26476,
-32073, 33621, 930, 28803, -42791, 44716, 38164, 12302, -1739, 11421,
73385, -7613, 14297, 38155, -414, 77587, 24338, -21415, 29367, 42639,
13901, -288, 51027, -11827, 91260, 43407, 88521, -15186, 70572, -12049,
5090, -12208, -56374, 15520, -623, -7742, 50825, 11199, -14894, 40892,
59591, -31356, -28696, -57842, -87751, -33744, -28436, -28945, -40287,
37957, -35638, 33401, -61534, 14870, 40292, 70366, -10803, 102290,
-71719, -85251, 7902, -22409, 75009, 99927, 35298, -1175, -762, -34744,
-10587, -47574, -62629, -19581, -43659, -54369, -32250, -39545, 15225,
-24454, 11241, -67308, -30148, 39929, 37639, 14383, -73475, -77636,
-81048, -35992, 41601, -90143, 76937, -8112, 56588, 9124, -40094,
-32340, 13253, 10898, -51639, 36390, 12086, -1885, 100714, -28561,
-23784, -18735, 18916, 16286, 10742, -87360, -13697, 10689, -19477,
-29770, 5060, 20189, -8297, 112407, 47071, 47743, 45519, -4109, 17468,
-68831, 78325, -6481, -21641, -19459, 30919, 96115, 8607, 53341, 32105,
-16211, 23538, 57259, -76272, -40583, 62093, 38511, -34255, -40665,
-40604, -37606, -15274, 33156, -13885, 103636, 118678, -14101, -92682,
-100791, 2634, 63791, 98266, 19286, -34590, -21067, -71130, 25380,
-40839, -27614, -26060, 52358, -15537, 27138, -6749, 36269, -33306,
13207, -91084, -5540, -57116, 69548, 44169, -57742, -41234, -103327,
-62904, -8566, 41149, -12866, 71188, 23980, 1838, 58230, 73950, 5594,
43113, -8159, -15925, 6911, 85598, -75016, -16214, -62726, -39016,
8618, -63882, -4299, 23182, 49959, 49342, -3238, -24913, -37138, 78361,
32451, 6337, -11438, -36241, -37737, 8169, -3077, -24829, 57953, 53016,
-31511, -91168, 12599, -41849, 41576, 55275, -62539, 47814, -62319,
12300, -32076, -55137, -84881, -27546, 4312, -3433, -54382, 113288,
-30157, 74469, 18219, 79880, -2124, 98911, 17655, -33499, -32861,
47242, -37393, 99765, 14831, -44483, 10800, -31617, -52710, 37406,
22105, 29704, -20050, 13778, 43683, 36628, 8494, 60964, -22644, 31550,
-17693, 33805, -124879, -12302, 19343, 20400, -30937, -21574, -34037,
-33380, 56539, -24993, -75513, -1527, 53563, 65407, -101, 53577, 37991,
18717, -23795, -8090, -47987, -94717, 41967, 5170, -14815, -94311,
17896, -17734, -57718, -774, -38410, 24830, 29682, 76480, 58802,
-46416, -20348, -61353, -68225, -68306, 23822, -31598, 42972, 36327,
28968, -65638, -21638, 24354, -8356, 26777, 52982, -11783, -44051,
-26467, -44721, -28435, -53265, -25574, -2669, 44155, 22946, -18454,
-30718, -11252, 58420, 8711, 67447, 4425, 41749, 67543, 43162, 11793,
-41907, 20477, -13080, 6559, -6104, -13244, 42853, 42935, 29793, 36730,
-28087, 28657, 17946, 7503, 7204, 21491, -27450, -24241, -98156,
-18082, -42613, -24928, 10775, -14842, -44127, 55910, 14777, 31151, -2194,
39206, -2100, -4211, 11827, -8918, -19471, 72567, 36447, -65590, -34861,
-17147, -45303, 9025, -7333, -35473, 11101, 11638, 3441, 6626, -41800,
9416, 13679, 33508, 40502, -60542, 16358, 8392, -43242, -35864, -34127,
-48721, 35878, 30598, 28630, 20279, -19983, -14638, -24455, -1851, -11344,
45150, 42051, 26034, -28889, -32382, -3527, -14532, 22564, -22346, 477,
11706, 28338, -25972, -9185, -22867, -12522, 32120, -4424, 11339, -33913,
-7184, 5101, -23552, -17115, -31401, -6104, 21906, 25708, 8406, 6317,
-7525, 5014, 20750, 20179, 22724, 11692, 13297, 2493, -253, -16841, -17339,
-6753, -4808, 2976, -10881, -10228, -13816, -12686, 1385, 2316, 2190, -875,
-1924], ZZ)
assert dup_mul(p1, p2, ZZ) == res
p1 = dup_normal([83, -61, -86, -24, 12, 43, -88, -9, 42, 55, -66, 74, 95,
-25, -12, 68, -99, 4, 45, 6, -15, -19, 78, 65, -55, 47, -13, 17, 86,
81, -58, -27, 50, -40, -24, 39, -41, -92, 75, 90, -1, 40, -15, -27,
-35, 68, 70, -64, -40, 78, -88, -58, -39, 69, 46, 12, 28, -94, -37,
-50, -80, -96, -61, 25, 1, 71, 4, 12, 48, 4, 34, -47, -75, 5, 48, 82,
88, 23, 98, 35, 17, -10, 48, -61, -95, 47, 65, -19, -66, -57, -6, -51,
-42, -89, 66, -13, 18, 37, 90, -23, 72, 96, -53, 0, 40, -73, -52, -68,
32, -25, -53, 79, -52, 18, 44, 73, -81, 31, -90, 70, 3, 36, 48, 76,
-24, -44, 23, 98, -4, 73, 69, 88, -70, 14, -68, 94, -78, -15, -64, -97,
-70, -35, 65, 88, 49, -53, -7, 12, -45, -7, 59, -94, 99, -2, 67, -60,
-71, 29, -62, -77, 1, 51, 17, 80, -20, -47, -19, 24, -9, 39, -23, 21,
-84, 10, 84, 56, -17, -21, -66, 85, 70, 46, -51, -22, -95, 78, -60,
-96, -97, -45, 72, 35, 30, -61, -92, -93, -60, -61, 4, -4, -81, -73,
46, 53, -11, 26, 94, 45, 14, -78, 55, 84, -68, 98, 60, 23, 100, -63,
68, 96, -16, 3, 56, 21, -58, 62, -67, 66, 85, 41, -79, -22, 97, -67,
82, 82, -96, -20, -7, 48, -67, 48, -9, -39, 78], ZZ)
p2 = dup_normal([52, 88, 76, 66, 9, -64, 46, -20, -28, 69, 60, 96, -36,
-92, -30, -11, -35, 35, 55, 63, -92, -7, 25, -58, 74, 55, -6, 4, 47,
-92, -65, 67, -45, 74, -76, 59, -6, 69, 39, 24, -71, -7, 39, -45, 60,
-68, 98, 97, -79, 17, 4, 94, -64, 68, -100, -96, -2, 3, 22, 96, 54,
-77, -86, 67, 6, 57, 37, 40, 89, -78, 64, -94, -45, -92, 57, 87, -26,
36, 19, 97, 25, 77, -87, 24, 43, -5, 35, 57, 83, 71, 35, 63, 61, 96,
-22, 8, -1, 96, 43, 45, 94, -93, 36, 71, -41, -99, 85, -48, 59, 52,
-17, 5, 87, -16, -68, -54, 76, -18, 100, 91, -42, -70, -66, -88, -12,
1, 95, -82, 52, 43, -29, 3, 12, 72, -99, -43, -32, -93, -51, 16, -20,
-12, -11, 5, 33, -38, 93, -5, -74, 25, 74, -58, 93, 59, -63, -86, 63,
-20, -4, -74, -73, -95, 29, -28, 93, -91, -2, -38, -62, 77, -58, -85,
-28, 95, 38, 19, -69, 86, 94, 25, -2, -4, 47, 34, -59, 35, -48, 29,
-63, -53, 34, 29, 66, 73, 6, 92, -84, 89, 15, 81, 93, 97, 51, -72, -78,
25, 60, 90, -45, 39, 67, -84, -62, 57, 26, -32, -56, -14, -83, 76, 5,
-2, 99, -100, 28, 46, 94, -7, 53, -25, 16, -23, -36, 89, -78, -63, 31,
1, 84, -99, -52, 76, 48, 90, -76, 44, -19, 54, -36, -9, -73, -100, -69,
31, 42, 25, -39, 76, -26, -8, -14, 51, 3, 37, 45, 2, -54, 13, -34, -92,
17, -25, -65, 53, -63, 30, 4, -70, -67, 90, 52, 51, 18, -3, 31, -45,
-9, 59, 63, -87, 22, -32, 29, -38, 21, 36, -82, 27, -11], ZZ)
res = dup_normal([4316, 4132, -3532, -7974, -11303, -10069, 5484, -3330,
-5874, 7734, 4673, 11327, -9884, -8031, 17343, 21035, -10570, -9285,
15893, 3780, -14083, 8819, 17592, 10159, 7174, -11587, 8598, -16479,
3602, 25596, 9781, 12163, 150, 18749, -21782, -12307, 27578, -2757,
-12573, 12565, 6345, -18956, 19503, -15617, 1443, -16778, 36851, 23588,
-28474, 5749, 40695, -7521, -53669, -2497, -18530, 6770, 57038, 3926,
-6927, -15399, 1848, -64649, -27728, 3644, 49608, 15187, -8902, -9480,
-7398, -40425, 4824, 23767, -7594, -6905, 33089, 18786, 12192, 24670,
31114, 35334, -4501, -14676, 7107, -59018, -21352, 20777, 19661, 20653,
33754, -885, -43758, 6269, 51897, -28719, -97488, -9527, 13746, 11644,
17644, -21720, 23782, -10481, 47867, 20752, 33810, -1875, 39918, -7710,
-40840, 19808, -47075, 23066, 46616, 25201, 9287, 35436, -1602, 9645,
-11978, 13273, 15544, 33465, 20063, 44539, 11687, 27314, -6538, -37467,
14031, 32970, -27086, 41323, 29551, 65910, -39027, -37800, -22232,
8212, 46316, -28981, -55282, 50417, -44929, -44062, 73879, 37573,
-2596, -10877, -21893, -133218, -33707, -25753, -9531, 17530, 61126,
2748, -56235, 43874, -10872, -90459, -30387, 115267, -7264, -44452,
122626, 14839, -599, 10337, 57166, -67467, -54957, 63669, 1202, 18488,
52594, 7205, -97822, 612, 78069, -5403, -63562, 47236, 36873, -154827,
-26188, 82427, -39521, 5628, 7416, 5276, -53095, 47050, 26121, -42207,
79021, -13035, 2499, -66943, 29040, -72355, -23480, 23416, -12885,
-44225, -42688, -4224, 19858, 55299, 15735, 11465, 101876, -39169,
51786, 14723, 43280, -68697, 16410, 92295, 56767, 7183, 111850, 4550,
115451, -38443, -19642, -35058, 10230, 93829, 8925, 63047, 3146, 29250,
8530, 5255, -98117, -115517, -76817, -8724, 41044, 1312, -35974, 79333,
-28567, 7547, -10580, -24559, -16238, 10794, -3867, 24848, 57770,
-51536, -35040, 71033, 29853, 62029, -7125, -125585, -32169, -47907,
156811, -65176, -58006, -15757, -57861, 11963, 30225, -41901, -41681,
31310, 27982, 18613, 61760, 60746, -59096, 33499, 30097, -17997, 24032,
56442, -83042, 23747, -20931, -21978, -158752, -9883, -73598, -7987,
-7333, -125403, -116329, 30585, 53281, 51018, -29193, 88575, 8264,
-40147, -16289, 113088, 12810, -6508, 101552, -13037, 34440, -41840,
101643, 24263, 80532, 61748, 65574, 6423, -20672, 6591, -10834, -71716,
86919, -92626, 39161, 28490, 81319, 46676, 106720, 43530, 26998, 57456,
-8862, 60989, 13982, 3119, -2224, 14743, 55415, -49093, -29303, 28999,
1789, 55953, -84043, -7780, -65013, 57129, -47251, 61484, 61994,
-78361, -82778, 22487, -26894, 9756, -74637, -15519, -4360, 30115,
42433, 35475, 15286, 69768, 21509, -20214, 78675, -21163, 13596, 11443,
-10698, -53621, -53867, -24155, 64500, -42784, -33077, -16500, 873,
-52788, 14546, -38011, 36974, -39849, -34029, -94311, 83068, -50437,
-26169, -46746, 59185, 42259, -101379, -12943, 30089, -59086, 36271,
22723, -30253, -52472, -70826, -23289, 3331, -31687, 14183, -857,
-28627, 35246, -51284, 5636, -6933, 66539, 36654, 50927, 24783, 3457,
33276, 45281, 45650, -4938, -9968, -22590, 47995, 69229, 5214, -58365,
-17907, -14651, 18668, 18009, 12649, -11851, -13387, 20339, 52472,
-1087, -21458, -68647, 52295, 15849, 40608, 15323, 25164, -29368,
10352, -7055, 7159, 21695, -5373, -54849, 101103, -24963, -10511,
33227, 7659, 41042, -69588, 26718, -20515, 6441, 38135, -63, 24088,
-35364, -12785, -18709, 47843, 48533, -48575, 17251, -19394, 32878,
-9010, -9050, 504, -12407, 28076, -3429, 25324, -4210, -26119, 752,
-29203, 28251, -11324, -32140, -3366, -25135, 18702, -31588, -7047,
-24267, 49987, -14975, -33169, 37744, -7720, -9035, 16964, -2807, -421,
14114, -17097, -13662, 40628, -12139, -9427, 5369, 17551, -13232, -16211,
9804, -7422, 2677, 28635, -8280, -4906, 2908, -22558, 5604, 12459, 8756,
-3980, -4745, -18525, 7913, 5970, -16457, 20230, -6247, -13812, 2505,
11899, 1409, -15094, 22540, -18863, 137, 11123, -4516, 2290, -8594, 12150,
-10380, 3005, 5235, -7350, 2535, -858], ZZ)
assert dup_mul(p1, p2, ZZ) == res
def test_dup_gcd():
assert dup_zz_heu_gcd([], [], ZZ) == ([], [], [])
assert dup_rr_prs_gcd([], [], ZZ) == ([], [], [])
assert dup_zz_heu_gcd([2], [], ZZ) == ([2], [1], [])
assert dup_rr_prs_gcd([2], [], ZZ) == ([2], [1], [])
assert dup_zz_heu_gcd([-2], [], ZZ) == ([2], [-1], [])
assert dup_rr_prs_gcd([-2], [], ZZ) == ([2], [-1], [])
assert dup_zz_heu_gcd([], [-2], ZZ) == ([2], [], [-1])
assert dup_rr_prs_gcd([], [-2], ZZ) == ([2], [], [-1])
assert dup_zz_heu_gcd([], [2, 4], ZZ) == ([2, 4], [], [1])
assert dup_rr_prs_gcd([], [2, 4], ZZ) == ([2, 4], [], [1])
assert dup_zz_heu_gcd([2, 4], [], ZZ) == ([2, 4], [1], [])
assert dup_rr_prs_gcd([2, 4], [], ZZ) == ([2, 4], [1], [])
assert dup_zz_heu_gcd([2], [2], ZZ) == ([2], [1], [1])
assert dup_rr_prs_gcd([2], [2], ZZ) == ([2], [1], [1])
assert dup_zz_heu_gcd([-2], [2], ZZ) == ([2], [-1], [1])
assert dup_rr_prs_gcd([-2], [2], ZZ) == ([2], [-1], [1])
assert dup_zz_heu_gcd([2], [-2], ZZ) == ([2], [1], [-1])
assert dup_rr_prs_gcd([2], [-2], ZZ) == ([2], [1], [-1])
assert dup_zz_heu_gcd([-2], [-2], ZZ) == ([2], [-1], [-1])
assert dup_rr_prs_gcd([-2], [-2], ZZ) == ([2], [-1], [-1])
assert dup_zz_heu_gcd([1, 2, 1], [1], ZZ) == ([1], [1, 2, 1], [1])
assert dup_rr_prs_gcd([1, 2, 1], [1], ZZ) == ([1], [1, 2, 1], [1])
assert dup_zz_heu_gcd([1, 2, 1], [2], ZZ) == ([1], [1, 2, 1], [2])
assert dup_rr_prs_gcd([1, 2, 1], [2], ZZ) == ([1], [1, 2, 1], [2])
assert dup_zz_heu_gcd([2, 4, 2], [2], ZZ) == ([2], [1, 2, 1], [1])
assert dup_rr_prs_gcd([2, 4, 2], [2], ZZ) == ([2], [1, 2, 1], [1])
assert dup_zz_heu_gcd([2], [2, 4, 2], ZZ) == ([2], [1], [1, 2, 1])
assert dup_rr_prs_gcd([2], [2, 4, 2], ZZ) == ([2], [1], [1, 2, 1])
assert dup_zz_heu_gcd([2, 4, 2], [1, 1], ZZ) == ([1, 1], [2, 2], [1])
assert dup_rr_prs_gcd([2, 4, 2], [1, 1], ZZ) == ([1, 1], [2, 2], [1])
assert dup_zz_heu_gcd([1, 1], [2, 4, 2], ZZ) == ([1, 1], [1], [2, 2])
assert dup_rr_prs_gcd([1, 1], [2, 4, 2], ZZ) == ([1, 1], [1], [2, 2])
f, g = [1, -31], [1, 0]
assert dup_zz_heu_gcd(f, g, ZZ) == ([1], f, g)
assert dup_rr_prs_gcd(f, g, ZZ) == ([1], f, g)
f = [1, 8, 21, 22, 8]
g = [1, 6, 11, 6]
h = [1, 3, 2]
cff = [1, 5, 4]
cfg = [1, 3]
assert dup_zz_heu_gcd(f, g, ZZ) == (h, cff, cfg)
assert dup_rr_prs_gcd(f, g, ZZ) == (h, cff, cfg)
f = [1, 0, 0, 0, -4]
g = [1, 0, 4, 0, 4]
h = [1, 0, 2]
cff = [1, 0, -2]
cfg = [1, 0, 2]
assert dup_zz_heu_gcd(f, g, ZZ) == (h, cff, cfg)
assert dup_rr_prs_gcd(f, g, ZZ) == (h, cff, cfg)
f = [1, 0, 1, 0, -3, -3, 8, 2, -5]
g = [3, 0, 5, -0, -4, -9, 21]
h = [1]
cff = f
cfg = g
assert dup_zz_heu_gcd(f, g, ZZ) == (h, cff, cfg)
assert dup_rr_prs_gcd(f, g, ZZ) == (h, cff, cfg)
f = dup_normal([1, 0, 1, 0, -3, -3, 8, 2, -5], QQ)
g = dup_normal([3, 0, 5, -0, -4, -9, 21], QQ)
h = dup_normal([1], QQ)
assert dup_qq_heu_gcd(f, g, QQ) == (h, cff, cfg)
assert dup_ff_prs_gcd(f, g, QQ) == (h, cff, cfg)
f = [
-352518131239247345597970242177235495263669787845475025293906825864749649589178600387510272,
0, 0, 0, 0, 0, 0,
46818041807522713962450042363465092040687472354933295397472942006618953623327997952,
0, 0, 0, 0, 0, 0,
378182690892293941192071663536490788434899030680411695933646320291525827756032,
0, 0, 0, 0, 0, 0,
112806468807371824947796775491032386836656074179286744191026149539708928,
0, 0, 0, 0, 0, 0,
-12278371209708240950316872681744825481125965781519138077173235712, 0,
0, 0, 0, 0, 0,
289127344604779611146960547954288113529690984687482920704, 0, 0, 0, 0,
0, 0, 19007977035740498977629742919480623972236450681, 0, 0, 0, 0, 0,
0, 311973482284542371301330321821976049
]
g = [
365431878023781158602430064717380211405897160759702125019136, 0, 0, 0,
0, 0, 0, 197599133478719444145775798221171663643171734081650688, 0, 0,
0, 0, 0, 0, -9504116979659010018253915765478924103928886144, 0, 0, 0,
0, 0, 0, -311973482284542371301330321821976049
]
f = dup_normal(f, ZZ)
g = dup_normal(g, ZZ)
assert dup_zz_heu_gcd(f, dup_diff(f, 1, ZZ), ZZ)[0] == g
assert dup_rr_prs_gcd(f, dup_diff(f, 1, ZZ), ZZ)[0] == g
f = [QQ(1, 2), QQ(1), QQ(1, 2)]
g = [QQ(1, 2), QQ(1, 2)]
h = [QQ(1), QQ(1)]
assert dup_qq_heu_gcd(f, g, QQ) == (h, g, [QQ(1, 2)])
assert dup_ff_prs_gcd(f, g, QQ) == (h, g, [QQ(1, 2)])
def test_dup_normal():
assert dup_normal([0,0,2,1,0,11,0], ZZ) == \
[ZZ(2),ZZ(1),ZZ(0),ZZ(11),ZZ(0)]
def init_normal_ANP(rep, mod, dom):
return ANP(dup_normal(rep, dom),
dup_normal(mod, dom), dom)
def test_dup_subresultants():
assert dup_resultant([], [], ZZ) == ZZ(0)
assert dup_resultant([ZZ(1)], [], ZZ) == ZZ(0)
assert dup_resultant([], [ZZ(1)], ZZ) == ZZ(0)
f = dup_normal([1,0,1,0,-3,-3,8,2,-5], ZZ)
g = dup_normal([3,0,5,0,-4,-9,21], ZZ)
a = dup_normal([15,0,-3,0,9], ZZ)
b = dup_normal([65,125,-245], ZZ)
c = dup_normal([9326,-12300], ZZ)
d = dup_normal([260708], ZZ)
assert dup_subresultants(f, g, ZZ) == [f, g, a, b, c, d]
assert dup_resultant(f, g, ZZ) == dup_LC(d, ZZ)
f = dup_normal([1,-2,1], ZZ)
g = dup_normal([1,0,-1], ZZ)
a = dup_normal([2,-2], ZZ)
assert dup_subresultants(f, g, ZZ) == [f, g, a]
assert dup_resultant(f, g, ZZ) == 0
f = dup_normal([1,0, 1], ZZ)
g = dup_normal([1,0,-1], ZZ)
a = dup_normal([-2], ZZ)
assert dup_subresultants(f, g, ZZ) == [f, g, a]
assert dup_resultant(f, g, ZZ) == 4
f = dup_normal([1,0,-1], ZZ)
g = dup_normal([1,-1,0,2], ZZ)
assert dup_resultant(f, g, ZZ) == 0
f = dup_normal([3,0,-1,0], ZZ)
g = dup_normal([5,0,1], ZZ)
assert dup_resultant(f, g, ZZ) == 64
f = dup_normal([1,-2,7], ZZ)
g = dup_normal([1,0,-1,5], ZZ)
assert dup_resultant(f, g, ZZ) == 265
f = dup_normal([1,-6,11,-6], ZZ)
g = dup_normal([1,-15,74,-120], ZZ)
assert dup_resultant(f, g, ZZ) == -8640
f = dup_normal([1,-6,11,-6], ZZ)
g = dup_normal([1,-10,29,-20], ZZ)
assert dup_resultant(f, g, ZZ) == 0
f = dup_normal([1,0,0,-1], ZZ)
g = dup_normal([1,2,2,-1], ZZ)
assert dup_resultant(f, g, ZZ) == 16
f = dup_normal([1,0,0,0,0,0,0,0,-2], ZZ)
g = dup_normal([1,-1], ZZ)
assert dup_resultant(f, g, ZZ) == -1
def init_normal_ANP(rep, mod, dom):
return ANP(dup_normal(rep, dom),
dup_normal(mod, dom), dom)
def test_dmp_zz_wang():
p = ZZ(nextprime(dmp_zz_mignotte_bound(w_1, 2, ZZ)))
assert p == ZZ(6291469)
t_1, k_1, e_1 = dmp_normal([[1], []], 1, ZZ), 1, ZZ(-14)
t_2, k_2, e_2 = dmp_normal([[1, 0]], 1, ZZ), 2, ZZ(3)
t_3, k_3, e_3 = dmp_normal([[1], [1, 0]], 1, ZZ), 2, ZZ(-11)
t_4, k_4, e_4 = dmp_normal([[1], [-1, 0]], 1, ZZ), 1, ZZ(-17)
T = [t_1, t_2, t_3, t_4]
K = [k_1, k_2, k_3, k_4]
E = [e_1, e_2, e_3, e_4]
T = zip(T, K)
A = [ZZ(-14), ZZ(3)]
S = dmp_eval_tail(w_1, A, 2, ZZ)
cs, s = dup_primitive(S, ZZ)
assert cs == 1 and s == S == \
dup_normal([1036728, 915552, 55748, 105621, -17304, -26841, -644], ZZ)
assert dmp_zz_wang_non_divisors(E, cs, 4, ZZ) == [7, 3, 11, 17]
assert dup_sqf_p(s, ZZ) and dup_degree(s) == dmp_degree(w_1, 2)
_, H = dup_zz_factor_sqf(s, ZZ)
h_1 = dup_normal([44, 42, 1], ZZ)
h_2 = dup_normal([126, -9, 28], ZZ)
h_3 = dup_normal([187, 0, -23], ZZ)
assert H == [h_1, h_2, h_3]
lc_1 = dmp_normal([[-4], [-4, 0]], 1, ZZ)
lc_2 = dmp_normal([[-1, 0, 0], []], 1, ZZ)
lc_3 = dmp_normal([[1], [], [-1, 0, 0]], 1, ZZ)
LC = [lc_1, lc_2, lc_3]
assert dmp_zz_wang_lead_coeffs(w_1, T, cs, E, H, A, 2, ZZ) == (w_1, H, LC)
H_1 = [
dmp_normal(t, 0, ZZ)
for t in [[44L, 42L, 1L], [126L, -9L, 28L], [187L, 0L, -23L]]
]
H_2 = [
dmp_normal(t, 1, ZZ)
for t in [[[-4, -12], [-3, 0], [1]], [[-9, 0], [-9], [-2, 0]],
[[1, 0, -9], [], [1, -9]]]
]
H_3 = [
dmp_normal(t, 1, ZZ)
for t in [[[-4, -12], [-3, 0], [1]], [[-9, 0], [-9], [-2, 0]],
[[1, 0, -9], [], [1, -9]]]
]
c_1 = dmp_normal([-70686, -5863, -17826, 2009, 5031, 74], 0, ZZ)
c_2 = dmp_normal(
[[9, 12, -45, -108, -324], [18, -216, -810, 0],
[2, 9, -252, -288, -945], [-30, -414, 0], [2, -54, -3, 81], [12, 0]],
1, ZZ)
c_3 = dmp_normal(
[[-36, -108, 0], [-27, -36, -108], [-8, -42, 0], [-6, 0, 9], [2, 0]],
1, ZZ)
T_1 = [dmp_normal(t, 0, ZZ) for t in [[-3, 0], [-2], [1]]]
T_2 = [dmp_normal(t, 1, ZZ) for t in [[[-1, 0], []], [[-3], []], [[-6]]]]
T_3 = [dmp_normal(t, 1, ZZ) for t in [[[]], [[]], [[-1]]]]
assert dmp_zz_diophantine(H_1, c_1, [], 5, p, 0, ZZ) == T_1
assert dmp_zz_diophantine(H_2, c_2, [ZZ(-14)], 5, p, 1, ZZ) == T_2
assert dmp_zz_diophantine(H_3, c_3, [ZZ(-14)], 5, p, 1, ZZ) == T_3
factors = dmp_zz_wang_hensel_lifting(w_1, H, LC, A, p, 2, ZZ)
assert dmp_expand(factors, 2, ZZ) == w_1
def test_dup_gcd():
assert dup_zz_heu_gcd([], [], ZZ) == ([], [], [])
assert dup_rr_prs_gcd([], [], ZZ) == ([], [], [])
assert dup_zz_heu_gcd([2], [], ZZ) == ([2], [1], [])
assert dup_rr_prs_gcd([2], [], ZZ) == ([2], [1], [])
assert dup_zz_heu_gcd([-2], [], ZZ) == ([2], [-1], [])
assert dup_rr_prs_gcd([-2], [], ZZ) == ([2], [-1], [])
assert dup_zz_heu_gcd([], [-2], ZZ) == ([2], [], [-1])
assert dup_rr_prs_gcd([], [-2], ZZ) == ([2], [], [-1])
assert dup_zz_heu_gcd([], [2,4], ZZ) == ([2,4], [], [1])
assert dup_rr_prs_gcd([], [2,4], ZZ) == ([2,4], [], [1])
assert dup_zz_heu_gcd([2,4], [], ZZ) == ([2,4], [1], [])
assert dup_rr_prs_gcd([2,4], [], ZZ) == ([2,4], [1], [])
assert dup_zz_heu_gcd([2], [2], ZZ) == ([2], [1], [1])
assert dup_rr_prs_gcd([2], [2], ZZ) == ([2], [1], [1])
assert dup_zz_heu_gcd([-2], [2], ZZ) == ([2], [-1], [1])
assert dup_rr_prs_gcd([-2], [2], ZZ) == ([2], [-1], [1])
assert dup_zz_heu_gcd([2], [-2], ZZ) == ([2], [1], [-1])
assert dup_rr_prs_gcd([2], [-2], ZZ) == ([2], [1], [-1])
assert dup_zz_heu_gcd([-2], [-2], ZZ) == ([2], [-1], [-1])
assert dup_rr_prs_gcd([-2], [-2], ZZ) == ([2], [-1], [-1])
assert dup_zz_heu_gcd([1,2,1], [1], ZZ) == ([1], [1, 2, 1], [1])
assert dup_rr_prs_gcd([1,2,1], [1], ZZ) == ([1], [1, 2, 1], [1])
assert dup_zz_heu_gcd([1,2,1], [2], ZZ) == ([1], [1, 2, 1], [2])
assert dup_rr_prs_gcd([1,2,1], [2], ZZ) == ([1], [1, 2, 1], [2])
assert dup_zz_heu_gcd([2,4,2], [2], ZZ) == ([2], [1, 2, 1], [1])
assert dup_rr_prs_gcd([2,4,2], [2], ZZ) == ([2], [1, 2, 1], [1])
assert dup_zz_heu_gcd([2], [2,4,2], ZZ) == ([2], [1], [1, 2, 1])
assert dup_rr_prs_gcd([2], [2,4,2], ZZ) == ([2], [1], [1, 2, 1])
assert dup_zz_heu_gcd([2,4,2], [1,1], ZZ) == ([1, 1], [2, 2], [1])
assert dup_rr_prs_gcd([2,4,2], [1,1], ZZ) == ([1, 1], [2, 2], [1])
assert dup_zz_heu_gcd([1,1], [2,4,2], ZZ) == ([1, 1], [1], [2, 2])
assert dup_rr_prs_gcd([1,1], [2,4,2], ZZ) == ([1, 1], [1], [2, 2])
f, g = [1, -31], [1, 0]
assert dup_zz_heu_gcd(f, g, ZZ) == ([1], f, g)
assert dup_rr_prs_gcd(f, g, ZZ) == ([1], f, g)
f = [1,8,21,22,8]
g = [1,6,11,6]
h = [1,3,2]
cff = [1,5,4]
cfg = [1,3]
assert dup_zz_heu_gcd(f, g, ZZ) == (h, cff, cfg)
assert dup_rr_prs_gcd(f, g, ZZ) == (h, cff, cfg)
f = [1,0,0,0,-4]
g = [1,0,4,0, 4]
h = [1,0,2]
cff = [1,0,-2]
cfg = [1,0, 2]
assert dup_zz_heu_gcd(f, g, ZZ) == (h, cff, cfg)
assert dup_rr_prs_gcd(f, g, ZZ) == (h, cff, cfg)
f = [1,0,1,0,-3,-3,8,2,-5]
g = [3,0,5,-0,-4,-9,21]
h = [1]
cff = f
cfg = g
assert dup_zz_heu_gcd(f, g, ZZ) == (h, cff, cfg)
assert dup_rr_prs_gcd(f, g, ZZ) == (h, cff, cfg)
f = dup_normal([1,0,1,0,-3,-3,8,2,-5], QQ)
g = dup_normal([3,0,5,-0,-4,-9,21], QQ)
h = dup_normal([1], QQ)
assert dup_qq_heu_gcd(f, g, QQ) == (h, cff, cfg)
assert dup_ff_prs_gcd(f, g, QQ) == (h, cff, cfg)
f = [-352518131239247345597970242177235495263669787845475025293906825864749649589178600387510272,
0, 0, 0, 0, 0, 0,
46818041807522713962450042363465092040687472354933295397472942006618953623327997952,
0, 0, 0, 0, 0, 0,
378182690892293941192071663536490788434899030680411695933646320291525827756032,
0, 0, 0, 0, 0, 0,
112806468807371824947796775491032386836656074179286744191026149539708928,
0, 0, 0, 0, 0, 0,
-12278371209708240950316872681744825481125965781519138077173235712,
0, 0, 0, 0, 0, 0,
289127344604779611146960547954288113529690984687482920704,
0, 0, 0, 0, 0, 0,
19007977035740498977629742919480623972236450681,
0, 0, 0, 0, 0, 0,
311973482284542371301330321821976049]
g = [365431878023781158602430064717380211405897160759702125019136,
0, 0, 0, 0, 0, 0,
197599133478719444145775798221171663643171734081650688,
0, 0, 0, 0, 0, 0,
-9504116979659010018253915765478924103928886144,
0, 0, 0, 0, 0, 0,
-311973482284542371301330321821976049]
f = dup_normal(f, ZZ)
g = dup_normal(g, ZZ)
assert dup_zz_heu_gcd(f, dup_diff(f, 1, ZZ), ZZ)[0] == g
assert dup_rr_prs_gcd(f, dup_diff(f, 1, ZZ), ZZ)[0] == g
f = [QQ(1,2),QQ(1),QQ(1,2)]
g = [QQ(1,2),QQ(1,2)]
h = [QQ(1), QQ(1)]
assert dup_qq_heu_gcd(f, g, QQ) == (h, g, [QQ(1,2)])
assert dup_ff_prs_gcd(f, g, QQ) == (h, g, [QQ(1,2)])
def test_dup_sub_term():
f = dup_normal([], ZZ)
assert dup_sub_term(f, ZZ(0), 0, ZZ) == dup_normal([], ZZ)
assert dup_sub_term(f, ZZ(1), 0, ZZ) == dup_normal([-1], ZZ)
assert dup_sub_term(f, ZZ(1), 1, ZZ) == dup_normal([-1, 0], ZZ)
assert dup_sub_term(f, ZZ(1), 2, ZZ) == dup_normal([-1, 0, 0], ZZ)
f = dup_normal([1,1,1], ZZ)
assert dup_sub_term(f, ZZ(2), 0, ZZ) == dup_normal([ 1, 1,-1], ZZ)
assert dup_sub_term(f, ZZ(2), 1, ZZ) == dup_normal([ 1,-1, 1], ZZ)
assert dup_sub_term(f, ZZ(2), 2, ZZ) == dup_normal([-1, 1, 1], ZZ)
assert dup_sub_term(f, ZZ(1), 3, ZZ) == dup_normal([-1, 1, 1, 1], ZZ)
assert dup_sub_term(f, ZZ(1), 4, ZZ) == dup_normal([-1, 0, 1, 1, 1], ZZ)
assert dup_sub_term(f, ZZ(1), 5, ZZ) == dup_normal([-1, 0, 0, 1, 1, 1], ZZ)
assert dup_sub_term(f, ZZ(1), 6, ZZ) == dup_normal([-1, 0, 0, 0, 1, 1, 1], ZZ)
assert dup_sub_term(f, ZZ(1), 2, ZZ) == dup_normal([1, 1], ZZ)
def test_dmp_zz_wang():
p = ZZ(nextprime(dmp_zz_mignotte_bound(w_1, 2, ZZ)))
assert p == ZZ(6291469)
t_1, k_1, e_1 = dmp_normal([[1],[]], 1, ZZ), 1, ZZ(-14)
t_2, k_2, e_2 = dmp_normal([[1, 0]], 1, ZZ), 2, ZZ(3)
t_3, k_3, e_3 = dmp_normal([[1],[ 1, 0]], 1, ZZ), 2, ZZ(-11)
t_4, k_4, e_4 = dmp_normal([[1],[-1, 0]], 1, ZZ), 1, ZZ(-17)
T = [t_1, t_2, t_3, t_4]
K = [k_1, k_2, k_3, k_4]
E = [e_1, e_2, e_3, e_4]
T = zip(T, K)
A = [ZZ(-14), ZZ(3)]
S = dmp_eval_tail(w_1, A, 2, ZZ)
cs, s = dup_primitive(S, ZZ)
assert cs == 1 and s == S == \
dup_normal([1036728, 915552, 55748, 105621, -17304, -26841, -644], ZZ)
assert dmp_zz_wang_non_divisors(E, cs, 4, ZZ) == [7, 3, 11, 17]
assert dup_sqf_p(s, ZZ) and dup_degree(s) == dmp_degree(w_1, 2)
_, H = dup_zz_factor_sqf(s, ZZ)
h_1 = dup_normal([44, 42, 1], ZZ)
h_2 = dup_normal([126, -9, 28], ZZ)
h_3 = dup_normal([187, 0, -23], ZZ)
assert H == [h_1, h_2, h_3]
lc_1 = dmp_normal([[-4], [-4,0]], 1, ZZ)
lc_2 = dmp_normal([[-1,0,0], []], 1, ZZ)
lc_3 = dmp_normal([[1], [], [-1,0,0]], 1, ZZ)
LC = [lc_1, lc_2, lc_3]
assert dmp_zz_wang_lead_coeffs(w_1, T, cs, E, H, A, 2, ZZ) == (w_1, H, LC)
H_1 = [ dmp_normal(t, 0, ZZ) for t in [[44L,42L,1L],[126L,-9L,28L],[187L,0L,-23L]] ]
H_2 = [ dmp_normal(t, 1, ZZ) for t in [[[-4,-12],[-3,0],[1]],[[-9,0],[-9],[-2,0]],[[1,0,-9],[],[1,-9]]] ]
H_3 = [ dmp_normal(t, 1, ZZ) for t in [[[-4,-12],[-3,0],[1]],[[-9,0],[-9],[-2,0]],[[1,0,-9],[],[1,-9]]] ]
c_1 = dmp_normal([-70686,-5863,-17826,2009,5031,74], 0, ZZ)
c_2 = dmp_normal([[9,12,-45,-108,-324],[18,-216,-810,0],[2,9,-252,-288,-945],[-30,-414,0],[2,-54,-3,81],[12,0]], 1, ZZ)
c_3 = dmp_normal([[-36,-108,0],[-27,-36,-108],[-8,-42,0],[-6,0,9],[2,0]], 1, ZZ)
T_1 = [ dmp_normal(t, 0, ZZ) for t in [[-3,0],[-2],[1]] ]
T_2 = [ dmp_normal(t, 1, ZZ) for t in [[[-1,0],[]],[[-3],[]],[[-6]]] ]
T_3 = [ dmp_normal(t, 1, ZZ) for t in [[[]],[[]],[[-1]]] ]
assert dmp_zz_diophantine(H_1, c_1, [], 5, p, 0, ZZ) == T_1
assert dmp_zz_diophantine(H_2, c_2, [ZZ(-14)], 5, p, 1, ZZ) == T_2
assert dmp_zz_diophantine(H_3, c_3, [ZZ(-14)], 5, p, 1, ZZ) == T_3
factors = dmp_zz_wang_hensel_lifting(w_1, H, LC, A, p, 2, ZZ)
assert dmp_expand(factors, 2, ZZ) == w_1
def test_dup_add_term():
f = dup_normal([], ZZ)
assert dup_add_term(f, ZZ(0), 0, ZZ) == dup_normal([], ZZ)
assert dup_add_term(f, ZZ(1), 0, ZZ) == dup_normal([1], ZZ)
assert dup_add_term(f, ZZ(1), 1, ZZ) == dup_normal([1, 0], ZZ)
assert dup_add_term(f, ZZ(1), 2, ZZ) == dup_normal([1, 0, 0], ZZ)
f = dup_normal([1,1,1], ZZ)
assert dup_add_term(f, ZZ(1), 0, ZZ) == dup_normal([1, 1, 2], ZZ)
assert dup_add_term(f, ZZ(1), 1, ZZ) == dup_normal([1, 2, 1], ZZ)
assert dup_add_term(f, ZZ(1), 2, ZZ) == dup_normal([2, 1, 1], ZZ)
assert dup_add_term(f, ZZ(1), 3, ZZ) == dup_normal([1, 1, 1, 1], ZZ)
assert dup_add_term(f, ZZ(1), 4, ZZ) == dup_normal([1, 0, 1, 1, 1], ZZ)
assert dup_add_term(f, ZZ(1), 5, ZZ) == dup_normal([1, 0, 0, 1, 1, 1], ZZ)
assert dup_add_term(f, ZZ(1), 6, ZZ) == dup_normal([1, 0, 0, 0, 1, 1, 1], ZZ)
assert dup_add_term(f,ZZ(-1), 2, ZZ) == dup_normal([1, 1], ZZ)
def test_dup_subresultants():
assert dup_resultant([], [], ZZ) == ZZ(0)
assert dup_resultant([ZZ(1)], [], ZZ) == ZZ(0)
assert dup_resultant([], [ZZ(1)], ZZ) == ZZ(0)
f = dup_normal([1, 0, 1, 0, -3, -3, 8, 2, -5], ZZ)
g = dup_normal([3, 0, 5, 0, -4, -9, 21], ZZ)
a = dup_normal([15, 0, -3, 0, 9], ZZ)
b = dup_normal([65, 125, -245], ZZ)
c = dup_normal([9326, -12300], ZZ)
d = dup_normal([260708], ZZ)
assert dup_subresultants(f, g, ZZ) == [f, g, a, b, c, d]
assert dup_resultant(f, g, ZZ) == dup_LC(d, ZZ)
f = dup_normal([1, -2, 1], ZZ)
g = dup_normal([1, 0, -1], ZZ)
a = dup_normal([2, -2], ZZ)
assert dup_subresultants(f, g, ZZ) == [f, g, a]
assert dup_resultant(f, g, ZZ) == 0
f = dup_normal([1, 0, 1], ZZ)
g = dup_normal([1, 0, -1], ZZ)
a = dup_normal([-2], ZZ)
assert dup_subresultants(f, g, ZZ) == [f, g, a]
assert dup_resultant(f, g, ZZ) == 4
f = dup_normal([1, 0, -1], ZZ)
g = dup_normal([1, -1, 0, 2], ZZ)
assert dup_resultant(f, g, ZZ) == 0
f = dup_normal([3, 0, -1, 0], ZZ)
g = dup_normal([5, 0, 1], ZZ)
assert dup_resultant(f, g, ZZ) == 64
f = dup_normal([1, -2, 7], ZZ)
g = dup_normal([1, 0, -1, 5], ZZ)
assert dup_resultant(f, g, ZZ) == 265
f = dup_normal([1, -6, 11, -6], ZZ)
g = dup_normal([1, -15, 74, -120], ZZ)
assert dup_resultant(f, g, ZZ) == -8640
f = dup_normal([1, -6, 11, -6], ZZ)
g = dup_normal([1, -10, 29, -20], ZZ)
assert dup_resultant(f, g, ZZ) == 0
f = dup_normal([1, 0, 0, -1], ZZ)
g = dup_normal([1, 2, 2, -1], ZZ)
assert dup_resultant(f, g, ZZ) == 16
f = dup_normal([1, 0, 0, 0, 0, 0, 0, 0, -2], ZZ)
g = dup_normal([1, -1], ZZ)
assert dup_resultant(f, g, ZZ) == -1
def test_dup_mul():
assert dup_mul([], [], ZZ) == []
assert dup_mul([], [ZZ(1)], ZZ) == []
assert dup_mul([ZZ(1)], [], ZZ) == []
assert dup_mul([ZZ(1)], [ZZ(1)], ZZ) == [ZZ(1)]
assert dup_mul([ZZ(5)], [ZZ(7)], ZZ) == [ZZ(35)]
assert dup_mul([], [], QQ) == []
assert dup_mul([], [QQ(1, 2)], QQ) == []
assert dup_mul([QQ(1, 2)], [], QQ) == []
assert dup_mul([QQ(1, 2)], [QQ(4, 7)], QQ) == [QQ(2, 7)]
assert dup_mul([QQ(5, 7)], [QQ(3, 7)], QQ) == [QQ(15, 49)]
f = dup_normal([3, 0, 0, 6, 1, 2], ZZ)
g = dup_normal([4, 0, 1, 0], ZZ)
h = dup_normal([12, 0, 3, 24, 4, 14, 1, 2, 0], ZZ)
assert dup_mul(f, g, ZZ) == h
assert dup_mul(g, f, ZZ) == h
f = dup_normal([2, 0, 0, 1, 7], ZZ)
h = dup_normal([4, 0, 0, 4, 28, 0, 1, 14, 49], ZZ)
assert dup_mul(f, f, ZZ) == h
K = FF(6)
assert dup_mul([K(2), K(1)], [K(3), K(4)], K) == [K(5), K(4)]
p1 = dup_normal([
79, -1, 78, -94, -10, 11, 32, -19, 78, 2, -89, 30, 73, 42, 85, 77, 83,
-30, -34, -2, 95, -81, 37, -49, -46, -58, -16, 37, 35, -11, -57, -15,
-31, 67, -20, 27, 76, 2, 70, 67, -65, 65, -26, -93, -44, -12, -92, 57,
-90, -57, -11, -67, -98, -69, 97, -41, 89, 33, 89, -50, 81, -31, 60,
-27, 43, 29, -77, 44, 21, -91, 32, -57, 33, 3, 53, -51, -38, -99, -84,
23, -50, 66, -100, 1, -75, -25, 27, -60, 98, -51, -87, 6, 8, 78, -28,
-95, -88, 12, -35, 26, -9, 16, -92, 55, -7, -86, 68, -39, -46, 84, 94,
45, 60, 92, 68, -75, -74, -19, 8, 75, 78, 91, 57, 34, 14, -3, -49, 65,
78, -18, 6, -29, -80, -98, 17, 13, 58, 21, 20, 9, 37, 7, -30, -53, -20,
34, 67, -42, 89, -22, 73, 43, -6, 5, 51, -8, -15, -52, -22, -58, -72,
-3, 43, -92, 82, 83, -2, -13, -23, -60, 16, -94, -8, -28, -95, -72, 63,
-90, 76, 6, -43, -100, -59, 76, 3, 3, 46, -85, 75, 62, -71, -76, 88,
97, -72, -1, 30, -64, 72, -48, 14, -78, 58, 63, -91, 24, -87, -27, -80,
-100, -44, 98, 70, 100, -29, -38, 11, 77, 100, 52, 86, 65, -5, -42,
-81, -38, -42, 43, -2, -70, -63, -52
], ZZ)
p2 = dup_normal([
65, -19, -47, 1, 90, 81, -15, -34, 25, -75, 9, -83, 50, -5, -44, 31, 1,
70, -7, 78, 74, 80, 85, 65, 21, 41, 66, 19, -40, 63, -21, -27, 32, 69,
83, 34, -35, 14, 81, 57, -75, 32, -67, -89, -100, -61, 46, 84, -78,
-29, -50, -94, -24, -32, -68, -16, 100, -7, -72, -89, 35, 82, 58, 81,
-92, 62, 5, -47, -39, -58, -72, -13, 84, 44, 55, -25, 48, -54, -31,
-56, -11, -50, -84, 10, 67, 17, 13, -14, 61, 76, -64, -44, -40, -96,
11, -11, -94, 2, 6, 27, -6, 68, -54, 66, -74, -14, -1, -24, -73, 96,
89, -11, -89, 56, -53, 72, -43, 96, 25, 63, -31, 29, 68, 83, 91, -93,
-19, -38, -40, 40, -12, -19, -79, 44, 100, -66, -29, -77, 62, 39, -8,
11, -97, 14, 87, 64, 21, -18, 13, 15, -59, -75, -99, -88, 57, 54, 56,
-67, 6, -63, -59, -14, 28, 87, -20, -39, 84, -91, -2, 49, -75, 11, -24,
-95, 36, 66, 5, 25, -72, -40, 86, 90, 37, -33, 57, -35, 29, -18, 4,
-79, 64, -17, -27, 21, 29, -5, -44, -87, -24, 52, 78, 11, -23, -53, 36,
42, 21, -68, 94, -91, -51, -21, 51, -76, 72, 31, 24, -48, -80, -9, 37,
-47, -6, -8, -63, -91, 79, -79, -100, 38, -20, 38, 100, 83, -90, 87,
63, -36, 82, -19, 18, -98, -38, 26, 98, -70, 79, 92, 12, 12, 70, 74,
36, 48, -13, 31, 31, -47, -71, -12, -64, 36, -42, 32, -86, 60, 83, 70,
55, 0, 1, 29, -35, 8, -82, 8, -73, -46, -50, 43, 48, -5, -86, -72, 44,
-90, 19, 19, 5, -20, 97, -13, -66, -5, 5, -69, 64, -30, 41, 51, 36, 13,
-99, -61, 94, -12, 74, 98, 68, 24, 46, -97, -87, -6, -27, 82, 62, -11,
-77, 86, 66, -47, -49, -50, 13, 18, 89, -89, 46, -80, 13, 98, -35, -36,
-25, 12, 20, 26, -52, 79, 27, 79, 100, 8, 62, -58, -28, 37
], ZZ)
res = dup_normal([
5135, -1566, 1376, -7466, 4579, 11710, 8001, -7183, -3737, -7439, 345,
-10084, 24522, -1201, 1070, -10245, 9582, 9264, 1903, 23312, 18953,
10037, -15268, -5450, 6442, -6243, -3777, 5110, 10936, -16649, -6022,
16255, 31300, 24818, 31922, 32760, 7854, 27080, 15766, 29596, 7139,
31945, -19810, 465, -38026, -3971, 9641, 465, -19375, 5524, -30112,
-11960, -12813, 13535, 30670, 5925, -43725, -14089, 11503, -22782,
6371, 43881, 37465, -33529, -33590, -39798, -37854, -18466, -7908,
-35825, -26020, -36923, -11332, -5699, 25166, -3147, 19885, 12962,
-20659, -1642, 27723, -56331, -24580, -11010, -20206, 20087, -23772,
-16038, 38580, 20901, -50731, 32037, -4299, 26508, 18038, -28357,
31846, -7405, -20172, -15894, 2096, 25110, -45786, 45918, -55333,
-31928, -49428, -29824, -58796, -24609, -15408, 69, -35415, -18439,
10123, -20360, -65949, 33356, -20333, 26476, -32073, 33621, 930, 28803,
-42791, 44716, 38164, 12302, -1739, 11421, 73385, -7613, 14297, 38155,
-414, 77587, 24338, -21415, 29367, 42639, 13901, -288, 51027, -11827,
91260, 43407, 88521, -15186, 70572, -12049, 5090, -12208, -56374,
15520, -623, -7742, 50825, 11199, -14894, 40892, 59591, -31356, -28696,
-57842, -87751, -33744, -28436, -28945, -40287, 37957, -35638, 33401,
-61534, 14870, 40292, 70366, -10803, 102290, -71719, -85251, 7902,
-22409, 75009, 99927, 35298, -1175, -762, -34744, -10587, -47574,
-62629, -19581, -43659, -54369, -32250, -39545, 15225, -24454, 11241,
-67308, -30148, 39929, 37639, 14383, -73475, -77636, -81048, -35992,
41601, -90143, 76937, -8112, 56588, 9124, -40094, -32340, 13253, 10898,
-51639, 36390, 12086, -1885, 100714, -28561, -23784, -18735, 18916,
16286, 10742, -87360, -13697, 10689, -19477, -29770, 5060, 20189,
-8297, 112407, 47071, 47743, 45519, -4109, 17468, -68831, 78325, -6481,
-21641, -19459, 30919, 96115, 8607, 53341, 32105, -16211, 23538, 57259,
-76272, -40583, 62093, 38511, -34255, -40665, -40604, -37606, -15274,
33156, -13885, 103636, 118678, -14101, -92682, -100791, 2634, 63791,
98266, 19286, -34590, -21067, -71130, 25380, -40839, -27614, -26060,
52358, -15537, 27138, -6749, 36269, -33306, 13207, -91084, -5540,
-57116, 69548, 44169, -57742, -41234, -103327, -62904, -8566, 41149,
-12866, 71188, 23980, 1838, 58230, 73950, 5594, 43113, -8159, -15925,
6911, 85598, -75016, -16214, -62726, -39016, 8618, -63882, -4299,
23182, 49959, 49342, -3238, -24913, -37138, 78361, 32451, 6337, -11438,
-36241, -37737, 8169, -3077, -24829, 57953, 53016, -31511, -91168,
12599, -41849, 41576, 55275, -62539, 47814, -62319, 12300, -32076,
-55137, -84881, -27546, 4312, -3433, -54382, 113288, -30157, 74469,
18219, 79880, -2124, 98911, 17655, -33499, -32861, 47242, -37393,
99765, 14831, -44483, 10800, -31617, -52710, 37406, 22105, 29704,
-20050, 13778, 43683, 36628, 8494, 60964, -22644, 31550, -17693, 33805,
-124879, -12302, 19343, 20400, -30937, -21574, -34037, -33380, 56539,
-24993, -75513, -1527, 53563, 65407, -101, 53577, 37991, 18717, -23795,
-8090, -47987, -94717, 41967, 5170, -14815, -94311, 17896, -17734,
-57718, -774, -38410, 24830, 29682, 76480, 58802, -46416, -20348,
-61353, -68225, -68306, 23822, -31598, 42972, 36327, 28968, -65638,
-21638, 24354, -8356, 26777, 52982, -11783, -44051, -26467, -44721,
-28435, -53265, -25574, -2669, 44155, 22946, -18454, -30718, -11252,
58420, 8711, 67447, 4425, 41749, 67543, 43162, 11793, -41907, 20477,
-13080, 6559, -6104, -13244, 42853, 42935, 29793, 36730, -28087, 28657,
17946, 7503, 7204, 21491, -27450, -24241, -98156, -18082, -42613,
-24928, 10775, -14842, -44127, 55910, 14777, 31151, -2194, 39206,
-2100, -4211, 11827, -8918, -19471, 72567, 36447, -65590, -34861,
-17147, -45303, 9025, -7333, -35473, 11101, 11638, 3441, 6626, -41800,
9416, 13679, 33508, 40502, -60542, 16358, 8392, -43242, -35864, -34127,
-48721, 35878, 30598, 28630, 20279, -19983, -14638, -24455, -1851,
-11344, 45150, 42051, 26034, -28889, -32382, -3527, -14532, 22564,
-22346, 477, 11706, 28338, -25972, -9185, -22867, -12522, 32120, -4424,
11339, -33913, -7184, 5101, -23552, -17115, -31401, -6104, 21906,
25708, 8406, 6317, -7525, 5014, 20750, 20179, 22724, 11692, 13297,
2493, -253, -16841, -17339, -6753, -4808, 2976, -10881, -10228, -13816,
-12686, 1385, 2316, 2190, -875, -1924
], ZZ)
assert dup_mul(p1, p2, ZZ) == res
p1 = dup_normal([
83, -61, -86, -24, 12, 43, -88, -9, 42, 55, -66, 74, 95, -25, -12, 68,
-99, 4, 45, 6, -15, -19, 78, 65, -55, 47, -13, 17, 86, 81, -58, -27,
50, -40, -24, 39, -41, -92, 75, 90, -1, 40, -15, -27, -35, 68, 70, -64,
-40, 78, -88, -58, -39, 69, 46, 12, 28, -94, -37, -50, -80, -96, -61,
25, 1, 71, 4, 12, 48, 4, 34, -47, -75, 5, 48, 82, 88, 23, 98, 35, 17,
-10, 48, -61, -95, 47, 65, -19, -66, -57, -6, -51, -42, -89, 66, -13,
18, 37, 90, -23, 72, 96, -53, 0, 40, -73, -52, -68, 32, -25, -53, 79,
-52, 18, 44, 73, -81, 31, -90, 70, 3, 36, 48, 76, -24, -44, 23, 98, -4,
73, 69, 88, -70, 14, -68, 94, -78, -15, -64, -97, -70, -35, 65, 88, 49,
-53, -7, 12, -45, -7, 59, -94, 99, -2, 67, -60, -71, 29, -62, -77, 1,
51, 17, 80, -20, -47, -19, 24, -9, 39, -23, 21, -84, 10, 84, 56, -17,
-21, -66, 85, 70, 46, -51, -22, -95, 78, -60, -96, -97, -45, 72, 35,
30, -61, -92, -93, -60, -61, 4, -4, -81, -73, 46, 53, -11, 26, 94, 45,
14, -78, 55, 84, -68, 98, 60, 23, 100, -63, 68, 96, -16, 3, 56, 21,
-58, 62, -67, 66, 85, 41, -79, -22, 97, -67, 82, 82, -96, -20, -7, 48,
-67, 48, -9, -39, 78
], ZZ)
p2 = dup_normal([
52, 88, 76, 66, 9, -64, 46, -20, -28, 69, 60, 96, -36, -92, -30, -11,
-35, 35, 55, 63, -92, -7, 25, -58, 74, 55, -6, 4, 47, -92, -65, 67,
-45, 74, -76, 59, -6, 69, 39, 24, -71, -7, 39, -45, 60, -68, 98, 97,
-79, 17, 4, 94, -64, 68, -100, -96, -2, 3, 22, 96, 54, -77, -86, 67, 6,
57, 37, 40, 89, -78, 64, -94, -45, -92, 57, 87, -26, 36, 19, 97, 25,
77, -87, 24, 43, -5, 35, 57, 83, 71, 35, 63, 61, 96, -22, 8, -1, 96,
43, 45, 94, -93, 36, 71, -41, -99, 85, -48, 59, 52, -17, 5, 87, -16,
-68, -54, 76, -18, 100, 91, -42, -70, -66, -88, -12, 1, 95, -82, 52,
43, -29, 3, 12, 72, -99, -43, -32, -93, -51, 16, -20, -12, -11, 5, 33,
-38, 93, -5, -74, 25, 74, -58, 93, 59, -63, -86, 63, -20, -4, -74, -73,
-95, 29, -28, 93, -91, -2, -38, -62, 77, -58, -85, -28, 95, 38, 19,
-69, 86, 94, 25, -2, -4, 47, 34, -59, 35, -48, 29, -63, -53, 34, 29,
66, 73, 6, 92, -84, 89, 15, 81, 93, 97, 51, -72, -78, 25, 60, 90, -45,
39, 67, -84, -62, 57, 26, -32, -56, -14, -83, 76, 5, -2, 99, -100, 28,
46, 94, -7, 53, -25, 16, -23, -36, 89, -78, -63, 31, 1, 84, -99, -52,
76, 48, 90, -76, 44, -19, 54, -36, -9, -73, -100, -69, 31, 42, 25, -39,
76, -26, -8, -14, 51, 3, 37, 45, 2, -54, 13, -34, -92, 17, -25, -65,
53, -63, 30, 4, -70, -67, 90, 52, 51, 18, -3, 31, -45, -9, 59, 63, -87,
22, -32, 29, -38, 21, 36, -82, 27, -11
], ZZ)
res = dup_normal([
4316, 4132, -3532, -7974, -11303, -10069, 5484, -3330, -5874, 7734,
4673, 11327, -9884, -8031, 17343, 21035, -10570, -9285, 15893, 3780,
-14083, 8819, 17592, 10159, 7174, -11587, 8598, -16479, 3602, 25596,
9781, 12163, 150, 18749, -21782, -12307, 27578, -2757, -12573, 12565,
6345, -18956, 19503, -15617, 1443, -16778, 36851, 23588, -28474, 5749,
40695, -7521, -53669, -2497, -18530, 6770, 57038, 3926, -6927, -15399,
1848, -64649, -27728, 3644, 49608, 15187, -8902, -9480, -7398, -40425,
4824, 23767, -7594, -6905, 33089, 18786, 12192, 24670, 31114, 35334,
-4501, -14676, 7107, -59018, -21352, 20777, 19661, 20653, 33754, -885,
-43758, 6269, 51897, -28719, -97488, -9527, 13746, 11644, 17644,
-21720, 23782, -10481, 47867, 20752, 33810, -1875, 39918, -7710,
-40840, 19808, -47075, 23066, 46616, 25201, 9287, 35436, -1602, 9645,
-11978, 13273, 15544, 33465, 20063, 44539, 11687, 27314, -6538, -37467,
14031, 32970, -27086, 41323, 29551, 65910, -39027, -37800, -22232,
8212, 46316, -28981, -55282, 50417, -44929, -44062, 73879, 37573,
-2596, -10877, -21893, -133218, -33707, -25753, -9531, 17530, 61126,
2748, -56235, 43874, -10872, -90459, -30387, 115267, -7264, -44452,
122626, 14839, -599, 10337, 57166, -67467, -54957, 63669, 1202, 18488,
52594, 7205, -97822, 612, 78069, -5403, -63562, 47236, 36873, -154827,
-26188, 82427, -39521, 5628, 7416, 5276, -53095, 47050, 26121, -42207,
79021, -13035, 2499, -66943, 29040, -72355, -23480, 23416, -12885,
-44225, -42688, -4224, 19858, 55299, 15735, 11465, 101876, -39169,
51786, 14723, 43280, -68697, 16410, 92295, 56767, 7183, 111850, 4550,
115451, -38443, -19642, -35058, 10230, 93829, 8925, 63047, 3146, 29250,
8530, 5255, -98117, -115517, -76817, -8724, 41044, 1312, -35974, 79333,
-28567, 7547, -10580, -24559, -16238, 10794, -3867, 24848, 57770,
-51536, -35040, 71033, 29853, 62029, -7125, -125585, -32169, -47907,
156811, -65176, -58006, -15757, -57861, 11963, 30225, -41901, -41681,
31310, 27982, 18613, 61760, 60746, -59096, 33499, 30097, -17997, 24032,
56442, -83042, 23747, -20931, -21978, -158752, -9883, -73598, -7987,
-7333, -125403, -116329, 30585, 53281, 51018, -29193, 88575, 8264,
-40147, -16289, 113088, 12810, -6508, 101552, -13037, 34440, -41840,
101643, 24263, 80532, 61748, 65574, 6423, -20672, 6591, -10834, -71716,
86919, -92626, 39161, 28490, 81319, 46676, 106720, 43530, 26998, 57456,
-8862, 60989, 13982, 3119, -2224, 14743, 55415, -49093, -29303, 28999,
1789, 55953, -84043, -7780, -65013, 57129, -47251, 61484, 61994,
-78361, -82778, 22487, -26894, 9756, -74637, -15519, -4360, 30115,
42433, 35475, 15286, 69768, 21509, -20214, 78675, -21163, 13596, 11443,
-10698, -53621, -53867, -24155, 64500, -42784, -33077, -16500, 873,
-52788, 14546, -38011, 36974, -39849, -34029, -94311, 83068, -50437,
-26169, -46746, 59185, 42259, -101379, -12943, 30089, -59086, 36271,
22723, -30253, -52472, -70826, -23289, 3331, -31687, 14183, -857,
-28627, 35246, -51284, 5636, -6933, 66539, 36654, 50927, 24783, 3457,
33276, 45281, 45650, -4938, -9968, -22590, 47995, 69229, 5214, -58365,
-17907, -14651, 18668, 18009, 12649, -11851, -13387, 20339, 52472,
-1087, -21458, -68647, 52295, 15849, 40608, 15323, 25164, -29368,
10352, -7055, 7159, 21695, -5373, -54849, 101103, -24963, -10511,
33227, 7659, 41042, -69588, 26718, -20515, 6441, 38135, -63, 24088,
-35364, -12785, -18709, 47843, 48533, -48575, 17251, -19394, 32878,
-9010, -9050, 504, -12407, 28076, -3429, 25324, -4210, -26119, 752,
-29203, 28251, -11324, -32140, -3366, -25135, 18702, -31588, -7047,
-24267, 49987, -14975, -33169, 37744, -7720, -9035, 16964, -2807, -421,
14114, -17097, -13662, 40628, -12139, -9427, 5369, 17551, -13232,
-16211, 9804, -7422, 2677, 28635, -8280, -4906, 2908, -22558, 5604,
12459, 8756, -3980, -4745, -18525, 7913, 5970, -16457, 20230, -6247,
-13812, 2505, 11899, 1409, -15094, 22540, -18863, 137, 11123, -4516,
2290, -8594, 12150, -10380, 3005, 5235, -7350, 2535, -858
], ZZ)
assert dup_mul(p1, p2, ZZ) == res