本文整理汇总了Python中sympy.polys.densebasic.dmp_degree函数的典型用法代码示例。如果您正苦于以下问题：Python dmp_degree函数的具体用法？Python dmp_degree怎么用？Python dmp_degree使用的例子？那么恭喜您, 这里精选的函数代码示例或许可以为您提供帮助。
在下文中一共展示了dmp_degree函数的20个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于我们的系统推荐出更棒的Python代码示例。
示例1: dmp_sub
def dmp_sub(f, g, u, K):
"""Subtract dense polynomials in `K[X]`. """
if not u:
return dup_sub(f, g, K)
df = dmp_degree(f, u)
if df < 0:
return dmp_neg(g, u, K)
dg = dmp_degree(g, u)
if dg < 0:
return f
v = u-1
if df == dg:
return dmp_strip([ dmp_sub(a, b, v, K) for a, b in zip(f, g) ], u)
else:
k = abs(df - dg)
if df > dg:
h, f = f[:k], f[k:]
else:
h, g = dmp_neg(g[:k], u, K), g[k:]
return h + [ dmp_sub(a, b, v, K) for a, b in zip(f, g) ]
开发者ID:Aang，项目名称:sympy，代码行数:28，代码来源:densearith.py
示例2: dmp_mul
def dmp_mul(f, g, u, K):
"""Multiply dense polynomials in `K[X]`. """
if not u:
return dup_mul(f, g, K)
if f == g:
return dmp_sqr(f, u, K)
df = dmp_degree(f, u)
if df < 0:
return f
dg = dmp_degree(g, u)
if dg < 0:
return g
h, v = [], u-1
for i in xrange(0, df+dg+1):
coeff = dmp_zero(v)
for j in xrange(max(0, i-dg), min(df, i)+1):
coeff = dmp_add(coeff, dmp_mul(f[j], g[i-j], v, K), v, K)
h.append(coeff)
return h
开发者ID:Aang，项目名称:sympy，代码行数:29，代码来源:densearith.py
示例3: dmp_prem
def dmp_prem(f, g, u, K):
"""Polynomial pseudo-remainder in `K[X]`. """
if not u:
return dup_prem(f, g, K)
df = dmp_degree(f, u)
dg = dmp_degree(g, u)
if dg < 0:
raise ZeroDivisionError("polynomial division")
r = f
if df < dg:
return r
N = df - dg + 1
lc_g = dmp_LC(g, K)
while True:
dr = dmp_degree(r, u)
if dr < dg:
break
lc_r = dmp_LC(r, K)
j, N = dr-dg, N-1
R = dmp_mul_term(r, lc_g, 0, u, K)
G = dmp_mul_term(g, lc_r, j, u, K)
r = dmp_sub(R, G, u, K)
c = dmp_pow(lc_g, N, u-1, K)
return dmp_mul_term(r, c, 0, u, K)
开发者ID:Aang，项目名称:sympy，代码行数:35，代码来源:densearith.py
示例4: _dmp_simplify_gcd
def _dmp_simplify_gcd(f, g, u, K):
"""Try to eliminate ``x_0`` from GCD computation in ``K[X]``. """
df = dmp_degree(f, u)
dg = dmp_degree(g, u)
if df > 0 and dg > 0:
return None
if not (df or dg):
F = dmp_LC(f, K)
G = dmp_LC(g, K)
else:
if not df:
F = dmp_LC(f, K)
G = dmp_content(g, u, K)
else:
F = dmp_content(f, u, K)
G = dmp_LC(g, K)
v = u - 1
h = dmp_gcd(F, G, v, K)
cff = [ dmp_exquo(cf, h, v, K) for cf in f ]
cfg = [ dmp_exquo(cg, h, v, K) for cg in g ]
return [h], cff, cfg
开发者ID:addisonc，项目名称:sympy，代码行数:26，代码来源:euclidtools.py
示例5: dmp_sqf_list
def dmp_sqf_list(f, u, K, all=False):
"""
Return square-free decomposition of a polynomial in ``K[X]``.
Examples
========
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.sqfreetools import dmp_sqf_list
>>> f = ZZ.map([[1], [2, 0], [1, 0, 0], [], [], []])
>>> dmp_sqf_list(f, 1, ZZ)
(1, [([[1], [1, 0]], 2), ([[1], []], 3)])
>>> dmp_sqf_list(f, 1, ZZ, all=True)
(1, [([[1]], 1), ([[1], [1, 0]], 2), ([[1], []], 3)])
"""
if not u:
return dup_sqf_list(f, K, all=all)
if not K.has_CharacteristicZero:
return dmp_gf_sqf_list(f, u, K, all=all)
if K.has_Field or not K.is_Exact:
coeff = dmp_ground_LC(f, u, K)
f = dmp_ground_monic(f, u, K)
else:
coeff, f = dmp_ground_primitive(f, u, K)
if K.is_negative(dmp_ground_LC(f, u, K)):
f = dmp_neg(f, u, K)
coeff = -coeff
if dmp_degree(f, u) <= 0:
return coeff, []
result, i = [], 1
h = dmp_diff(f, 1, u, K)
g, p, q = dmp_inner_gcd(f, h, u, K)
while True:
d = dmp_diff(p, 1, u, K)
h = dmp_sub(q, d, u, K)
if dmp_zero_p(h, u):
result.append((p, i))
break
g, p, q = dmp_inner_gcd(p, h, u, K)
if all or dmp_degree(g, u) > 0:
result.append((g, i))
i += 1
return coeff, result
开发者ID:FireJade，项目名称:sympy，代码行数:59，代码来源:sqfreetools.py
示例6: dmp_sqf_list
def dmp_sqf_list(f, u, K, all=False):
"""
Return square-free decomposition of a polynomial in ``K[X]``.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y = ring("x,y", ZZ)
>>> f = x**5 + 2*x**4*y + x**3*y**2
>>> R.dmp_sqf_list(f)
(1, [(x + y, 2), (x, 3)])
>>> R.dmp_sqf_list(f, all=True)
(1, [(1, 1), (x + y, 2), (x, 3)])
"""
if not u:
return dup_sqf_list(f, K, all=all)
if K.is_FiniteField:
return dmp_gf_sqf_list(f, u, K, all=all)
if K.has_Field:
coeff = dmp_ground_LC(f, u, K)
f = dmp_ground_monic(f, u, K)
else:
coeff, f = dmp_ground_primitive(f, u, K)
if K.is_negative(dmp_ground_LC(f, u, K)):
f = dmp_neg(f, u, K)
coeff = -coeff
if dmp_degree(f, u) <= 0:
return coeff, []
result, i = [], 1
h = dmp_diff(f, 1, u, K)
g, p, q = dmp_inner_gcd(f, h, u, K)
while True:
d = dmp_diff(p, 1, u, K)
h = dmp_sub(q, d, u, K)
if dmp_zero_p(h, u):
result.append((p, i))
break
g, p, q = dmp_inner_gcd(p, h, u, K)
if all or dmp_degree(g, u) > 0:
result.append((g, i))
i += 1
return coeff, result
开发者ID:alhirzel，项目名称:sympy，代码行数:58，代码来源:sqfreetools.py
示例7: dmp_zz_collins_resultant
def dmp_zz_collins_resultant(f, g, u, K):
"""
Collins's modular resultant algorithm in `Z[X]`.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y = ring("x,y", ZZ)
>>> f = x + y + 2
>>> g = 2*x*y + x + 3
>>> R.dmp_zz_collins_resultant(f, g)
-2*y**2 - 5*y + 1
"""
n = dmp_degree(f, u)
m = dmp_degree(g, u)
if n < 0 or m < 0:
return dmp_zero(u - 1)
A = dmp_max_norm(f, u, K)
B = dmp_max_norm(g, u, K)
a = dmp_ground_LC(f, u, K)
b = dmp_ground_LC(g, u, K)
v = u - 1
B = K(2)*K.factorial(K(n + m))*A**m*B**n
r, p, P = dmp_zero(v), K.one, K.one
while P <= B:
p = K(nextprime(p))
while not (a % p) or not (b % p):
p = K(nextprime(p))
F = dmp_ground_trunc(f, p, u, K)
G = dmp_ground_trunc(g, p, u, K)
try:
R = dmp_zz_modular_resultant(F, G, p, u, K)
except HomomorphismFailed:
continue
if K.is_one(P):
r = R
else:
r = dmp_apply_pairs(r, R, _collins_crt, (P, p, K), v, K)
P *= p
return r
开发者ID:AdrianPotter，项目名称:sympy，代码行数:57，代码来源:euclidtools.py
示例8: dmp_zz_collins_resultant
def dmp_zz_collins_resultant(f, g, u, K):
"""
Collins's modular resultant algorithm in `Z[X]`.
Examples
========
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.euclidtools import dmp_zz_collins_resultant
>>> f = ZZ.map([[1], [1, 2]])
>>> g = ZZ.map([[2, 1], [3]])
>>> dmp_zz_collins_resultant(f, g, 1, ZZ)
[-2, -5, 1]
"""
n = dmp_degree(f, u)
m = dmp_degree(g, u)
if n < 0 or m < 0:
return dmp_zero(u-1)
A = dmp_max_norm(f, u, K)
B = dmp_max_norm(g, u, K)
a = dmp_ground_LC(f, u, K)
b = dmp_ground_LC(g, u, K)
v = u - 1
B = K(2)*K.factorial(n+m)*A**m*B**n
r, p, P = dmp_zero(v), K.one, K.one
while P <= B:
p = K(nextprime(p))
while not (a % p) or not (b % p):
p = K(nextprime(p))
F = dmp_ground_trunc(f, p, u, K)
G = dmp_ground_trunc(g, p, u, K)
try:
R = dmp_zz_modular_resultant(F, G, p, u, K)
except HomomorphismFailed:
continue
if K.is_one(P):
r = R
else:
r = dmp_apply_pairs(r, R, _collins_crt, (P, p, K), v, K)
P *= p
return r
开发者ID:dyao-vu，项目名称:meta-core，代码行数:57，代码来源:euclidtools.py
示例9: dmp_pdiv
def dmp_pdiv(f, g, u, K):
"""
Polynomial pseudo-division in ``K[X]``.
Examples
========
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.densearith import dmp_pdiv
>>> f = ZZ.map([[1], [1, 0], []])
>>> g = ZZ.map([[2], [2]])
>>> dmp_pdiv(f, g, 1, ZZ)
([[2], [2, -2]], [[-4, 4]])
"""
if not u:
return dup_pdiv(f, g, K)
df = dmp_degree(f, u)
dg = dmp_degree(g, u)
if dg < 0:
raise ZeroDivisionError("polynomial division")
q, r = dmp_zero(u), f
if df < dg:
return q, r
N = df - dg + 1
lc_g = dmp_LC(g, K)
while True:
dr = dmp_degree(r, u)
if dr < dg:
break
lc_r = dmp_LC(r, K)
j, N = dr-dg, N-1
Q = dmp_mul_term(q, lc_g, 0, u, K)
q = dmp_add_term(Q, lc_r, j, u, K)
R = dmp_mul_term(r, lc_g, 0, u, K)
G = dmp_mul_term(g, lc_r, j, u, K)
r = dmp_sub(R, G, u, K)
c = dmp_pow(lc_g, N, u-1, K)
q = dmp_mul_term(q, c, 0, u, K)
r = dmp_mul_term(r, c, 0, u, K)
return q, r
开发者ID:SwaathiRamesh，项目名称:sympy，代码行数:56，代码来源:densearith.py
示例10: dmp_pdiv
def dmp_pdiv(f, g, u, K):
"""
Polynomial pseudo-division in ``K[X]``.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y = ring("x,y", ZZ)
>>> R.dmp_pdiv(x**2 + x*y, 2*x + 2)
(2*x + 2*y - 2, -4*y + 4)
"""
if not u:
return dup_pdiv(f, g, K)
df = dmp_degree(f, u)
dg = dmp_degree(g, u)
if dg < 0:
raise ZeroDivisionError("polynomial division")
q, r, dr = dmp_zero(u), f, df
if df < dg:
return q, r
N = df - dg + 1
lc_g = dmp_LC(g, K)
while True:
lc_r = dmp_LC(r, K)
j, N = dr - dg, N - 1
Q = dmp_mul_term(q, lc_g, 0, u, K)
q = dmp_add_term(Q, lc_r, j, u, K)
R = dmp_mul_term(r, lc_g, 0, u, K)
G = dmp_mul_term(g, lc_r, j, u, K)
r = dmp_sub(R, G, u, K)
_dr, dr = dr, dmp_degree(r, u)
if dr < dg:
break
elif not (dr < _dr):
raise PolynomialDivisionFailed(f, g, K)
c = dmp_pow(lc_g, N, u - 1, K)
q = dmp_mul_term(q, c, 0, u, K)
r = dmp_mul_term(r, c, 0, u, K)
return q, r
开发者ID:QuaBoo，项目名称:sympy，代码行数:55，代码来源:densearith.py
示例11: dmp_ff_div
def dmp_ff_div(f, g, u, K):
"""
Polynomial division with remainder over a field.
Examples
========
>>> from sympy.polys.domains import QQ
>>> from sympy.polys.densearith import dmp_ff_div
>>> f = QQ.map([[1], [1, 0], []])
>>> g = QQ.map([[2], [2]])
>>> dmp_ff_div(f, g, 1, QQ)
([[1/2], [1/2, -1/2]], [[-1/1, 1/1]])
"""
if not u:
return dup_ff_div(f, g, K)
df = dmp_degree(f, u)
dg = dmp_degree(g, u)
if dg < 0:
raise ZeroDivisionError("polynomial division")
q, r = dmp_zero(u), f
if df < dg:
return q, r
lc_g, v = dmp_LC(g, K), u-1
while True:
dr = dmp_degree(r, u)
if dr < dg:
break
lc_r = dmp_LC(r, K)
c, R = dmp_ff_div(lc_r, lc_g, v, K)
if not dmp_zero_p(R, v):
break
j = dr - dg
q = dmp_add_term(q, c, j, u, K)
h = dmp_mul_term(g, c, j, u, K)
r = dmp_sub(r, h, u, K)
return q, r
开发者ID:SwaathiRamesh，项目名称:sympy，代码行数:54，代码来源:densearith.py
示例12: dmp_rr_div
def dmp_rr_div(f, g, u, K):
"""
Multivariate division with remainder over a ring.
**Examples**
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.densearith import dmp_rr_div
>>> f = ZZ.map([[1], [1, 0], []])
>>> g = ZZ.map([[2], [2]])
>>> dmp_rr_div(f, g, 1, ZZ)
([[]], [[1], [1, 0], []])
"""
if not u:
return dup_rr_div(f, g, K)
df = dmp_degree(f, u)
dg = dmp_degree(g, u)
if dg < 0:
raise ZeroDivisionError("polynomial division")
q, r = dmp_zero(u), f
if df < dg:
return q, r
lc_g, v = dmp_LC(g, K), u-1
while True:
dr = dmp_degree(r, u)
if dr < dg:
break
lc_r = dmp_LC(r, K)
c, R = dmp_rr_div(lc_r, lc_g, v, K)
if not dmp_zero_p(R, v):
break
j = dr - dg
q = dmp_add_term(q, c, j, u, K)
h = dmp_mul_term(g, c, j, u, K)
r = dmp_sub(r, h, u, K)
return q, r
开发者ID:101man，项目名称:sympy，代码行数:53，代码来源:densearith.py
示例13: dmp_rr_div
def dmp_rr_div(f, g, u, K):
"""
Multivariate division with remainder over a ring.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y = ring("x,y", ZZ)
>>> R.dmp_rr_div(x**2 + x*y, 2*x + 2)
(0, x**2 + x*y)
"""
if not u:
return dup_rr_div(f, g, K)
df = dmp_degree(f, u)
dg = dmp_degree(g, u)
if dg < 0:
raise ZeroDivisionError("polynomial division")
q, r = dmp_zero(u), f
if df < dg:
return q, r
lc_g, v = dmp_LC(g, K), u - 1
while True:
dr = dmp_degree(r, u)
if dr < dg:
break
lc_r = dmp_LC(r, K)
c, R = dmp_rr_div(lc_r, lc_g, v, K)
if not dmp_zero_p(R, v):
break
j = dr - dg
q = dmp_add_term(q, c, j, u, K)
h = dmp_mul_term(g, c, j, u, K)
r = dmp_sub(r, h, u, K)
return q, r
开发者ID:Acebulf，项目名称:sympy，代码行数:51，代码来源:densearith.py
示例14: dmp_ff_div
def dmp_ff_div(f, g, u, K):
"""
Polynomial division with remainder over a field.
Examples
========
>>> from sympy.polys import ring, QQ
>>> R, x,y = ring("x,y", QQ)
>>> R.dmp_ff_div(x**2 + x*y, 2*x + 2)
(1/2*x + 1/2*y - 1/2, -y + 1)
"""
if not u:
return dup_ff_div(f, g, K)
df = dmp_degree(f, u)
dg = dmp_degree(g, u)
if dg < 0:
raise ZeroDivisionError("polynomial division")
q, r, dr = dmp_zero(u), f, df
if df < dg:
return q, r
lc_g, v = dmp_LC(g, K), u - 1
while True:
lc_r = dmp_LC(r, K)
c, R = dmp_ff_div(lc_r, lc_g, v, K)
if not dmp_zero_p(R, v):
break
j = dr - dg
q = dmp_add_term(q, c, j, u, K)
h = dmp_mul_term(g, c, j, u, K)
r = dmp_sub(r, h, u, K)
_dr, dr = dr, dmp_degree(r, u)
if dr < dg:
break
elif not (dr < _dr):
raise PolynomialDivisionFailed(f, g, K)
return q, r
开发者ID:QuaBoo，项目名称:sympy，代码行数:51，代码来源:densearith.py
示例15: dmp_prem
def dmp_prem(f, g, u, K):
"""
Polynomial pseudo-remainder in ``K[X]``.
**Examples**
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.densearith import dmp_prem
>>> f = ZZ.map([[1], [1, 0], []])
>>> g = ZZ.map([[2], [2]])
>>> dmp_prem(f, g, 1, ZZ)
[[-4, 4]]
"""
if not u:
return dup_prem(f, g, K)
df = dmp_degree(f, u)
dg = dmp_degree(g, u)
if dg < 0:
raise ZeroDivisionError("polynomial division")
r = f
if df < dg:
return r
N = df - dg + 1
lc_g = dmp_LC(g, K)
while True:
dr = dmp_degree(r, u)
if dr < dg:
break
lc_r = dmp_LC(r, K)
j, N = dr-dg, N-1
R = dmp_mul_term(r, lc_g, 0, u, K)
G = dmp_mul_term(g, lc_r, j, u, K)
r = dmp_sub(R, G, u, K)
c = dmp_pow(lc_g, N, u-1, K)
return dmp_mul_term(r, c, 0, u, K)
开发者ID:101man，项目名称:sympy，代码行数:49，代码来源:densearith.py
示例16: dmp_discriminant
def dmp_discriminant(f, u, K):
"""
Computes discriminant of a polynomial in `K[X]`.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y,z,t = ring("x,y,z,t", ZZ)
>>> R.dmp_discriminant(x**2*y + x*z + t)
-4*y*t + z**2
"""
if not u:
return dup_discriminant(f, K)
d, v = dmp_degree(f, u), u - 1
if d <= 0:
return dmp_zero(v)
else:
s = (-1)**((d*(d - 1)) // 2)
c = dmp_LC(f, K)
r = dmp_resultant(f, dmp_diff(f, 1, u, K), u, K)
c = dmp_mul_ground(c, K(s), v, K)
return dmp_quo(r, c, v, K)
开发者ID:AdrianPotter，项目名称:sympy，代码行数:29，代码来源:euclidtools.py
示例17: dmp_discriminant
def dmp_discriminant(f, u, K):
"""
Computes discriminant of a polynomial in ``K[X]``.
**Examples**
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.euclidtools import dmp_discriminant
>>> f = ZZ.map([[[[1]], [[]]], [[[1], []]], [[[1, 0]]]])
>>> dmp_discriminant(f, 3, ZZ)
[[[-4, 0]], [[1], [], []]]
"""
if not u:
return dup_discriminant(f, K)
d, v = dmp_degree(f, u), u-1
if d <= 0:
return dmp_zero(v)
else:
s = (-1)**((d*(d-1)) // 2)
c = dmp_LC(f, K)
r = dmp_resultant(f, dmp_diff(f, 1, u, K), u, K)
c = dmp_mul_ground(c, K(s), v, K)
return dmp_exquo(r, c, v, K)
开发者ID:addisonc，项目名称:sympy，代码行数:30，代码来源:euclidtools.py
示例18: dmp_sqr
def dmp_sqr(f, u, K):
"""Square dense polynomials in `K[X]`. """
if not u:
return dup_sqr(f, K)
df = dmp_degree(f, u)
if df < 0:
return f
h, v = [], u-1
for i in xrange(0, 2*df+1):
c = dmp_zero(v)
jmin = max(0, i-df)
jmax = min(i, df)
n = jmax - jmin + 1
jmax = jmin + n // 2 - 1
for j in xrange(jmin, jmax+1):
c = dmp_add(c, dmp_mul(f[j], f[i-j], v, K), v, K)
c = dmp_mul_ground(c, 2, v, K)
if n & 1:
elem = dmp_sqr(f[jmax+1], v, K)
c = dmp_add(c, elem, v, K)
h.append(c)
return h
开发者ID:Aang，项目名称:sympy，代码行数:34，代码来源:densearith.py
示例19: dmp_prem
def dmp_prem(f, g, u, K):
"""
Polynomial pseudo-remainder in ``K[X]``.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y = ring("x,y", ZZ)
>>> R.dmp_prem(x**2 + x*y, 2*x + 2)
-4*y + 4
"""
if not u:
return dup_prem(f, g, K)
df = dmp_degree(f, u)
dg = dmp_degree(g, u)
if dg < 0:
raise ZeroDivisionError("polynomial division")
r = f
if df < dg:
return r
N = df - dg + 1
lc_g = dmp_LC(g, K)
while True:
dr = dmp_degree(r, u)
if dr < dg:
break
lc_r = dmp_LC(r, K)
j, N = dr - dg, N - 1
R = dmp_mul_term(r, lc_g, 0, u, K)
G = dmp_mul_term(g, lc_r, j, u, K)
r = dmp_sub(R, G, u, K)
c = dmp_pow(lc_g, N, u - 1, K)
return dmp_mul_term(r, c, 0, u, K)
开发者ID:Acebulf，项目名称:sympy，代码行数:47，代码来源:densearith.py
示例20: dmp_mul
def dmp_mul(f, g, u, K):
"""
Multiply dense polynomials in ``K[X]``.
Examples
========
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.densearith import dmp_mul
>>> f = ZZ.map([[1, 0], [1]])
>>> g = ZZ.map([[1], []])
>>> dmp_mul(f, g, 1, ZZ)
[[1, 0], [1], []]
"""
if not u:
return dup_mul(f, g, K)
if f == g:
return dmp_sqr(f, u, K)
df = dmp_degree(f, u)
if df < 0:
return f
dg = dmp_degree(g, u)
if dg < 0:
return g
h, v = [], u-1
for i in xrange(0, df+dg+1):
coeff = dmp_zero(v)
for j in xrange(max(0, i-dg), min(df, i)+1):
coeff = dmp_add(coeff, dmp_mul(f[j], g[i-j], v, K), v, K)
h.append(coeff)
return dmp_strip(h, u)
开发者ID:SwaathiRamesh，项目名称:sympy，代码行数:44，代码来源:densearith.py
注：本文中的sympy.polys.densebasic.dmp_degree函数示例由纯净天空整理自Github/MSDocs等源码及文档管理平台，相关代码片段筛选自各路编程大神贡献的开源项目，源码版权归原作者所有，传播和使用请参考对应项目的License；未经允许，请勿转载。 |
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