本文整理汇总了Python中sympy.polys.densetools.dmp_diff函数的典型用法代码示例。如果您正苦于以下问题：Python dmp_diff函数的具体用法？Python dmp_diff怎么用？Python dmp_diff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_diff函数的12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_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2: 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3: test_dmp_diff_in
def test_dmp_diff_in():
assert dmp_diff_in(f_6, 2, 1, 3, ZZ) == \
dmp_swap(dmp_diff(dmp_swap(f_6, 0, 1, 3, ZZ), 2, 3, ZZ), 0, 1, 3, ZZ)
assert dmp_diff_in(f_6, 3, 1, 3, ZZ) == \
dmp_swap(dmp_diff(dmp_swap(f_6, 0, 1, 3, ZZ), 3, 3, ZZ), 0, 1, 3, ZZ)
assert dmp_diff_in(f_6, 2, 2, 3, ZZ) == \
dmp_swap(dmp_diff(dmp_swap(f_6, 0, 2, 3, ZZ), 2, 3, ZZ), 0, 2, 3, ZZ)
assert dmp_diff_in(f_6, 3, 2, 3, ZZ) == \
dmp_swap(dmp_diff(dmp_swap(f_6, 0, 2, 3, ZZ), 3, 3, ZZ), 0, 2, 3, ZZ)
开发者ID:FireJade，项目名称:sympy，代码行数:9，代码来源:test_densetools.py
示例4: dmp_sqf_part
def dmp_sqf_part(f, u, K):
"""
Returns square-free part of a polynomial in ``K[X]``.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y = ring("x,y", ZZ)
>>> R.dmp_sqf_part(x**3 + 2*x**2*y + x*y**2)
x**2 + x*y
"""
if not u:
return dup_sqf_part(f, K)
if K.is_FiniteField:
return dmp_gf_sqf_part(f, u, K)
if dmp_zero_p(f, u):
return f
if K.is_negative(dmp_ground_LC(f, u, K)):
f = dmp_neg(f, u, K)
gcd = dmp_gcd(f, dmp_diff(f, 1, u, K), u, K)
sqf = dmp_quo(f, gcd, u, K)
if K.has_Field:
return dmp_ground_monic(sqf, u, K)
else:
return dmp_ground_primitive(sqf, u, K)[1]
开发者ID:alhirzel，项目名称:sympy，代码行数:33，代码来源:sqfreetools.py
示例5: 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6: 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7: dmp_sqf_part
def dmp_sqf_part(f, u, K):
"""
Returns square-free part of a polynomial in ``K[X]``.
Examples
========
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.sqfreetools import dmp_sqf_part
>>> f = ZZ.map([[1], [2, 0], [1, 0, 0], []])
>>> dmp_sqf_part(f, 1, ZZ)
[[1], [1, 0], []]
"""
if not u:
return dup_sqf_part(f, K)
if not K.has_CharacteristicZero:
return dmp_gf_sqf_part(f, u, K)
if dmp_zero_p(f, u):
return f
if K.is_negative(dmp_ground_LC(f, u, K)):
f = dmp_neg(f, u, K)
gcd = dmp_gcd(f, dmp_diff(f, 1, u, K), u, K)
sqf = dmp_quo(f, gcd, u, K)
if K.has_Field or not K.is_Exact:
return dmp_ground_monic(sqf, u, K)
else:
return dmp_ground_primitive(sqf, u, K)[1]
开发者ID:FireJade，项目名称:sympy，代码行数:35，代码来源:sqfreetools.py
示例8: dmp_sqf_p
def dmp_sqf_p(f, u, K):
"""
Return ``True`` if ``f`` is a square-free polynomial in ``K[X]``.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y = ring("x,y", ZZ)
>>> R.dmp_sqf_p(x**2 + 2*x*y + y**2)
False
>>> R.dmp_sqf_p(x**2 + y**2)
True
"""
if dmp_zero_p(f, u):
return True
else:
return not dmp_degree(dmp_gcd(f, dmp_diff(f, 1, u, K), u, K), u)
开发者ID:alhirzel，项目名称:sympy，代码行数:20，代码来源:sqfreetools.py
示例9: dmp_sqf_p
def dmp_sqf_p(f, u, K):
"""
Return ``True`` if ``f`` is a square-free polynomial in ``K[X]``.
**Examples**
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.sqfreetools import dmp_sqf_p
>>> f = ZZ.map([[1], [2, 0], [1, 0, 0]])
>>> dmp_sqf_p(f, 1, ZZ)
False
>>> f = ZZ.map([[1], [], [1, 0, 0]])
>>> dmp_sqf_p(f, 1, ZZ)
True
"""
if dmp_zero_p(f, u):
return True
else:
return not dmp_degree(dmp_gcd(f, dmp_diff(f, 1, u, K), u, K), u)
开发者ID:101man，项目名称:sympy，代码行数:22，代码来源:sqfreetools.py
示例10: test_dmp_diff_eval_in
def test_dmp_diff_eval_in():
assert dmp_diff_eval_in(f_6, 2, 7, 1, 3, ZZ) == \
dmp_eval(dmp_diff(dmp_swap(f_6, 0, 1, 3, ZZ), 2, 3, ZZ), 7, 3, ZZ)
开发者ID:FireJade，项目名称:sympy，代码行数:3，代码来源:test_densetools.py
示例11: test_dmp_diff
def test_dmp_diff():
assert dmp_diff([], 1, 0, ZZ) == []
assert dmp_diff([[]], 1, 1, ZZ) == [[]]
assert dmp_diff([[[]]], 1, 2, ZZ) == [[[]]]
assert dmp_diff([[[1], [2]]], 1, 2, ZZ) == [[[]]]
assert dmp_diff([[[1]], [[]]], 1, 2, ZZ) == [[[1]]]
assert dmp_diff([[[3]], [[1]], [[]]], 1, 2, ZZ) == [[[6]], [[1]]]
assert dmp_diff([1, -1, 0, 0, 2], 1, 0, ZZ) == \
dup_diff([1, -1, 0, 0, 2], 1, ZZ)
assert dmp_diff(f_6, 0, 3, ZZ) == f_6
assert dmp_diff(f_6, 1, 3, ZZ) == dmp_diff(f_6, 1, 3, ZZ)
assert dmp_diff(
f_6, 2, 3, ZZ) == dmp_diff(dmp_diff(f_6, 1, 3, ZZ), 1, 3, ZZ)
assert dmp_diff(f_6, 3, 3, ZZ) == dmp_diff(
dmp_diff(dmp_diff(f_6, 1, 3, ZZ), 1, 3, ZZ), 1, 3, ZZ)
K = FF(23)
F_6 = dmp_normal(f_6, 3, K)
assert dmp_diff(F_6, 0, 3, K) == F_6
assert dmp_diff(F_6, 1, 3, K) == dmp_diff(F_6, 1, 3, K)
assert dmp_diff(F_6, 2, 3, K) == dmp_diff(dmp_diff(F_6, 1, 3, K), 1, 3, K)
assert dmp_diff(F_6, 3, 3, K) == dmp_diff(
dmp_diff(dmp_diff(F_6, 1, 3, K), 1, 3, K), 1, 3, K)
开发者ID:FireJade，项目名称:sympy，代码行数:28，代码来源:test_densetools.py
示例12: test_dup_sqf
def test_dup_sqf():
assert dup_sqf_part([], ZZ) == []
assert dup_sqf_p([], ZZ) == True
assert dup_sqf_part([7], ZZ) == [1]
assert dup_sqf_p([7], ZZ) == True
assert dup_sqf_part([2,2], ZZ) == [1,1]
assert dup_sqf_p([2,2], ZZ) == True
assert dup_sqf_part([1,0,1,1], ZZ) == [1,0,1,1]
assert dup_sqf_p([1,0,1,1], ZZ) == True
assert dup_sqf_part([-1,0,1,1], ZZ) == [1,0,-1,-1]
assert dup_sqf_p([-1,0,1,1], ZZ) == True
assert dup_sqf_part([2,3,0,0], ZZ) == [2,3,0]
assert dup_sqf_p([2,3,0,0], ZZ) == False
assert dup_sqf_part([-2,3,0,0], ZZ) == [2,-3,0]
assert dup_sqf_p([-2,3,0,0], ZZ) == False
assert dup_sqf_list([], ZZ) == (0, [])
assert dup_sqf_list([1], ZZ) == (1, [])
assert dup_sqf_list([1,0], ZZ) == (1, [([1,0], 1)])
assert dup_sqf_list([2,0,0], ZZ) == (2, [([1,0], 2)])
assert dup_sqf_list([3,0,0,0], ZZ) == (3, [([1,0], 3)])
assert dup_sqf_list([ZZ(2),ZZ(4),ZZ(2)], ZZ) == \
(ZZ(2), [([ZZ(1),ZZ(1)], 2)])
assert dup_sqf_list([QQ(2),QQ(4),QQ(2)], QQ) == \
(QQ(2), [([QQ(1),QQ(1)], 2)])
assert dup_sqf_list([-1,1,0,0,1,-1], ZZ) == \
(-1, [([1,1,1,1], 1), ([1,-1], 2)])
assert dup_sqf_list([1,0,6,0,12,0,8,0,0], ZZ) == \
(1, [([1,0], 2), ([1,0,2], 3)])
K = FF(2)
f = map(K, [1,0,1])
assert dup_sqf_list(f, K) == \
(K(1), [([K(1),K(1)], 2)])
K = FF(3)
f = map(K, [1,0,0,2,0,0,2,0,0,1,0])
assert dup_sqf_list(f, K) == \
(K(1), [([K(1), K(0)], 1),
([K(1), K(1)], 3),
([K(1), K(2)], 6)])
f = [1,0,0,1]
g = map(K, f)
assert dup_sqf_part(f, ZZ) == f
assert dup_sqf_part(g, K) == [K(1), K(1)]
assert dup_sqf_p(f, ZZ) == True
assert dup_sqf_p(g, K) == False
A = [[1],[],[-3],[],[6]]
D = [[1],[],[-5],[],[5],[],[4]]
f, g = D, dmp_sub(A, dmp_mul(dmp_diff(D, 1, 1, ZZ), [[1,0]], 1, ZZ), 1, ZZ)
res = dmp_resultant(f, g, 1, ZZ)
assert dup_sqf_list(res, ZZ) == (45796, [([4,0,1], 3)])
assert dup_sqf_list_include([DMP([1, 0, 0, 0], ZZ), DMP([], ZZ), DMP([], ZZ)], ZZ[x]) == \
[([DMP([1, 0, 0, 0], ZZ)], 1), ([DMP([1], ZZ), DMP([], ZZ)], 2)]
开发者ID:101man，项目名称:sympy，代码行数:73，代码来源:test_sqfreetools.py
注：本文中的sympy.polys.densetools.dmp_diff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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