本文整理汇总了Python中sympy.polys.densebasic.dmp_LC函数的典型用法代码示例。如果您正苦于以下问题：Python dmp_LC函数的具体用法？Python dmp_LC怎么用？Python dmp_LC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_LC函数的15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，您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: _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示例2: 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)示例3: 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示例4: 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示例5: 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示例6: 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示例7: 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示例8: 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示例9: 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)示例10: dmp_content
def dmp_content(f, u, K):
"""
Returns GCD of multivariate coefficients.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y, = ring("x,y", ZZ)
>>> R.dmp_content(2*x*y + 6*x + 4*y + 12)
2*y + 6
"""
cont, v = dmp_LC(f, K), u - 1
if dmp_zero_p(f, u):
return cont
for c in f[1:]:
cont = dmp_gcd(cont, c, v, K)
if dmp_one_p(cont, v, K):
break
if K.is_negative(dmp_ground_LC(cont, v, K)):
return dmp_neg(cont, v, K)
else:
return cont示例11: dmp_eval
def dmp_eval(f, a, u, K):
"""
Evaluate a polynomial at ``x_0 = a`` in ``K[X]`` using the Horner scheme.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y = ring("x,y", ZZ)
>>> R.dmp_eval(2*x*y + 3*x + y + 2, 2)
5*y + 8
"""
if not u:
return dup_eval(f, a, K)
if not a:
return dmp_TC(f, K)
result, v = dmp_LC(f, K), u - 1
for coeff in f[1:]:
result = dmp_mul_ground(result, a, v, K)
result = dmp_add(result, coeff, v, K)
return result示例12: 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)示例13: dmp_eval
def dmp_eval(f, a, u, K):
"""
Evaluate a polynomial at ``x_0 = a`` in ``K[X]`` using the Horner scheme.
Examples
========
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.densetools import dmp_eval
>>> f = ZZ.map([[2, 3], [1, 2]])
>>> dmp_eval(f, 2, 1, ZZ)
[5, 8]
"""
if not u:
return dup_eval(f, a, K)
if not a:
return dmp_TC(f, K)
result, v = dmp_LC(f, K), u - 1
for coeff in f[1:]:
result = dmp_mul_ground(result, a, v, K)
result = dmp_add(result, coeff, v, K)
return result示例14: dmp_content
def dmp_content(f, u, K):
"""
Returns GCD of multivariate coefficients.
**Examples**
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.euclidtools import dmp_content
>>> f = ZZ.map([[2, 6], [4, 12]])
>>> dmp_content(f, 1, ZZ)
[2, 6]
"""
cont, v = dmp_LC(f, K), u-1
if dmp_zero_p(f, u):
return cont
for c in f[1:]:
cont = dmp_gcd(cont, c, v, K)
if dmp_one_p(cont, v, K):
break
if K.is_negative(dmp_ground_LC(cont, v, K)):
return dmp_neg(cont, v, K)
else:
return cont示例15: 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)