如何使用 Tuple/Array/Vector 从 Python (ctypes) 调用 PARI/GP？
How to use Tuple/Array/Vector to call PARI/GP from Python (ctypes)?
我想调用 PARI/GP from Python. I need to use ellisdivisible(E; P; n;{&Q}) function of PARI (see function no 3.15.35 on page 441 in this link:)，所以我必须传递 2 个向量或数组（例如，E = ellinit([0,-1,1,0,0], K);P = [0,0];），我该怎么做？
要从 Python (given by Thomas Baruchel) 调用单个 argument/variable 的 PARI 函数（在 C 中），我们有类似下面的内容 -
import ctypes
# load the library
pari=ctypes.cdll.LoadLibrary("libpari.so")
# set the right return type of the functions
pari.stoi.restype = ctypes.POINTER(ctypes.c_long)
pari.nextprime.restype = ctypes.POINTER(ctypes.c_long)
# initialize the library
pari.pari_init(2**19,0)
def nextprime(v):
g = pari.nextprime(pari.stoi(ctypes.c_long(v))) # nextprime(argument) is a PARI function
return pari.itos(g)
print( nextprime(456) )
例如我试过 -
h=(0,0,0, 4,6)
pari.stoi.restype = ctypes.POINTER(ctypes.c_long*5)
pari.ellinit.restype = ctypes.POINTER(ctypes.c_long)
def ellinit(v):
g = pari.ellinit(pari.stoi(ctypes.c_long(v)*5))
return pari.itos(g)
print(ellinit(h))
我遇到以下错误 -
File "C:\Users\miron\Desktop\trash5\x\f.py", line 68, in <module>
print( ellinit(h) )
File "C:\Users\miron\Desktop\trash5\x\f.py", line 62, in ellinit
g = pari.ellinit(pari.stoi(ctypes.c_long(v)*5))
TypeError: an integer is required (got type tuple)
如何传递 tuple/array/vector？谢谢。
编辑：
尝试获取 ellisdivisible(E; P; n;{&Q}) -
失败
from ctypes import *
pari = cdll.LoadLibrary("C:\Program Files\Python37\Pari64-2-11-3\libpari.dll")
pari.stoi.restype = POINTER(c_long)
pari.cgetg.restype = POINTER(POINTER(c_long))
pari.ellinit.restype = POINTER(POINTER(c_long))
#-------------------------CHANGE 1
pari.ellisdivisible.restype = c_long
Q = pari.stoi(c_long(0))
#-------------------------
(t_VEC, t_COL, t_MAT) = (17, 18, 19) # incomplete
precision = c_long(38)
pari.pari_init(2 ** 19, 0)
def t_vec(numbers):
l = len(numbers) + 1
p1 = pari.cgetg(c_long(l), c_long(t_VEC))
for i in range(1, l):
p1[i] = pari.stoi(c_long(numbers[i - 1]))
return p1
def main():
h = (0, 0, 0, 0, 1)
P=(0,0)
res = pari.ellinit(t_vec(h), pari.stoi(c_long(1)), precision)
#---------------CHANGE 2
# res = pari.ellinit(t_vec(h), pari.stoi(c_long(1)), precision).disc
y = pari.ellisdivisible(res, t_vec(P), pari.stoi(c_long(5)), byref(Q))
print(pari.itos(y))
#---------------
for i in range(1, 13):
print(pari.itos(res[i]))
if __name__ == '__main__':
main()
错误是 -
Traceback (most recent call last):
File "C:\Users\miron\Desktop\trash5\x\ex - Copy (2).py", line 34, in <module>
main()
File "C:\Users\miron\Desktop\trash5\x\ex - Copy (2).py", line 28, in main
print(pari.itos(y))
OSError: exception: access violation reading 0x0000000000000009
Python 元组或 C 数组不能直接使用，因为 PARI 使用 PARI/GP 特定向量，其中 type/length 在第一个元素中编码。
在第 4.4.1 节 Creation of PARI objects 中说：
The basic function which creates a PARI object is GEN cgetg(long l, long t) l specifies the number of longwords to be allocated to the object, and t is the type of the object, in symbolic form (see Section 4.5 for the list of these). The precise effect of this function is as follows: it first creates on the PARI stack a chunk of memory of size length longwords, and saves the address of the chunk which it will in the end return. If the stack has been used up, a message to the effect that “the PARI stack overflows” is printed, and an error raised. Otherwise, it sets the type and length of the PARI object. In effect, it fills its first codeword (z[0]).
见https://pari.math.u-bordeaux.fr/pub/pari/manuals/2.7.6/libpari.pdf
在本文档的示例中，您可以看到要创建一个包含 两个 元素的向量，它的大小为 l=3 得到一个合适的载体。实际数字向量的第一个元素不是从索引 0 开始，而是从索引 1 开始（请参阅本 PDF 文档中的第 4.5.15 节）。
与
git clone http://pari.math.u-bordeaux.fr/git/pari.git
可以获取PARI的源代码。
你可以在 src/headers/parigen.h 的末尾看到不同的类型。它是一个枚举，我们需要的类型是 t_VEC。对应的整数为17.
因此，我们现在可以定义一个将元组转换为 GP 向量的小函数，如下所示：
def t_vec(numbers):
l = len(numbers) + 1
p1 = pari.cgetg(c_long(l), c_long(t_VEC))
for i in range(1, l):
p1[i] = pari.stoi(c_long(numbers[i - 1]))
return p1
然后我们可以这样调用 ellinit：
h = (0, 0, 0, 4, 6)
res = pari.ellinit(t_vec(h), pari.stoi(c_long(1)), precision)
为了使用您的 [0, 0, 0, 4, 6] 参数对其进行测试，您可以从命令行调用 GP：
? ellinit([0, 0, 0, 4, 6], 1)
%1 = [0, 0, 0, 4, 6, 0, 8, 24, -16, -192, -5184, -19648, 110592/307, Vecsmall([1]), [Vecsmall([128, -1])], [0, 0, 0, 0, 0, 0, 0, 0]]
引用的 PDF 文档第 441 页上的示例的小型、独立 Python 程序可能如下所示：
from ctypes import *
pari = cdll.LoadLibrary("libpari.so")
pari.stoi.restype = POINTER(c_long)
pari.cgetg.restype = POINTER(POINTER(c_long))
pari.ellinit.restype = POINTER(POINTER(c_long))
pari.ellisdivisible.restype = c_long
pari.nfinit0.restype = POINTER(c_long)
pari.polcyclo_eval.restype = POINTER(c_long)
pari.fetch_user_var.restype = c_long
pari.pol_x.restype = POINTER(c_long)
(t_VEC, t_COL, t_MAT) = (17, 18, 19) # incomplete
precision = c_long(38)
pari.pari_init(2 ** 19, 0)
def t_vec(numbers):
l = len(numbers) + 1
p1 = pari.cgetg(c_long(l), c_long(t_VEC))
for i in range(1, l):
p1[i] = pari.stoi(c_long(numbers[i - 1]))
return p1
def main():
t = pari.pol_x(pari.fetch_user_var(bytes("t", "utf8")))
Q = pari.pol_x(pari.fetch_user_var(bytes("Q", "utf8")))
K = pari.nfinit0(pari.polcyclo_eval(11, t), c_long(0), precision)
h = (0, -1, 1, 0, 0)
res = pari.ellinit(t_vec(h), K, precision)
P = (0, 0)
y = pari.ellisdivisible(res, t_vec(P), pari.stoi(c_long(5)), byref(Q))
pari.pari_printf(bytes("Q: %Ps\n", "utf8"), Q)
print("ellisdivisible =", y)
if __name__ == '__main__':
main()
测试
现在我们可以调用 Python 程序，并将它与交互式 GP 程序的输出进行比较，它实际上给出了相同的结果：
Q: [Mod(-t^7 - t^6 - t^5 - t^4 + 1, t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1), Mod(-t^9 - 2*t^8 - 2*t^7 - 3*t^6 - 3*t^5 - 2*t^4 - 2*t^3 - t^2 - 1, t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1)]
ellisdivisible = 1
我想调用 PARI/GP from Python. I need to use ellisdivisible(E; P; n;{&Q}) function of PARI (see function no 3.15.35 on page 441 in this link:)，所以我必须传递 2 个向量或数组（例如，E = ellinit([0,-1,1,0,0], K);P = [0,0];），我该怎么做？
要从 Python (given by Thomas Baruchel) 调用单个 argument/variable 的 PARI 函数（在 C 中），我们有类似下面的内容 -
import ctypes
# load the library
pari=ctypes.cdll.LoadLibrary("libpari.so")
# set the right return type of the functions
pari.stoi.restype = ctypes.POINTER(ctypes.c_long)
pari.nextprime.restype = ctypes.POINTER(ctypes.c_long)
# initialize the library
pari.pari_init(2**19,0)
def nextprime(v):
g = pari.nextprime(pari.stoi(ctypes.c_long(v))) # nextprime(argument) is a PARI function
return pari.itos(g)
print( nextprime(456) )
例如我试过 -
h=(0,0,0, 4,6)
pari.stoi.restype = ctypes.POINTER(ctypes.c_long*5)
pari.ellinit.restype = ctypes.POINTER(ctypes.c_long)
def ellinit(v):
g = pari.ellinit(pari.stoi(ctypes.c_long(v)*5))
return pari.itos(g)
print(ellinit(h))
我遇到以下错误 -
File "C:\Users\miron\Desktop\trash5\x\f.py", line 68, in <module>
print( ellinit(h) )
File "C:\Users\miron\Desktop\trash5\x\f.py", line 62, in ellinit
g = pari.ellinit(pari.stoi(ctypes.c_long(v)*5))
TypeError: an integer is required (got type tuple)
如何传递 tuple/array/vector？谢谢。
编辑：
尝试获取 ellisdivisible(E; P; n;{&Q}) -
from ctypes import *
pari = cdll.LoadLibrary("C:\Program Files\Python37\Pari64-2-11-3\libpari.dll")
pari.stoi.restype = POINTER(c_long)
pari.cgetg.restype = POINTER(POINTER(c_long))
pari.ellinit.restype = POINTER(POINTER(c_long))
#-------------------------CHANGE 1
pari.ellisdivisible.restype = c_long
Q = pari.stoi(c_long(0))
#-------------------------
(t_VEC, t_COL, t_MAT) = (17, 18, 19) # incomplete
precision = c_long(38)
pari.pari_init(2 ** 19, 0)
def t_vec(numbers):
l = len(numbers) + 1
p1 = pari.cgetg(c_long(l), c_long(t_VEC))
for i in range(1, l):
p1[i] = pari.stoi(c_long(numbers[i - 1]))
return p1
def main():
h = (0, 0, 0, 0, 1)
P=(0,0)
res = pari.ellinit(t_vec(h), pari.stoi(c_long(1)), precision)
#---------------CHANGE 2
# res = pari.ellinit(t_vec(h), pari.stoi(c_long(1)), precision).disc
y = pari.ellisdivisible(res, t_vec(P), pari.stoi(c_long(5)), byref(Q))
print(pari.itos(y))
#---------------
for i in range(1, 13):
print(pari.itos(res[i]))
if __name__ == '__main__':
main()
错误是 -
Traceback (most recent call last):
File "C:\Users\miron\Desktop\trash5\x\ex - Copy (2).py", line 34, in <module>
main()
File "C:\Users\miron\Desktop\trash5\x\ex - Copy (2).py", line 28, in main
print(pari.itos(y))
OSError: exception: access violation reading 0x0000000000000009
Python 元组或 C 数组不能直接使用，因为 PARI 使用 PARI/GP 特定向量，其中 type/length 在第一个元素中编码。
在第 4.4.1 节 Creation of PARI objects 中说：
The basic function which creates a PARI object is GEN cgetg(long l, long t) l specifies the number of longwords to be allocated to the object, and t is the type of the object, in symbolic form (see Section 4.5 for the list of these). The precise effect of this function is as follows: it first creates on the PARI stack a chunk of memory of size length longwords, and saves the address of the chunk which it will in the end return. If the stack has been used up, a message to the effect that “the PARI stack overflows” is printed, and an error raised. Otherwise, it sets the type and length of the PARI object. In effect, it fills its first codeword (z[0]).
见https://pari.math.u-bordeaux.fr/pub/pari/manuals/2.7.6/libpari.pdf
在本文档的示例中，您可以看到要创建一个包含 两个 元素的向量，它的大小为 l=3 得到一个合适的载体。实际数字向量的第一个元素不是从索引 0 开始，而是从索引 1 开始（请参阅本 PDF 文档中的第 4.5.15 节）。
与
git clone http://pari.math.u-bordeaux.fr/git/pari.git
可以获取PARI的源代码。
你可以在 src/headers/parigen.h 的末尾看到不同的类型。它是一个枚举，我们需要的类型是 t_VEC。对应的整数为17.
因此，我们现在可以定义一个将元组转换为 GP 向量的小函数，如下所示：
def t_vec(numbers):
l = len(numbers) + 1
p1 = pari.cgetg(c_long(l), c_long(t_VEC))
for i in range(1, l):
p1[i] = pari.stoi(c_long(numbers[i - 1]))
return p1
然后我们可以这样调用 ellinit：
h = (0, 0, 0, 4, 6)
res = pari.ellinit(t_vec(h), pari.stoi(c_long(1)), precision)
为了使用您的 [0, 0, 0, 4, 6] 参数对其进行测试，您可以从命令行调用 GP：
? ellinit([0, 0, 0, 4, 6], 1)
%1 = [0, 0, 0, 4, 6, 0, 8, 24, -16, -192, -5184, -19648, 110592/307, Vecsmall([1]), [Vecsmall([128, -1])], [0, 0, 0, 0, 0, 0, 0, 0]]
引用的 PDF 文档第 441 页上的示例的小型、独立 Python 程序可能如下所示：
from ctypes import *
pari = cdll.LoadLibrary("libpari.so")
pari.stoi.restype = POINTER(c_long)
pari.cgetg.restype = POINTER(POINTER(c_long))
pari.ellinit.restype = POINTER(POINTER(c_long))
pari.ellisdivisible.restype = c_long
pari.nfinit0.restype = POINTER(c_long)
pari.polcyclo_eval.restype = POINTER(c_long)
pari.fetch_user_var.restype = c_long
pari.pol_x.restype = POINTER(c_long)
(t_VEC, t_COL, t_MAT) = (17, 18, 19) # incomplete
precision = c_long(38)
pari.pari_init(2 ** 19, 0)
def t_vec(numbers):
l = len(numbers) + 1
p1 = pari.cgetg(c_long(l), c_long(t_VEC))
for i in range(1, l):
p1[i] = pari.stoi(c_long(numbers[i - 1]))
return p1
def main():
t = pari.pol_x(pari.fetch_user_var(bytes("t", "utf8")))
Q = pari.pol_x(pari.fetch_user_var(bytes("Q", "utf8")))
K = pari.nfinit0(pari.polcyclo_eval(11, t), c_long(0), precision)
h = (0, -1, 1, 0, 0)
res = pari.ellinit(t_vec(h), K, precision)
P = (0, 0)
y = pari.ellisdivisible(res, t_vec(P), pari.stoi(c_long(5)), byref(Q))
pari.pari_printf(bytes("Q: %Ps\n", "utf8"), Q)
print("ellisdivisible =", y)
if __name__ == '__main__':
main()
测试
现在我们可以调用 Python 程序，并将它与交互式 GP 程序的输出进行比较，它实际上给出了相同的结果：
Q: [Mod(-t^7 - t^6 - t^5 - t^4 + 1, t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1), Mod(-t^9 - 2*t^8 - 2*t^7 - 3*t^6 - 3*t^5 - 2*t^4 - 2*t^3 - t^2 - 1, t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1)]
ellisdivisible = 1