如何使用Tuple/Array/Vector从Python（ctypes）调用PARI/GP？

Question

我想从Python调用PARI/GP。我需要使用PARI(see function no 3.15.35 on page 441 in this link:)的ellisdivisible(E; P; n;{&Q})函数，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];），我是如何做到的

要从Python(given by Thomas Baruchel)调用单参数/变量的PARI函数（在C中），我们有如下内容-

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))

我犯了以下错误-

   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)

如何传递元组/数组/向量？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

Answer 1

Python元组或C数组不能直接使用，因为PARI使用的是PARI/GP特定向量，其中类型/长度在第一个元素中编码

在第4.4.1节{}中，它说：

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，需要使用大小l=3来调用它，以获得合适的向量。实际数字向量的第一个元素不是以索引0开始，而是以索引1开始（参见本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

在这里，您可以在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。相应的整数是17

因此，我们现在可以定义一个小函数，将元组转换为GP向量，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

然后我们可以调用ellinit，因此：

h = (0, 0, 0, 4, 6)
res = pari.ellinit(t_vec(h), pari.stoi(c_long(1)), precision)

为了使用[0,0,0,4,6]参数对其进行测试，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页示例中的一个小型、自包含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，并将其与交互式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