Python 如何同时使用Z3py和Sympy

我正在尝试对矩阵执行一些符号计算（将符号作为矩阵的一个条目），然后我将有一些可能的解决方案。我的目标是根据约束选择解决方案/解决方案

例如，

M

是一个矩阵，其中有一个元素作为

符号

。 这个矩阵有两个特征值，一个是正的，一个是负的。使用z3，我试图找出唯一的负值，但我无法做到这一点，因为a被定义为一个符号，除非我将其转换为实值，否则我无法将其作为约束写入

我该怎么办？有没有办法将（符号）转换为实数或整数，以便我可以将其用作约束

s.add（a>0）

从sympy导入*
从z3进口*
从数学导入*
a=符号（'a'）
M=矩阵（[[a，2]，[3，4]]）M=M.本征值（）；
s=解算器（）
s、 添加（m一种可能性是将sympy表达式转换为stings，修改它们以表示z3表达式，然后调用python的eval将它们计算为z3表达式。更准确地说：

将Symphy表达式转换为字符串。只需调用Python的str（），即可从Symphy表达式生成字符串
将不等/等号附加到每个字符串（“>0”、“小于0”、“大于等于0”或“”）中
eval
和
exec
的替代方法是遍历sympy表达式并构造相应的z3表达式。下面是一些代码：

from z3 import Real, Sqrt 
from sympy.core import Mul, Expr, Add, Pow, Symbol, Number

def sympy_to_z3(sympy_var_list, sympy_exp):
    'convert a sympy expression to a z3 expression. This returns (z3_vars, z3_expression)'

    z3_vars = []
    z3_var_map = {}

    for var in sympy_var_list:
        name = var.name
        z3_var = Real(name)
        z3_var_map[name] = z3_var
        z3_vars.append(z3_var)

    result_exp = _sympy_to_z3_rec(z3_var_map, sympy_exp)

    return z3_vars, result_exp

def _sympy_to_z3_rec(var_map, e):
    'recursive call for sympy_to_z3()'

    rv = None

    if not isinstance(e, Expr):
        raise RuntimeError("Expected sympy Expr: " + repr(e))

    if isinstance(e, Symbol):
        rv = var_map.get(e.name)

        if rv == None:
            raise RuntimeError("No var was corresponds to symbol '" + str(e) + "'")

    elif isinstance(e, Number):
        rv = float(e)
    elif isinstance(e, Mul):
        rv = _sympy_to_z3_rec(var_map, e.args[0])

        for child in e.args[1:]:
            rv *= _sympy_to_z3_rec(var_map, child)
    elif isinstance(e, Add):
        rv = _sympy_to_z3_rec(var_map, e.args[0])

        for child in e.args[1:]:
            rv += _sympy_to_z3_rec(var_map, child)
    elif isinstance(e, Pow):
        term = _sympy_to_z3_rec(var_map, e.args[0])
        exponent = _sympy_to_z3_rec(var_map, e.args[1])

        if exponent == 0.5:
            # sqrt
            rv = Sqrt(term)
        else:
            rv = term**exponent

    if rv == None:
        raise RuntimeError("Type '" + str(type(e)) + "' is not yet implemented for convertion to a z3 expresion. " + \
                            "Subexpression was '" + str(e) + "'.")

    return rv

下面是一个使用代码的示例：

from sympy import symbols
from z3 import Solver, sat

var_list = x, y = symbols("x y")

sympy_exp = -x**2 + y + 1
z3_vars, z3_exp = sympy_to_z3(var_list, sympy_exp)

z3_x = z3_vars[0]
z3_y = z3_vars[1]

s = Solver()
s.add(z3_exp == 0) # add a constraint with converted expression
s.add(z3_y >= 0) # add an extra constraint

result = s.check()

if result == sat:
    m = s.model()

    print "SAT at x={}, y={}".format(m[z3_x], m[z3_y])
else:
    print "UNSAT"

运行此命令将生成解决约束的输出
y>=0
和
-x^2+y+1==0
：

SAT at x=2，y=3
我正在尝试运行此代码，但它在最后一行识别出一个错误。请指定您为str\u ineq\u list和syms传递的参数值。我将检查哪里出错，并相应地修改/澄清答案。
from z3 import Real, Sqrt 
from sympy.core import Mul, Expr, Add, Pow, Symbol, Number

def sympy_to_z3(sympy_var_list, sympy_exp):
    'convert a sympy expression to a z3 expression. This returns (z3_vars, z3_expression)'

    z3_vars = []
    z3_var_map = {}

    for var in sympy_var_list:
        name = var.name
        z3_var = Real(name)
        z3_var_map[name] = z3_var
        z3_vars.append(z3_var)

    result_exp = _sympy_to_z3_rec(z3_var_map, sympy_exp)

    return z3_vars, result_exp

def _sympy_to_z3_rec(var_map, e):
    'recursive call for sympy_to_z3()'

    rv = None

    if not isinstance(e, Expr):
        raise RuntimeError("Expected sympy Expr: " + repr(e))

    if isinstance(e, Symbol):
        rv = var_map.get(e.name)

        if rv == None:
            raise RuntimeError("No var was corresponds to symbol '" + str(e) + "'")

    elif isinstance(e, Number):
        rv = float(e)
    elif isinstance(e, Mul):
        rv = _sympy_to_z3_rec(var_map, e.args[0])

        for child in e.args[1:]:
            rv *= _sympy_to_z3_rec(var_map, child)
    elif isinstance(e, Add):
        rv = _sympy_to_z3_rec(var_map, e.args[0])

        for child in e.args[1:]:
            rv += _sympy_to_z3_rec(var_map, child)
    elif isinstance(e, Pow):
        term = _sympy_to_z3_rec(var_map, e.args[0])
        exponent = _sympy_to_z3_rec(var_map, e.args[1])

        if exponent == 0.5:
            # sqrt
            rv = Sqrt(term)
        else:
            rv = term**exponent

    if rv == None:
        raise RuntimeError("Type '" + str(type(e)) + "' is not yet implemented for convertion to a z3 expresion. " + \
                            "Subexpression was '" + str(e) + "'.")

    return rv

from sympy import symbols
from z3 import Solver, sat

var_list = x, y = symbols("x y")

sympy_exp = -x**2 + y + 1
z3_vars, z3_exp = sympy_to_z3(var_list, sympy_exp)

z3_x = z3_vars[0]
z3_y = z3_vars[1]

s = Solver()
s.add(z3_exp == 0) # add a constraint with converted expression
s.add(z3_y >= 0) # add an extra constraint

result = s.check()

if result == sat:
    m = s.model()

    print "SAT at x={}, y={}".format(m[z3_x], m[z3_y])
else:
    print "UNSAT"