how to change a string into Multivariate Polynomial Ring
时间: 2024-02-01 14:16:10 浏览: 32
To change a string into a multivariate polynomial ring, we first need to specify the variables and the field over which the polynomials are defined. Let's assume we want to define a polynomial ring over the field of rational numbers with two variables x and y. Here's how you can do it in Python using the SymPy library:
```python
from sympy import symbols, QQ
# define the variables
x, y = symbols('x y')
# define the polynomial ring
R = QQ[x, y]
```
Now, let's say we have a string representing a polynomial, such as "3*x**2*y - 5*x*y + 2*y**2". We can create a polynomial object in the defined polynomial ring as follows:
```python
from sympy import sympify
# define the string representation of the polynomial
poly_str = "3*x**2*y - 5*x*y + 2*y**2"
# convert the string to a polynomial object in the polynomial ring
poly = R(sympify(poly_str))
```
Now we have a polynomial object `poly` in the multivariate polynomial ring `R`. We can perform various operations on this polynomial, such as adding, multiplying, differentiating, etc.