#範例3-1：多項式= （x+2y+3)**2
#可以輸出在畫面顯示方程式的latex格式
from sympy.interactive import printing
printing.init_printing(use_latex=True)
from sympy import *

x = symbols('x')

#一元多項式
f = poly(x**2+2*x+1)
display(f)

#一元多項式，相乘，展開
f = poly((x+3)*(x+5))
print(f)

#多項式相除
g = poly((x**3+x**2+x+1)/(x-2))
display(g)

#二元多項式
x,y = symbols('x y')
f = poly('(x+2*y+3)**2')
display(f)

#一元函數求對應值：f(x=2)
#求值f(x=3)，兩種寫法：(1) f.subs({x:3}。（2）f.subs(x,3)
f = Function('y')(x)
f = (x+2)**2
print('f(x=2)=',f.subs({x:3}))
print('f(x=2)=',f.subs(x, 3))

#二元函數求值：g(x=2,y=1)
g = Function('g')(x,y)
g = (x+2*y+3)**2
print('g(x=2,y=1) = ', g.subs({x:2, y:1}))