三行搞定拉格朗日多项式

mayaview

我看Mathematica版有人用Mathematica写拉格朗日多项式，我来个Sympy的版本：
[code=Python width=600px]def LagrangPoly(x,order,i,xi=None):
    if xi==None:
        xi=symbols('x:%d'%(order+1))
    index = range(order+1)
    index.pop(i)
    return prod([(x-xi[j])/(xi-xi[j]) for j in index])[/code]功能还行，动态生成变量x=symbols('x')LagrangPoly(x,5,0)
[size=16.799999237060547px](x–x1)(x–x2)(x–x3)(x–x4)(x–x5)(x0–x1)(x0–x2)(x0−x3)(x0–x4)(x0–x5)
也可以做数值行的，比如下面可以做二次单元的形函数：x=symbols('x')simplify(LagrangPoly(x,2,0,[-1,0,1])),simplify(LagrangPoly(x,2,1,[-1,0,1])),simplify(LagrangPoly(x,2,2,[-1,0,1]))
[size=16.799999237060547px](12x(x−1),–x2+1,12x(x+1))

saaya