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Interpolation basis

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        INTUITION PHASE in solving Lagrange interpolation problem:
        STEP 0:
        a[1:]-a[:-1]
        
        a[::2][1:]-a[::2][:-1]
        a[1::2][1:]-a[1::2][:-1]
        
        c[::3][:-1]=a[::3][1:]-a[::3][:-1]
        c[1::3][:-1]=a[1::3][1:]-a[1::3][:-1]
        c[2::3][:-1]=a[2::3][1:]-a[2::3][:-1]
        c[3::3][:-1]=a[3::3][1:]-a[3::3][:-1]
        c[4::3][:-1]=a[4::3][1:]-a[4::3][:-1]
        c[5::3][:-1]=a[5::3][1:]-a[5::3][:-1]
        c[6::3][:-1]=a[6::3][1:]-a[6::3][:-1]
        6=9-3
        
        for i in range(len(a)-1-3):
           c[i::3]=a[i::3][1:]-a[i::3][:-1]
    
        STEP 1:
        c[::9]
        c=d=ones((n+1,n))
        c[0]=a
        c[1]=f
        
        QUESTIONs:
        +c=ones((n+1),n)#i.e lines below
        +c=ones((n+1),n)
        +j from 1 or 2 ?
        +if from 1 what menans i
        
        STEP 5:
        c[0]=a[1:]-a[:-1]
        for j in range(len(a)-1+1)[2:]:
           for i in range(len(a)-1-j+1):
              c[j-1][i::j][:-1]=a[i::j][1:]-a[i::j][:-1]
           d[j+2]=(d[j+1][1:]-d[j+1][:-1])/float(c[j+2])
    
        SOME USEFUL REMARKs:
        f = implemented_function(Function('f'), lambda x: x+1)
        func = lambdify(x, f(x))
        func(4)
        expr=sp.parsing.sympy_parser.parse_expr("sin(x)+x**2")
        sp.diff(expr)
        ff=sp.lambdify(x,sp.diff(expr),"numpy")
        
        TESTS: 
        import src.lagrange as lg
        lg.lagrangeInterp(listX=[pi,2*pi,3*pi,2*pi])
        lg.lagrangeInterp(listX=[0,-2,0.5,2/3.],func='x*sin(pi*x)')
        lg.lagrangeInterp(listX=[-1,-1,1,1],func="sin(pi*x)")
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        DECRCIPTION:
        find len(points)-1 derivation of function func
        
        step1 (find b):
        
        b[n]=a[n]
        for k=n-1,...,1 do
        b[k]=a[k]+(x0-x[k])b[k+1]
        b[1] is f'(x0)
        
        step2:
        a=b
        and try agen step1
        after k+1 steps 
        b[1]=f'(x0),...,b[k]=f^{k}(x0)
        
        INPUT:
        func-whom derivations we want to find
        x0 is point to find derivations in
        points will be generated in small area near x0 as Chebyshev points
        
        questions:
        +x0 from left in points?
        +check array.copy's
        
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