Re: How to express a Product (special case) in Mathematica?
- To: mathgroup at smc.vnet.net
- Subject: [mg59113] Re: [mg59094] How to express a Product (special case) in Mathematica?
- From: Adriano Pascoletti <pascolet at dimi.uniud.it>
- Date: Fri, 29 Jul 2005 00:41:50 -0400 (EDT)
- References: <200507280628.CAA12454@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
David, if Ts = {-1, 0, 2, 3} is a list of t's define a variable, say t, and get the main ingredients for building the functions you want In[2]:= variable=t; data={{variable,Ts[[#]]},Drop[Ts,{#}]}&/@Range[Length[Ts]] Out[3]= {{{t,-1},{0,2,3}},{{t,0},{-1,2,3}},{{t,2},{-1,0,3}},{{t,3},{-1,0,2}}} define the functions MapIndexed[(Ï?[#2ã??1ã?? - 1] = Function[Evaluate@variable, Evaluate[#[[1]]/#[[2]] &[Times @@@ Outer[Plus, #[[1]], -#[[2]]]]]]) &, data]; here they are In[5]:= Ï?[2][y]//InputForm Out[5]//InputForm= -((-3 + y)*y*(1 + y))/6 Plot[Evaluate[Ï?[#][x] & /@ Range[0, Length[Ts] - 1]], {x, -2, 4}, GridLines -> Automatic]; Adriano Pascoletti Il giorno 28 lug 2005, alle ore 08:28, vdavidster at gmail.com ha scritto: > If you're familiar with the Lagrange interpolation polynomial, you'll > know that the coefficient term, phi, is defined as follows: > > n > phi_j (t) = TT (t - t_i) > i=0 ----------- > i!=j (t_j - t_i) > > Or in LaTeX notation: > > \phi_j(t) = \prod^{n}_{\stackrel{i=0}{i \neq j}} \frac{(t - t_i)}{(t_j > - t_i)} > > Or in graphical form: > http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html > > How do I do that in Mathematica? > How do I specify a product that skips a value in its iterator, i? > (i.e. > i != j) > > Thanks! > > David > > ------------------------------------------------------------------------ -------- Adriano Pascoletti Dipartimento di Matematica e Informatica Universita' di Udine Via delle scienze 206 I-33100 Udine Italy
- References:
- How to express a Product (special case) in Mathematica?
- From: vdavidster@gmail.com
- How to express a Product (special case) in Mathematica?