       Re: Create and use a set of values for variables

• To: mathgroup at smc.vnet.net
• Subject: [mg107521] Re: [mg107519] Create and use a set of values for variables
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Tue, 16 Feb 2010 03:50:28 -0500 (EST)

```There are lots of different ways

y[x_] = a*x^2 + b*x + c;

sub[d_, e_, f_] = {b -> d + e, c -> 2 f, a -> d^2};

def = {{1, 4, 6}, {2, 3, 7}, {5, 5, 1}};

Method 1

y[x] /. sub[1, 4, 6]

x^2 + 5*x + 12

y[x] /. sub @@ # & /@ def

{x^2 + 5*x + 12, 4*x^2 + 5*x + 14,
25*x^2 + 10*x + 2}

Method 2

With[{d = 2, e = 3, f = 7}, y[x] /. sub[d, e, f]]

4*x^2 + 5*x + 14

With[{d = #[], e = #[], f = #[]},
y[x] /. sub[d, e, f]] & /@ def

{x^2 + 5*x + 12, 4*x^2 + 5*x + 14,
25*x^2 + 10*x + 2}

Method 3

y2[d_, e_, f_][x_] = y[x] /. sub[d, e, f];

y2[5, 5, 1][x]

25*x^2 + 10*x + 2

(y2 @@ #)[x] & /@ def

{x^2 + 5*x + 12, 4*x^2 + 5*x + 14,
25*x^2 + 10*x + 2}

Bob Hanlon

---- Menl <szegersnl at gmail.com> wrote:

=============
Hi,

I try to find a method of doing the following in Mathematica.

I have some function y[x_]=a x^2 + b x + c
Now I want some list which hold values for a, b and c. that are dependend on some lower level values d, e and f.

vars1=[{d=1, e=4, f=6},{b=d+e, c=2f, a = d^2}]
vars2=[{d=2, e=3, f=7},{b=d+e, c=2f, a = d^2}]
vars3=[{d=5, e=5, f=1},{b=d+e, c=2f, a = d^2}]

and use these sets with the original function when I need it.

This line will not work as intended of course but I hope it makes it clear what I try to do. The key is I would like to not evaluate these values outside this vars, so the original function stays unevaluated.

Something like this I tried to do with either the functions Block or With, but both evaluate the values for a, b and c. I would like to make several such sets of variables without evaluating them so I can use them as desired, to plot the original function with several sets of vars.

```

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