# Substituting multiple values

What is the best way of substituting a list (or vector or whatever) of values into an expression? For example, suppose I have

z = var('x y')
zvals = (1, 2)
w = x^2 + y^2


and want to substitute zvals for z in the expression w. I have tried the following commands:

w.subs(z=zvals)                        #doesn't work
w.subs({z:zvals})                      #doesn't work
w.subs(x=1,y=2)                        #fine, but cumbersome if z has many elements
w.subs(z=zvals,z=zvals)    #doesn't work
w.subs({z:zvals,z:zvals})  #fine, and could turn this into a loop
#if there are many variables, but ugly
w.subs(dict(zip(z,zvals)))             #best I can come up with


As far as I can see, none of this behaviour changes if z and zvals are vectors or lists instead of tuples.

Is there a simpler way of doing this? Also, why doesn't the fourth attempt work when the fifth one does - is this down to a limitation of Python?

EDIT: I also realised that you can do w.subs(z==zvals) but w.subs(z==zvals,z==zvals) won't work - why is this?

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I would do it this way:

sage: z = var('x y')
sage: zvals = (1, 2)
sage: w(x,y)=x^2+y^2


Note that w explicitly lists the order of arguments...

sage: w(*zvals)
5


Python documentation of the *mylist syntax is here.

Here is another way:

sage: w(1,2)
5
sage: w(x=zvals, y=zvals)
5

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