Re: Plot Magic Voodoo ???

• To: mathgroup at smc.vnet.net
• Subject: [mg90949] Re: Plot Magic Voodoo ???
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Thu, 31 Jul 2008 02:57:04 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <g6q0nb\$qeo\$1@smc.vnet.net>

```beckman wrote:

> Consider the following:
>
> z := {L == x y, y == x, x == y}
>
> Solve[z, {L}] --->  {{L->y^2}}
>
> no surprises. now,
>
> Plot[L /. Solve[z, {L}][[1]], {y, 1, 10}]
>
> Works exactly as one would expect, BUT, this also works
>
> Plot[L /. Solve[z, {L}][[1]], {x, 1, 10}]
>
> BUT, the first argument of Plot is L /. Solve[z, {L}][[1]], which is
> y^2, so my brain said that
>
> Plot[L /. Solve[z, {L}][[1]], {x, 1, 10}] ---> Plot[y^2, {x, 1, 10}]
>
> which, of course, cannot work. Btw,
>
> Plot[L /. Solve[z, {L}][[1]], {q, 1, 10}]
>
> does not work, so SOMEHOW, Plot is magically peeking at the innards of
> the Solve expression, and is NOT evaluating it, and noticing that x is
> a free variable in the set of equations, z, and ... my brain is
> melting

Trace[] is to the Mathematica user what the crystal ball is to the
magician :) Below, you can see that first a value is assigned to y, x,
or q by Plot, only then Solve[] is called.

z := {L == x y, y == x, x == y}

Plot[L /. Solve[z, {L}][[1]], {y, 1, 10}] // Trace

{Plot[L/.Solve[z,{L}][[1]],{y,1,10}],{y=.,Null},{y=.,Null},
{{y}=.,{y=.},{y=.,Null},{Null}},{{{{z,{L==x y,y==x,x==y},
{{{y,1.00018},x 1.00018,1.00018 x},L==1.00018},
{{y,1.00018},1.00018==x},{{y,1.00018},x==1.00018},
{L==1.00018 x,1.00018==x,x==1.00018}},
Solve[{L==1.00018 x,1.00018==x,x==1.00018},{L}],{{L->1.00037}}},
{{L->1.00037}}[[1]],{L->1.00037}},L/.{L->1.00037},1.00037},
{y=.,Null},{y=.,Null},{y=.,Null},{y=.,Null},
[...]

Plot[L /. Solve[z, {L}][[1]], {x, 1, 10}] // Trace

{Plot[L/.Solve[z,{L}][[1]],{x,1,10}],{x=.,Null},{x=.,Null},
{{x}=.,{x=.},{x=.,Null},{Null}},{{{{z,{L==x y,y==x,x==y},
{{{x,1.00018},1.00018 y},L==1.00018 y},
{{x,1.00018},y==1.00018},{{x,1.00018},1.00018==y},
{L==1.00018 y,y==1.00018,1.00018==y}},
Solve[{L==1.00018 y,y==1.00018,1.00018==y},{L}],
{{L->1.00037}}},{{L->1.00037}}[[1]],{L->1.00037}},
L/.{L->1.00037},1.00037},{x=.,Null},{x=.,Null},{x=.,Null},
[...]

Plot[L /. Solve[z, {L}][[1]], {q, 1, 10}] // Trace

{Plot[L/.Solve[z,{L}][[1]],{q,1,10}],{q=.,Null},{q=.,Null},
{{q}=.,{q=.},{q=.,Null},{Null}},{{{{z,{L==x y,y==x,x==y}},
Solve[{L==x y,y==x,x==y},{L}],{{L->y^2}}},{{L->y^2}}[[1]],
{L->y^2}},L/.{L->y^2},y^2},{{q}=.,{q=.},{q=.,Null},{Null}},
{{q}=.,{q=.},{q=.,Null},{Null}},{{q}=.,{q=.},{q=.,Null},{Null}},
{{q}=.,{q=.},{q=.,Null},{Null}},{{q}=.,{q=.},{q=.,Null},
[...]

Regards,
-- Jean-Marc

```

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