Why Does Mathematica Output Unexpected Results with Derivative Rules?

[unih]

Hi!
Please help the idiot
In[] = D[p[x,t],x,t]/.{Derivative[n_,m_][p_][q__]->a^(n+m)}
Out[] = a²

In[] = D[p[x,t],x,t]/.{Derivative[n__][p_][q__]->a^Plus[n]}
Out[] = a

WTF? Why not a²?

In the simplest case
In[] = D[p[x,t],x,t]/.{Derivative[n__][p_][q__]->Plus[n]}
Out []=Sequence[1, 1]

In[] = D[p[x,t],x,t]/.{Derivative[n__][p_][q__]->Plus[n,1]}
Out []= 3
Works!

In[] = D[p[x,t],x,t]/.{Derivative[n__][p_][q__]->(Plus[n,1]-1)}
Out []= Sequence[1, 1]
What hell is going on?

Thank you very much!

 

[Simon_Tyler]

It's because you are using Rule instead of RuleDelayed.
This means that the right-hand-side of the rule gets evaluated before you want it to.
So Plus[n] gets turned into n before n gets replaced with anything. The rule then fires n gets replaced with Sequence[1,1] explaining your last line.

Everything works as you want if you use
Derivative[n__][p_][q__] :> a^Plus[n]
instead of you original
Derivative[n__][p_][q__] -> a^Plus[n]

Another option would be
Derivative[n_,m___][p_][q__] :> a^Plus[n,m]
which would still work in the case of
Derivative[n__][p_][q__] -> a^Plus[n]

The place where the use of Rule instead of RuleDelayed becomes really problematic is if a term on the RHS already has a value. For example, compare the output of
n = 5;
D[p[x, t], x, t] /. {Derivative[n__][p_][q__] -> a^Plus[n]}
with
n = 5;
D[p[x, t], x, t] /. {Derivative[n__][p_][q__] :> a^Plus[n]}
From version 6 and above, Mathematica has syntax highlighting, so you can tell whether a variable is defined, undefined or localized by its color (black, blue or green respectively).

 

[unih]

Thank you VERY VERY MUCH! I have no words to tell how you helped me

 

[Simon_Tyler]

Not a problem!

 

[alphy]

Hello,

I am not familiar with Mathematica, but it seems like you are trying to use the Derivative function to find the derivative of p(x,t) with respect to x and t. The first two lines of your code show that you are using the rule that the derivative of p(x,t) with respect to x and t is equal to a^(n+m), where n and m are the order of the derivatives. This means that the output should be a^2, as you mentioned.

However, in the next two lines, you are using a different rule that the derivative of p(x,t) with respect to x and t is equal to a^Plus[n], where Plus[n] represents the sum of the orders of the derivatives. This means that the output should be a, as you mentioned.

In the last two lines, you are using a slightly modified rule where you are adding 1 to the sum of the orders of the derivatives. This means that the output should be a+1, which is equal to 3 in this case.

I cannot say for sure why the outputs are different in each case without further context or knowledge of Mathematica. But it seems like the rules you are using are not consistent, which could be causing the confusion. I would suggest checking the documentation or seeking help from a Mathematica expert to better understand how to use the Derivative function and rules in Mathematica.

I hope this helps. Good luck with your work!