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John Fredsted

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20 years, 171 days
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These are replies submitted by John Fredsted

Yes, you certainly can...

John Fredsted 2238
November 20 2007
0 0
You can do something like: 
eq := isolate(
	+(1/R1+1/R2)*(diff(V2(t), t))
	-(diff(V1(t), t))/R1+(V2(t)-V1(t))/L
	+C*(diff(V2(t), `$`(t, 2))) = 0
,V1(t)):
subs(
	{diff(V1(t),t) = s,diff(V2(t),t) = s,diff(V2(t),t$2) = s^2},
	rhs(eq) = lhs(eq)
);

Yes, you certainly can...

John Fredsted 2238
November 20 2007
You can do something like: 
eq := isolate(
	+(1/R1+1/R2)*(diff(V2(t), t))
	-(diff(V1(t), t))/R1+(V2(t)-V1(t))/L
	+C*(diff(V2(t), `$`(t, 2))) = 0
,V1(t)):
subs(
	{diff(V1(t),t) = s,diff(V2(t),t) = s,diff(V2(t),t$2) = s^2},
	rhs(eq) = lhs(eq)
);

Laplace transform?...

John Fredsted 2238
November 20 2007
0 0
Are you talking about performing a Laplace transform of the differential equation?

Laplace transform?...

John Fredsted 2238
November 20 2007
Are you talking about performing a Laplace transform of the differential equation?

Quite right...

John Fredsted 2238
November 16 2007
0 0
Your are of course quite right. The second order derivatives must be examined too. For a local maximum it must be negative, and for a local minimum it must be positive. Obviously, it is too many years ago I learned about this in high school. Thanks for refreshing my memory.

Quite right...

John Fredsted 2238
November 16 2007
Your are of course quite right. The second order derivatives must be examined too. For a local maximum it must be negative, and for a local minimum it must be positive. Obviously, it is too many years ago I learned about this in high school. Thanks for refreshing my memory.

Second argument included...

John Fredsted 2238
November 16 2007
0 0
Thanks for that important improvement which I have now included in the post above. I was surprised to see that my original function failed for the simple expression you give, because I did test that function on a couple of expressions most of which were more complicated. Now the expression you give combines correctly: 
fullCombine(2*sin(t)+sqrt(3)*cos(t));

7^(1/2)*cos(-arctan(2/3*3^(1/2))+t)
PS: Thanks for not making your post a reply to mine, thereby making it possible for me to include your improvement.

Second argument included...

John Fredsted 2238
November 16 2007
Thanks for that important improvement which I have now included in the post above. I was surprised to see that my original function failed for the simple expression you give, because I did test that function on a couple of expressions most of which were more complicated. Now the expression you give combines correctly: 
fullCombine(2*sin(t)+sqrt(3)*cos(t));

7^(1/2)*cos(-arctan(2/3*3^(1/2))+t)
PS: Thanks for not making your post a reply to mine, thereby making it possible for me to include your improvement.

Lesser beauty...

John Fredsted 2238
November 14 2007
Thanks for your comment concerning the superfluous backquotes, which I actually did consider leaving out. I agree with you that the new specially tailored fromTree has less beauty than the original one has.

Beers, 3rd...

John Fredsted 2238
November 14 2007
Sounds nice. I also prefer small quiet places (with no noisy drunken people present).

Thanks...

John Fredsted 2238
November 14 2007
Thanks for your kind words.

Improvement...

John Fredsted 2238
November 14 2007
You are quite right that fromTree fails for expressions which contains lists and/or sets. I was not aware of that. Thanks for pointing that out to me. Maybe it is just me fooling around or misreading your post, but I cannot get any of the four versions of improvement your suggest to work for a list or a set. I think I have improved fromTree as follows (implementing at the same time your tip concerning seq and the global variable i): 
fromTree := x -> `if`(op(x) = x, x,
	subs({`list`=`[]`,`set`=`{}`},x[1])(map(fromTree,x[2..-1])[])
):
An example: 
> expr := {[1,2,{3,4}],int(exp(cos(x)),x)}:
> tree := toTree(expr);
> fromTree(tree);
tree := [set, [list, 1, 2, [set, 3, 4]], [int, [exp, [cos, x]], x]]
             {[1, 2, {3, 4}], int(exp(cos(x)), x)}

Beers...

John Fredsted 2238
November 14 2007
Thank you guys. I will have to be careful not to switch in my address book the "l" and "x" of your names, otherwise I would end up in the wrong town :-), as also Alex seems to be aware of. Munich is famous for its Oktoberfest. I have once visited it. I was very much impressed with the waitresses carrying around so many large beer mugs. What is the record, Axel?

I apologize...

John Fredsted 2238
November 13 2007
I apologize for having behaved unreasonably. I guess I reacted the way I did because I had hoped for some (obvious, to me) recognition as I felt that I had made something a little cool. Maybe a bit childish of me!? On the other hand, do we not all need a little recognition once in a while?

Clarification...

John Fredsted 2238
November 13 2007
Thanks for your kindness. I want to point out, though, that what discourages me is not that it turns out that there is nothing novel about my contribution but solely the way this fact is being delivered.
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