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Science Forum Index » Math - Symbolic Forum » Is this a LambertW question?
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| charlesrkiss |
 Posted: Sun Apr 27, 2008 6:11 am |
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I revised the original post. Please let it die.
I need to find m; X, and Y is known:
X = (m*Y)^[1/(m+1)]
Is this a LambertW function question?
Bcause I need some Python code; I like the Python code in Wikipedia
for LambertW, is this a similar problem?
BTW, in my application, Y is actually a function of two parameters,
distance "a" and time, "t": f(a,t) = a^3/2t, where a < 1 is known. So,
I need an X for every Y input. Does that make any sense? :)
The problem is that X is subject to other constraints. When m = 2,
one can say that:
1/Y = 2/X^3, the derivative of a negative inverse square.
but sadly, understanding m, as a function of time, is being difficult.
So I'm having trouble figuring out how to solve for m, or even
conceptualizing how to approach the problem, for that matter... |
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| Daniel Lichtblau |
| Posted: Sun Apr 27, 2008 6:46 am |
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On Apr 27, 11:11 am, charlesrkiss <charles.k...@gmail.com> wrote:
Quote: I revised the original post. Please let it die.
I need to find m; X, and Y is known:
X = (m*Y)^[1/(m+1)]
Is this a LambertW function question?
Bcause I need some Python code; I like the Python code in Wikipedia
for LambertW, is this a similar problem?
BTW, in my application, Y is actually a function of two parameters,
distance "a" and time, "t": f(a,t) = a^3/2t, where a < 1 is known. So,
I need an X for every Y input. Does that make any sense? :)
The problem is that X is subject to other constraints. When m = 2,
one can say that:
1/Y = 2/X^3, the derivative of a negative inverse square.
but sadly, understanding m, as a function of time, is being difficult.
So I'm having trouble figuring out how to solve for m, or even
conceptualizing how to approach the problem, for that matter...
To address the first question, yes, you can get a result in terms of
the Lambert W function (ProductLog, in Mathematica).
In[7]:= Solve[x == (m*y)^(1/(m + 1)), m]
During evaluation of In[7]:= InverseFunction::ifun: Inverse functions
\
are being used. Values may be lost for multivalued inverses. \
\[RightSkeleton]
During evaluation of In[7]:= Solve::ifun: Inverse functions are being
\
used by Solve, so some solutions may not be found; use Reduce for \
complete solution information. \[RightSkeleton]
Out[7]= {{m -> -(ProductLog[-((x*Log[x])/y)]/Log[x])}}
As for the other particulars, I'll point out that this function has
branches indexed by the integers. In mathematica the default (shown
above) is indexed as the 0 branch, and you might modify e.g. using
ProductLog[n,...] to get the nth branch. This might help you to alter
m in some possibly useful manner. Offhand I do not see it being
helpful for making x conform to any constraints.
Daniel Lichtblau
Wolfram Research |
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| David W. Cantrell |
| Posted: Sun Apr 27, 2008 11:51 am |
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charlesrkiss <charles.kiss@gmail.com> wrote:
Quote: I revised the original post. Please let it die.
You posted your question (original and revision) _separately_ both here and
in sci.math.num analysis. That is not a good thing to do. If you think your
question really needs to appear in more than one group, you should instead
crosspost.
Your question has now already been answered in that other group.
David
Quote: I need to find m; X, and Y is known:
X = (m*Y)^[1/(m+1)]
Is this a LambertW function question?
Bcause I need some Python code; I like the Python code in Wikipedia
for LambertW, is this a similar problem?
BTW, in my application, Y is actually a function of two parameters,
distance "a" and time, "t": f(a,t) = a^3/2t, where a < 1 is known. So,
I need an X for every Y input. Does that make any sense? :)
The problem is that X is subject to other constraints. When m = 2,
one can say that:
1/Y = 2/X^3, the derivative of a negative inverse square.
but sadly, understanding m, as a function of time, is being difficult.
So I'm having trouble figuring out how to solve for m, or even
conceptualizing how to approach the problem, for that matter... |
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| charlesrkiss |
| Posted: Sun Apr 27, 2008 5:42 pm |
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On Apr 27, 12:51 pm, David W. Cantrell <DWCantr...@sigmaxi.net> wrote:
Quote: charlesrkiss <charles.k...@gmail.com> wrote:
I revised the original post. Please let it die.
You posted your question (original and revision) _separately_ both here and
in sci.math.num analysis. That is not a good thing to do. If you think your
question really needs to appear in more than one group, you should instead
crosspost.
Your question has now already been answered in that other group.
David
I need to find m; X, and Y is known:
X = (m*Y)^[1/(m+1)]
Is this a LambertW function question?
Bcause I need some Python code; I like the Python code in Wikipedia
for LambertW, is this a similar problem?
BTW, in my application, Y is actually a function of two parameters,
distance "a" and time, "t": f(a,t) = a^3/2t, where a < 1 is known. So,
I need an X for every Y input. Does that make any sense? :)
The problem is that X is subject to other constraints. When m = 2,
one can say that:
1/Y = 2/X^3, the derivative of a negative inverse square.
but sadly, understanding m, as a function of time, is being difficult.
So I'm having trouble figuring out how to solve for m, or even
conceptualizing how to approach the problem, for that matter...
I knew I was doing something "not good" when I posted into two groups,
but didn't know about cross-posting. I'll figure it out, thanks. |
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