info
Google Groups no longer supports new Usenet posts or subscriptions. Historical content remains viewable.
Dismiss
Groups keyboard shortcuts have been updated
Dismiss
See shortcuts
Derivatives Output as TraditionalForm
77 views
Skip to first unread message
mathgroup
Jan 20, 2012, 1:50:29 AM1/20/12
to
The following code was offered in a Wolfram Blog to make Derivatives print
out as they would be written with pencil and paper rather then f^(0,1)[x,y] for example....which is standard Mathematica output....here is the code(written by Simon, I think was his name).....the original Blog had a Wolfram program pdConv ...however, you had to apply it to each expression whereas this code , once run, does it throughout the Notebook....
Derivative/:MakeBoxes[Derivative[inds__][g_][vars__],TraditionalForm]:=ToB oxes[Apply[Defer[D[g[vars],##]]&,Transpose[{{vars},{inds}}]/.{{var_,0}:>Sequence[],{var_,1}:>{var}}],TraditionalForm]
I have 2 Questions....
(1) Why isnt this code standard within Mathematica rather then having to be Coded by the user?....I used to do all this with Format which was a Royal Nightmare by comparison.........I have never seen what purpose this output f^(0,1)[x,y] served.......or does it???
(2) Second....if I want to modify this code to get output as df/dx rather then df[x,y]/dx, , for example , how do I change it?
I also wanted to present this Code in case there are others who don't know about it and might find it useful for their work....
thanks.....Jerry Blimbaum
out as they would be written with pencil and paper rather then f^(0,1)[x,y] for example....which is standard Mathematica output....here is the code(written by Simon, I think was his name).....the original Blog had a Wolfram program pdConv ...however, you had to apply it to each expression whereas this code , once run, does it throughout the Notebook....
Derivative/:MakeBoxes[Derivative[inds__][g_][vars__],TraditionalForm]:=ToB oxes[Apply[Defer[D[g[vars],##]]&,Transpose[{{vars},{inds}}]/.{{var_,0}:>Sequence[],{var_,1}:>{var}}],TraditionalForm]
I have 2 Questions....
(1) Why isnt this code standard within Mathematica rather then having to be Coded by the user?....I used to do all this with Format which was a Royal Nightmare by comparison.........I have never seen what purpose this output f^(0,1)[x,y] served.......or does it???
(2) Second....if I want to modify this code to get output as df/dx rather then df[x,y]/dx, , for example , how do I change it?
I also wanted to present this Code in case there are others who don't know about it and might find it useful for their work....
thanks.....Jerry Blimbaum
Oleksandr Rasputinov
Jan 21, 2012, 5:26:10 AM1/21/12
to
On Fri, 20 Jan 2012 06:50:29 -0000, mathgroup <fizz...@knology.net>
wrote:
> The following code was offered in a Wolfram Blog to make Derivatives
> print
> out as they would be written with pencil and paper rather then
> f^(0,1)[x,y] for example....which is standard Mathematica output....here
> is the code(written by Simon, I think was his name).....the original
> Blog had a Wolfram program pdConv ...however, you had to apply it to
> each expression whereas this code , once run, does it throughout the
> Notebook....
>
>
> Derivative/:MakeBoxes[Derivative[inds__][g_][vars__],TraditionalForm]:=ToBoxes[Apply[Defer[D[g[vars],##]]&,Transpose[{{vars},{inds}}]/.{{var_,0}:>Sequence[],{var_,1}:>{var}}],TraditionalForm]
especially non-standard about it. If you don't like it, you can change it,
as the code example demonstrates. As for why Mathematica doesn't use the
more typical notation in TraditionalForm output, I don't know for sure,
but I would hazard a guess that it is so that TraditionalForm can be
re-interpreted into StandardForm without having to be littered with
InterpretationBoxes to clarify the ambiguous notation. Implementing such
features is not free, of course, so maybe WRI took the view that their
time was better spent doing other things.
>
> (2) Second....if I want to modify this code to get output as
> df/dx rather then df[x,y]/dx, , for example , how do I change it?
Derivative/:MakeBoxes[Derivative[inds__][g_][vars__],TraditionalForm]:=ToBoxes[Apply[Defer[D[g,##]]&,Transpose[{{vars},{inds}}]/.{{var_,0}:>Sequence[],{var_,1}:>{var}}],TraditionalForm]
wrote:
> The following code was offered in a Wolfram Blog to make Derivatives
> out as they would be written with pencil and paper rather then
> f^(0,1)[x,y] for example....which is standard Mathematica output....here
> is the code(written by Simon, I think was his name).....the original
> Blog had a Wolfram program pdConv ...however, you had to apply it to
> each expression whereas this code , once run, does it throughout the
> Notebook....
>
>
>
>
> I have 2 Questions....
>
> (1) Why isnt this code standard within Mathematica rather then having
> to be Coded by the user?....I used to do all this with Format which
> was a Royal Nightmare by comparison.........I have never seen what
> purpose this output f^(0,1)[x,y] served.......or does it???
The notation Mathematica uses is less commonly seen but there is nothing
>
> I have 2 Questions....
>
> (1) Why isnt this code standard within Mathematica rather then having
> to be Coded by the user?....I used to do all this with Format which
> was a Royal Nightmare by comparison.........I have never seen what
> purpose this output f^(0,1)[x,y] served.......or does it???
especially non-standard about it. If you don't like it, you can change it,
as the code example demonstrates. As for why Mathematica doesn't use the
more typical notation in TraditionalForm output, I don't know for sure,
but I would hazard a guess that it is so that TraditionalForm can be
re-interpreted into StandardForm without having to be littered with
InterpretationBoxes to clarify the ambiguous notation. Implementing such
features is not free, of course, so maybe WRI took the view that their
time was better spent doing other things.
>
> (2) Second....if I want to modify this code to get output as
> df/dx rather then df[x,y]/dx, , for example , how do I change it?
JUN
Jan 22, 2012, 7:22:38 AM1/22/12
to
On Jan 21, 2:26 am, "Oleksandr Rasputinov"
<oleksandr_rasputi...@hmamail.com> wrote:
> On Fri, 20 Jan 2012 06:50:29 -0000, mathgroup <fizzym...@knology.net>
If you look at the comments on that blog,
http://blog.wolfram.com/2011/12/15/mathematica-qa-series-converting-to-conventional-mathematical-typesetting/
you'll see that there were some problems with that approach. E.g., try
the above definition with this derivative:
D[f[g[x]] + h[x, y], {x, 2}] // TraditionalForm
I wouldn't consider the result acceptable. That's why I suggested a
different approach on that page:
Derivative /:
MakeBoxes[Derivative[\[Alpha]__][f1_][vars__Symbol],
TraditionalForm] := Module[{bb, dd, sp},
MakeBoxes[dd, _] ^=
If[Length[{\[Alpha]}] == 1, "\[DifferentialD]", "\[PartialD]"];
MakeBoxes[sp, _] ^= "\[ThinSpace]";
bb /: MakeBoxes[bb[x__], _] := RowBox[Map[ToBoxes[#] &, {x}]];
FractionBox[ToBoxes[bb[dd^Plus[\[Alpha]], f1]],
ToBoxes[Apply[bb,
Riffle[Map[bb[dd, #] &,
Select[({vars}^{\[Alpha]}), (# =!= 1 &)]], sp]]]]
]
Jens
<oleksandr_rasputi...@hmamail.com> wrote:
> On Fri, 20 Jan 2012 06:50:29 -0000, mathgroup <fizzym...@knology.net>
> wrote:
>
>
>
>
>
>
>
>
>
> > The following code was offered in a Wolfram Blog to make Derivatives
> > print
> > out as they would be written with pencil and paper rather then
> > f^(0,1)[x,y] for example....which is standard Mathematica output....here
> > is the code(written by Simon, I think was his name).....the original
> > Blog had a Wolfram program pdConv ...however, you had to apply it to
> > each expression whereas this code , once run, does it throughout the
> > Notebook....
>
> > Derivative/:MakeBoxes[Derivative[inds__][g_][vars__],TraditionalForm]:=ToBo xes[Apply[Defer[D[g[vars],##]]&,Transpose[{{vars},{inds}}]/.{{var_,0}:>Sequ ence[],{var_,1}:>{var}}],TraditionalForm]
>
>
>
>
>
>
>
>
>
> > The following code was offered in a Wolfram Blog to make Derivatives
> > out as they would be written with pencil and paper rather then
> > f^(0,1)[x,y] for example....which is standard Mathematica output....here
> > is the code(written by Simon, I think was his name).....the original
> > Blog had a Wolfram program pdConv ...however, you had to apply it to
> > each expression whereas this code , once run, does it throughout the
> > Notebook....
>
>
> > I have 2 Questions....
>
> > (1) Why isnt this code standard within Mathematica rather then having
> > to be Coded by the user?....I used to do all this with Format which
> > was a Royal Nightmare by comparison.........I have never seen what
> > purpose this output f^(0,1)[x,y] served.......or does it???
>
> The notation Mathematica uses is less commonly seen but there is nothing
> especially non-standard about it. If you don't like it, you can change it,
> as the code example demonstrates. As for why Mathematica doesn't use the
> more typical notation in TraditionalForm output, I don't know for sure,
> but I would hazard a guess that it is so that TraditionalForm can be
> re-interpreted into StandardForm without having to be littered with
> InterpretationBoxes to clarify the ambiguous notation. Implementing such
> features is not free, of course, so maybe WRI took the view that their
> time was better spent doing other things.
>
>
>
> > (2) Second....if I want to modify this code to get output as
> > df/dx rather then df[x,y]/dx, , for example , how do I change it?
>
> Derivative/:MakeBoxes[Derivative[inds__][g_][vars__],TraditionalForm]:=
ToBo xes[Apply[Defer[D[g,##]]&,Transpose[{{vars},{inds}}]/.{{var_,0}:>Sequence[] ,{var_,1}:>{var}}],TraditionalForm]
> > I have 2 Questions....
>
> > (1) Why isnt this code standard within Mathematica rather then having
> > to be Coded by the user?....I used to do all this with Format which
> > was a Royal Nightmare by comparison.........I have never seen what
> > purpose this output f^(0,1)[x,y] served.......or does it???
>
> The notation Mathematica uses is less commonly seen but there is nothing
> especially non-standard about it. If you don't like it, you can change it,
> as the code example demonstrates. As for why Mathematica doesn't use the
> more typical notation in TraditionalForm output, I don't know for sure,
> but I would hazard a guess that it is so that TraditionalForm can be
> re-interpreted into StandardForm without having to be littered with
> InterpretationBoxes to clarify the ambiguous notation. Implementing such
> features is not free, of course, so maybe WRI took the view that their
> time was better spent doing other things.
>
>
>
> > (2) Second....if I want to modify this code to get output as
> > df/dx rather then df[x,y]/dx, , for example , how do I change it?
>
> Derivative/:MakeBoxes[Derivative[inds__][g_][vars__],TraditionalForm]:=
If you look at the comments on that blog,
http://blog.wolfram.com/2011/12/15/mathematica-qa-series-converting-to-conventional-mathematical-typesetting/
you'll see that there were some problems with that approach. E.g., try
the above definition with this derivative:
D[f[g[x]] + h[x, y], {x, 2}] // TraditionalForm
I wouldn't consider the result acceptable. That's why I suggested a
different approach on that page:
Derivative /:
MakeBoxes[Derivative[\[Alpha]__][f1_][vars__Symbol],
TraditionalForm] := Module[{bb, dd, sp},
MakeBoxes[dd, _] ^=
If[Length[{\[Alpha]}] == 1, "\[DifferentialD]", "\[PartialD]"];
MakeBoxes[sp, _] ^= "\[ThinSpace]";
bb /: MakeBoxes[bb[x__], _] := RowBox[Map[ToBoxes[#] &, {x}]];
FractionBox[ToBoxes[bb[dd^Plus[\[Alpha]], f1]],
ToBoxes[Apply[bb,
Riffle[Map[bb[dd, #] &,
Select[({vars}^{\[Alpha]}), (# =!= 1 &)]], sp]]]]
]
Jens
A Retey
Jan 22, 2012, 7:21:06 AM1/22/12
to
Hi,
> I have 2 Questions....
>
> (1) Why isnt this code standard within Mathematica rather then
> having to be Coded by the user?....I used to do all this with Format
> which was a Royal Nightmare by comparison.........I have never seen
> what purpose this output f^(0,1)[x,y] served.......or does
> it???
I don't want to start a discussion about whether it was a good decision
to use that notation as the standard, but I think it probably is
interesting to mention what the rational behind it might be:
A derivative can be seen as something that acts on a function rather
than an expression, and that includes functions in a programming
language sense. It then is natural to think about argument slots rather
than named variables, and the StandardForm of Derivative reflects that.
When writing programs I find it very convenient to work with "function"
objects compared to expressions since it avoids all kinds of
complications with localizations and name spaces of those "artifical"
symbols which actually implicitly are just used as named arguments for
functions. If you wonder what I'm talking about, look at how this will
work without ever defining names for the arguments:
f = #1^2*#2^3 &
Derivative[0,1][f]
It probably needs a programmers viewpoint more than a mathematicians to
appreciate the "beauty" and usefulness of such a notation, but I think
with some good will you might see it...
hth,
albert
> I have 2 Questions....
>
> (1) Why isnt this code standard within Mathematica rather then
> having to be Coded by the user?....I used to do all this with Format
> which was a Royal Nightmare by comparison.........I have never seen
> what purpose this output f^(0,1)[x,y] served.......or does
> it???
to use that notation as the standard, but I think it probably is
interesting to mention what the rational behind it might be:
A derivative can be seen as something that acts on a function rather
than an expression, and that includes functions in a programming
language sense. It then is natural to think about argument slots rather
than named variables, and the StandardForm of Derivative reflects that.
When writing programs I find it very convenient to work with "function"
objects compared to expressions since it avoids all kinds of
complications with localizations and name spaces of those "artifical"
symbols which actually implicitly are just used as named arguments for
functions. If you wonder what I'm talking about, look at how this will
work without ever defining names for the arguments:
f = #1^2*#2^3 &
Derivative[0,1][f]
It probably needs a programmers viewpoint more than a mathematicians to
appreciate the "beauty" and usefulness of such a notation, but I think
with some good will you might see it...
hth,
albert
mathgroup
Jan 23, 2012, 2:57:09 AM1/23/12
to
Thank You for Responding....
what you wrote was very Interesting....I'm quite mundane when it comes to
Programming but I have enough background to appreciate what you
said.....Your example certainly gives food for thought....
In fact, I went back to some old work I had done....lo and behold, I had a
reason to use the form f^(0,1)[x,y] for something and when I tried it with
the new found Derivatives code, it didn’t work....I was able to fix it, etc.
but then I realized that perhaps the 'Raw Form' for the end user gives him
many more Options....it proved to be a much easier approach for what I was
trying to do....and actually made more sense..
So, again Wolfram has shown itself to be much Smarter then me...but that's
why I use Mathematica and like it so much...
Interesting how an answer can change your attitude.....I will never again
feel upset by this as output form..... f^(0,1)[x,y]
jerry B
-----Original Message-----
From: A Retey
Sent: Sunday, January 22, 2012 6:19 AM
Subject: Re: Derivatives Output as TraditionalForm
Hi,
> I have 2 Questions....
>
> (1) Why isnt this code standard within Mathematica rather then
> having to be Coded by the user?....I used to do all this with Format
> which was a Royal Nightmare by comparison.........I have never seen
> what purpose this output f^(0,1)[x,y] served.......or does
> it???
what you wrote was very Interesting....I'm quite mundane when it comes to
Programming but I have enough background to appreciate what you
said.....Your example certainly gives food for thought....
In fact, I went back to some old work I had done....lo and behold, I had a
reason to use the form f^(0,1)[x,y] for something and when I tried it with
the new found Derivatives code, it didn’t work....I was able to fix it, etc.
but then I realized that perhaps the 'Raw Form' for the end user gives him
many more Options....it proved to be a much easier approach for what I was
trying to do....and actually made more sense..
So, again Wolfram has shown itself to be much Smarter then me...but that's
why I use Mathematica and like it so much...
Interesting how an answer can change your attitude.....I will never again
feel upset by this as output form..... f^(0,1)[x,y]
jerry B
-----Original Message-----
From: A Retey
Sent: Sunday, January 22, 2012 6:19 AM
Subject: Re: Derivatives Output as TraditionalForm
Hi,
> I have 2 Questions....
>
> (1) Why isnt this code standard within Mathematica rather then
> having to be Coded by the user?....I used to do all this with Format
> which was a Royal Nightmare by comparison.........I have never seen
> what purpose this output f^(0,1)[x,y] served.......or does
> it???
JUN
Jan 24, 2012, 5:11:34 AM1/24/12
to
have, consider the following example from vector analysis.
Needs["VectorAnalysis`"];
SetCoordinates[Cartesian[x, y, z]];
a = Through[Array[
\!\(\*SubscriptBox[\("\<A\>"\), \({"\<x\>", "\<y\>", \
"\<z\>"}[\([\)\(#\)\(]\)]\)]\) &, 3][x, y, z]];
b = Through[Array[
\!\(\*SubscriptBox[\("\<B\>"\), \({"\<x\>", "\<y\>", \
"\<z\>"}[\([\)\(#\)\(]\)]\)]\) &, 3][x, y, z]];
MatrixForm[a]
MatrixForm[b]
Prove explicitly the following theorem which Mathematica tells us is
true:
Simplify[Curl[a\[Cross]b] ==
a Div[b] - b Div[a] + Map[b.Grad[#] &, a] - Map[a.Grad[#] &, b]]
It is nice that Mathematica says it's true, but we want to explain it
to our readers by going step by step. Unfortunately, writing out the
vectors is quite cumbersome. Even the left-hand side is already quite
long (not to mention the right side):
Curl[a\[Cross]b]
All this becomes much easier with the simplified traditional form, in
conjunction with some formatting specific to my problem:
Derivative /:
MakeBoxes[Derivative[\[Alpha]__][f1_][vars__Symbol],
TraditionalForm] :=
Module[{bb, dd, sp},
MakeBoxes[dd, _] ^=
If[Length[{\[Alpha]}] == 1, "\[DifferentialD]", "\[PartialD]"];
MakeBoxes[sp, _] ^= "\[ThinSpace]";
bb /: MakeBoxes[bb[x__], _] := RowBox[Map[ToBoxes[#] &, {x}]];
FractionBox[ToBoxes[bb[dd^Plus[\[Alpha]], f1]],
ToBoxes[Apply[bb,
Riffle[Map[bb[dd, #] &,
Select[({vars}^{\[Alpha]}), (# =!= 1 &)]], sp]]]]]
Module[{f, i, x},
HoldForm[expression // MatrixForm] /.
Subscript[f_, i_][x__] -> Subscript[f, i] // TraditionalForm]
The left-hand side of my desired equation is now:
Curl[a\[Cross]b] // nice
With this, you can now compare terms and recognize cancellations, etc.
So not everything is best done in StandardForm, and there is clearly a
place for a concise TraditionalForm.
Jens
0 new messages