nutnutman

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These are replies submitted by nutnutman

@Ronan 

This is an example of what I am trying to do.  example.mw

An example of a similar problem in mathematica is here.

http://mathematica.stackexchange.com/questions/16375/how-to-differentiate-formally/16390#16390

They talk about there being problems where trying to take the derivative of a summation that is of "symbolic length".  But, one person get around it by implementing kronecker deltas somehow (not familiar with mathematica notation).

Explicitly incorporating a kronecker delta doesn't semm very "clean" to me, but even so, I haven't the slightest idea how I would even do that.

 

 

 

 

@Ronan  I like this workaround for simple cases, but I feel like if I start getting into more complicated expressions, involving more terms and higher order derivatives, things will quickly become quite difficult to read.  Does Maple offer a more direct solution?  

The alternative way of displaying the legend works fine.  However, when I do show the legend the labels are still Polygons 1, Polygons 2, etc..  Is there a way of changing the name of these polygons besides the manual way?  I took a look at the reference and it did not seem applicable to filled regions.  Using the caption as a legend alternative could work, however for someone who is unfamiliar with the plot, it seems to me that it requires a little more thought to figure out.  A colorbar on the other hand is more instantly recognizable and I think just makes a more professional looking plot.

The alternative way of displaying the legend works fine.  However, when I do show the legend the labels are still Polygons 1, Polygons 2, etc..  Is there a way of changing the name of these polygons besides the manual way?  I took a look at the reference and it did not seem applicable to filled regions.  Using the caption as a legend alternative could work, however for someone who is unfamiliar with the plot, it seems to me that it requires a little more thought to figure out.  A colorbar on the other hand is more instantly recognizable and I think just makes a more professional looking plot.

In diagrams where a magnetic field is drawn perpendicular to the page the direction is represented by an "X", denoting fields into the page, and a dot, denoting fields coming out of the page.  That is whether you see the front end or back end of a traditional arrow.  So in your example, the point could also be an "X" giving us two directions.  Couldn't the size, shade or color of the "X" or dot then be used to represent magnitude? 

 

Also, I think direction along the fourth dimension could be represented by using a color scale that ranged from negative to positive values.  I could even decide that negative directions are represented by a dark shaded color scale and positive directions are represented by the same color scale but with a lighter shade.  I know that the resulting plot might be difficult to look at but it might still provide some insight if examined closely.

 

 

In diagrams where a magnetic field is drawn perpendicular to the page the direction is represented by an "X", denoting fields into the page, and a dot, denoting fields coming out of the page.  That is whether you see the front end or back end of a traditional arrow.  So in your example, the point could also be an "X" giving us two directions.  Couldn't the size, shade or color of the "X" or dot then be used to represent magnitude? 

 

Also, I think direction along the fourth dimension could be represented by using a color scale that ranged from negative to positive values.  I could even decide that negative directions are represented by a dark shaded color scale and positive directions are represented by the same color scale but with a lighter shade.  I know that the resulting plot might be difficult to look at but it might still provide some insight if examined closely.

 

 

Is it also possible to create a field plot for the same system of equations?

Is it also possible to create a field plot for the same system of equations?

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