DoingMath2018

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These are questions asked by DoingMath2018

My limited experience with Maple graphics consists so far of plotting simple graphs using plot(). Now I'd like to do one like this (digital signal-processing: discretely sampling a continuous signal):

In addition to the graph of the continuous function, I've drawn dots on the graph at integer x-values, and then I've dropped verticals from the dots to the x-axis.

There will always be a dot on the graph at x=0, and the horizontal distance from one dot to the next will always be constant within a single graph, but not always equal to 1. For example, in one graph the dots might be spaced 0, Pi, 2*Pi, etc. It would be nice to show numerical labels for the x-values of the dots in that case too.

What functions should I read about in the docs for this? Thank you.

Why doesn't this do the symbolic summation? Is there a way to get Maple to do it?

sum((-1)^n / n * x^n, n=1..infinity);

After two days of trying to take the Jacobian of a multi-variable mapping in Maple, I'm still finding no way. Here is an example of what I mean by "multi-variable mapping":

(x,y) -> x^2-y^2

Every AP high-school student knows how to take the partial derivatives of that, but Maple's "Jacobian" feature doesn't work on mappings. It only works on expressions.

So I spent today trying to leverage off the "D" feature, only to find it rendered useless by bugs: https://mapleprimes.com/questions/227007-How-To-Take-Partial-Derivative-Of-A-Mapping

It took me less than two days to do it in Mathematica, by way of comparison.

On the website, they show a photo of a man elated to be doing math in Maple, but that's not how it's gone for me. I'm cursing outloud, and my blood pressure is high. I'm angry that I lost money on a product that can't take the Jacobian of a mapping, and I'm angry that I lost two days of my life doing tedious debugging while paying money instead of getting paid for my work.

Maple pays math PhD's to release a commercial CAS that can't take the Jacobian of a mapping. So much for the value of a PhD.

Here's how to break Maple's 'D' function:

~$ cmaple mapleBug.mpl
    |\^/|     Maple 2018 (X86 64 WINDOWS)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2018
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> D[1]((x, y) ->x^2-y^2);
                                 (x, y) -> 2 x

> D[2]((x, y) ->x^2-y^2);
                                 (x, y) -> -2 y

> with(VectorCalculus):
> assume(x, 'real');
> assume(y, 'real');
> D[1]((x, y) ->x^2-y^2);
                                  (x, y) -> 0

> D[2]((x, y) ->x^2-y^2);
                                  (x, y) -> 0

> quit
memory used=2.4MB, alloc=8.3MB, time=0.06

~$

What if a person needs to have these lines:

> with(VectorCalculus):
> assume(x, 'real');
> assume(y, 'real');

and then he wants to take partial derivatives? Not possible? Once you load VectorCalculus and declare x and y real, Maple stops doing partial derivatives? Why.

example1 := (x -> (2 + 3));
example2 := (x -> int(1, y));

When I execute these, Maple evaluates the "2 + 3" into 5, but it does not evaluate the "int(1, y)" into "y". Why does it evaluate the former but not the latter?

Also, how can I modifiy example 2 so that it evaluates the "int(1, y)" and returns "x -> y"?

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