## 3068 Reputation

19 years, 329 days

Doug

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Math, USC, Columbia, SC 29208 E-mail: mailto:meade@math.sc.edu
Phone: (803) 777-6183 URL: http://www.math.sc.edu

## Email this blog...

A quick question about sending a blog entry to someone by e-mail via the "Email this blog" button: I almost missed the box to enter the e-mail addresses. I never expected this box to have all of the buttons for typesetting HTML or to upload/use file or worksheet. Shouldn't this field should just be a simple textbox? Doug

## Displaying Functions: A Request...

As new features are being built into upcoming releases of Maple, here is one request that would be very helpful for those of us who use Maple to teach lower-level (Calculus) students. Maple can work nicely with functions, but students are not always so comfortable with this language. Here's a current example. Suppose you want to find the tangent line to a function. We might work as follows.
> f := x -> sqrt(4-x^2);
/     2\
x -> sqrt\4 - x /
> df := D( f );           # typed, or from context-menu
x
x -> - ------------
/     2\
sqrt\4 - x /
> TL := f(1)+df(1)*(x-1); # tangent line at (1,sqrt(3))
(1/2)   1  (1/2)
3      - - 3      (x - 1)
3

This works nicely and looks fine. Now change the function.
f := x -> sin(x);
x -> sin(x)
df := D( f );           # typed, or from context-menu
cos
TL := f(1)+df(1)*(x-1); # tangent line at (1,sin(1))
sin(1) + cos(1) (x - 1)
This works fine, but does not LOOK good. The problem is that Maple is TOO SMART. It knows that the derivative function (x->cos(x)) is simply the cosine FUNCTION. Instead of the abbreviation (cos) I want to be able to tell Maple to show this result as (x->cos(x)).

## More solve curiosities...

It's a new day, but not a new problem. Yesterday I asked about solving inequalities with abs. Today I am looking at solving an equation with abs. Try the following:
restart;
q :=  sin(x)/x - 1:
test4 := y -> [ y,
solve( q=y, x ),
[solve( abs(q)=y, x )],
fsolve( q=y, x ),
fsolve( abs(q)=y, x ) ]:
test4(  0  );
test4( 0.1 );
test4( 0.5 );
test4( 1/2 );
test4(  1  );

[                         /sin(x)           \                -13]
[ 0,   0, [0],      fsolve|------ - 1 = 0, x|, 1.869896012 10   ]
[                         \  x              /                   ]

## Solving Inequalities with Piecewise and ...

Quick, what numbers x satisfy:
abs( x-2 ) < 1
solve( abs( x-2 ) < 1, x );
RealRange(Open(0), Open(2))
Now, change the RHS to 1. (floating-point 1):
solve( abs(x-1) < 1., x );
RealRange(1., Open(2.)), RealRange(Open(0.), Open(1.))
Of course, these two intervals can be combined to the one interval. Maple 10 did not have this problem. (I will explain what Maple 11 is doing later, I want the next paragraph to appear in the truncated version of this post.) This issue is important for those of us trying to use Maple in the classroom. While it's not difficult to explain what is going on, the point is that this is not the mathematics I am trying to teach and these issues are a distraction.

## Bug in simplify with assumptions...

Consider the following:
restart;
abs(x)/x;
|x|
---
x
simplify( (1) );
|x|
---
x
simplify( (1) ) assuming x>0;  # OK
1
simplify( (1) ) assuming x=0;  # OK
0
simplify( (1) ) assuming x>=0; # Uh-oh
1
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