How to translate from Maple to Maple TA?

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How to translate from Maple to Maple TA?

Posted on 2008-02-26 13:20 By sreid (

11)

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How do I ...? with Maple T.A.

I know how to solve a problem in Maple, but can't translate into Maple TA. I'm teaching elementary statistics, and want students to estimate a median using a cumulative frequency distribution.

In Maple, I randomly generate some intervals and frequencies. Then I define the CFD by giving the end points and the cumulative frequency, like;
(1) XY:= Array([[x0,cf0],[x1,cf1],[x2,cf2],[x3,cf3],[x4,cf4]]);

Then I use the endpoints to define a spline (the ogive or CFD). Then I invert it, and find the value of x that is equal to the y4/2:
(2) solve(CurveFitting[Spline](XY, x, degree=1)=(cf4)/2,x);

So, now I want to write a Maple TA question that gives the student random frequencies and asks them to estimate the median from the CFD. How do I write an algorithm to generate (2) as an answer? I've tried:
(3) $med=maple("map(x->solve(CurveFitting[Spline]($XY, y, degree=1)=x,y),$cf5/2)");
but I just get a message saying: Warning, solutions may have been lost

I'm using Maple TA 3.01 and therefore I've written the above in Maple 11.

Thanks in advance,

Stephen

why use map?

Comment on 2008-02-26 17:15 from Doug Meade ( Maple Rating 4

612)

Stephen,

Why do you need the extra map? Have you tried using:

$med=maple("solve(CurveFitting[Spline]($XY, x, degree=1)=$cf5/2,x)");

But, I believe the real problem is that some of the data in XY, or cf5, is not numeric. I get the solutions may be lost message if I call solve with symbolic values in XY.

Also, I notice that your XY ends with cf4 but you later refer to cf5. If all data is numeric, then I have no trouble.

Good luck

Doug

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

another issue

Comment on 2008-02-26 22:38 from Alex Smith ( Maple Rating 3

232)

Doug is probably right, something is not numeric.

But another observation is your use of an arrow.

If I set up a function in MapleTA by the construction

$f=maple("x->x^2");

then MapleTA throws errors. I find I need to use

$f=maple("proc(x) x^2 end");

$f=maple("unapply(x^2,x)");

How to invert a (spline) function in Maple?

Comment on 2008-03-04 14:08 from sreid (

11)

Thanks for the help. I changed to defining numeric values first, and cleaned my formulas up as suggested, and now it works the same in Maple and Maple TA. However, it doesn't work properly. An example:

A:=Array([[2.5,0],[4.5,3],[6.5,12],[8.5,25],[10.5,40],[12.5,47]]);

These (x,y) pairs are monotonically increasing.

evalf(solve(CurveFitting[Spline](A, x, degree = 1) = (47/2),x));

This finds the point on the spline connecting the points that marks the median. Maple gives two answers, however:

8.269230769, 8.300000000

When I check with my calculator, the first number gives 23.5 when substituted, but the second gives 23.7. When I perform a similar to find the first quartile (solve...=47/4,x) Maple (and Maple TA) gives three answers, the right one and two others.

If I plot the spline it is monotonically increasing, so the inverse shold be well defined. What don't I understand?

Thanks in advance.

Stephen

The problem with multiple answers

Comment on 2008-03-04 15:47 from sreid (

11)

I should add that the biggest problem is that Maple TA grades the right answer as wrong. I'm not sure how it obtains the other answer, so I'm not sure it that would be marked correct, or if it is expecting two answers. I probably would not have really looked at it if it accepted either answer. I'm not sure how likely it is that a student would stumble across Maple's "wrong" answer, so I don't know how big a problem that would be.

On a somewhat related note, if I feed it a sample of numbers with more than one mode, Maple's Mode function only reports the smallest one, and Maple TA will only accept that as the right answer. In that case I would like it to accept all of them as the only answer worth 100%.

TIA

Stephen