Issue 4: I am counting on M to be the gold standard with arbitrary precision. Some calc examples leave me puzzled. ... I really need to understand ... why the returned value is not to the requested precision.

Yep, this is a common hurdle when you start with Mathematica. If you write a decimal number with just a decimal point and no other indication about precision, it will assume default precision (something like 15 decimal digits). Wrapping such a number with N won't do anything, because N just tries to turn an expression into a number. N does allow you to specify precision (or just use the default), but it can only reduce precision, never increase it. One way to tell Mathematica what precision you want a number to be is to use the backtick:

0.9 (* this will have default precision *)
0.9`100 (* this will have 100 digits of precision *)

So, let's look at your EllipticK computation:

(* Start with infinite precision input and ask for 24 digits of precision in the output--generally the
safest way. The FullForm will show us the "true" value that Mathematica is using, not the simplified
display representation *)
N[EllipticK[49999999/50000000], 24] // FullForm
(* 10.25006118906640692521926382963816467107`24. *)

(* Start with a certain precision in your inputs and lose some during the computation. *)
EllipticK[0.99999998`24] // FullForm
(* 10.25006118906640692521926382963819144403`17.311756326608677 *)

(* Overspecify the starting precision to account for the loss in precision. *)
EllipticK[0.99999998`31] // FullForm
(* 10.25006118906640692521926382963816467854`24.311756326608673 *)

You'll probably want to start reading here: http://reference.wolfram.com/language/guide/PrecisionAndAccuracyControl.html

Thanks for the quick and clear responses. I think I have 3 of 4 items down OK. As far as directory set, I figured out that I need to use forward slash(/) in path definitions and not the backslash(), which gets interpreted as an ESC as you noted. In my case "D:/temp" works as input to Mathematica, while the std windows form is "D:\temp. I notice that the echoed return value is the std windows form.

I tried the transpose form you suggested, but it didn't work for me. See attached jpg of program and resulting csv output.

I set up a two-row numeric matrix with m1 = {{1, 2, 3}, {4, 5, 6}}.

Then using Export["test_num2.csv", m1], created the following: 1,2,3 4,5,6 as expected. Using Export["test_num2T.csv", Transpose[m1]] results in a file with 1,4 2,5 3,6 This is good. What I don't know how to do is to have a variable 'forget' its history. I tried a simple example: q=Pi qn=N[q,10] I expect qn to be a 10 decimal approximation to pi, a finite decimal and nothing more. Evaluating N[qn,10] and N[qn,20] give identical 10-digit results. qn is no longer pi, but a finite approx.Yeah! However, in the attached example, the line xn = N[Column[x/50], 20] does not seem to create a set of specific approximate decimal numbers, but seems to maintain its embedded history. How to fix so that the exported entries are as displayed in xn?

Lou

Attachments:

test2.csv

transpose-export.jpg

It might be better at this point to add a new question. By starting fresh you can isolate your new question, and then maybe folks can understand better what you're asking.

Since you're new to Mathematica, I'm going to be presumptuous and provide some guidance that you didn't ask for about something that commonly trips up newcomers.

Understand that NumberForm is just a special wrapper. Evaluate this:

NumberForm[1`20, 20]

The result will look something like this: 1.0000000000000000000. But if you look at the actual structure of the result by evaluating FullForm,

FullForm[NumberForm[1`20, 20]]

you'll see that it's

NumberForm[1.`20., 20]

NumberForm, and all of the related *Form functions are just wrappers that tell the front end how to display something. This can cause problems if you subsequently want to do calculations:

NumberForm[1`20, 20] + 1

The result displays as 1+1.0000000000000000000, because the evaluator doesn't know how to do arithmetic with NumberForm expressions, and the evaluator is looking at

Plus[1, NumberForm[1.`20., 20]]

There are many intricacies with the usage of NumberForm and of N. According to documentation,

NumberForm works on integers as well as approximate real numbers.

The number 1/50 is neither integer nor approximate real. You must first convert it to approximate with N. Also, you cannot apply NumberForm to a whole column, but only to single numbers:

Column[Map[NumberForm[N[#, 20], 20] &, {1, 2, 4, 6, 7, 49.999999}/50]]

This version may be easier to parse:

Column[{1, 2, 4, 6, 7, 49.999999}/50]
N[%, 30]
NumberForm[%, 20]

First you see the numbers as you typed them. Then you see what happens by calculating all exact numbers with 30 digits of precision but default display. Last we see all numbers that have at least 20 digits of precition displayed with 20 digits.

The matter is complicated. Don't get discouraged if you feel confused at the start.