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Questions tagged [number-representation]

Questions about interpretation of numeric input or how Mathematica stores and manipulates numbers internally.

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117 views

Is there a Real equivalent to FromDigits?

One can extract an Integer's digits using IntegerDigits and reassemble them into the Integer ...
4k views

How to implement Donald Knuth's up-arrow notation

How does one enter very large numbers in up-arrow notation? Up-arrow notation was created by Donald Knuth to write very large numbers in it iterated exponentiation form, for example 6↑↑3 = 6^6^6.
836 views

Converting strings of the form “1.34e5” to real numbers? [duplicate]

ToExpresssion doesn't understand real numbers of the form "1.34e5". How do I convert the string ...
487 views

Machine Epsilon

I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this: ...
730 views

How to work with large numbers

How do I browse very large numbers in mathematica, say $10^{{10}^{{10}^{1.414\ldots}}}$? By browse I mean finding the $k$th decimal place before or after the decimal point. Everything I have tried ...
200 views

The precision of the number

I have problem in Mathematica with unnecessary rounding which is caused by high precision. For example I have value a = 2.052685846*10^-1865, when I make ...
185 views

Square root of a value defined in a finite field?

I am trying to find the right way to compute the square root of a number defined in a finite field. For example, ...
276 views

NMinimize seems to call function with the same values multiple times

I have to minimize a function where the evaluation of one parameter set takes very long (around 5sec) and discovered alongside, that NMinimize seems to call this ...
892 views

Enter exact rational numbers easily with decimal notation

Is there a simple way to enter decimal numbers such as 0.123 so that Mathematica interprets it as an exact rational number 123/1000?
118 views

Function that returns the binary string given its index in lexicographic ordering

Index the binary strings in lexicographic order, so that the empty string " " corresponds to 0, the string "0" corresponds to 1, the string "1" to 2, and so on. I want a function that, given a ...
164 views

Showing AlgebraicNumber[1/2 (1 + Sqrt), {-3, 2}] in human-readable way

Is there a function to show algebraic numbers in Mathematica more conveniently? I am looking for something similar to MatrixForm for matrices. For example, I would like to view ...
39k views

Entering numbers in Scientific Notation?

I need to play with a lot of powers such as 10^-3. 1E-3 does not work for it. Is there any short form for it?
100 views

Avoid unnecessary truncation

Is there any way to change the general settings in Mathematica so that when I type e.g. 0.34*60000000 I get the output ...
8k views

Convert Integer to Real [duplicate]

Is there a preferred way of converting an Integer to a Real? What I'm using at the moment is ...
3k views

How to plot logarithmic scales

How can a simple logarithmic number line be drawn between any 2 integer values? The closest function I found in the documentation is LogLinearPlot[] and I've been ...
118 views

How to interpret and show an input number with the amount of significant digits given?

what can I do to have Mathematica intepret and show a number with exactly the amount of digits I gave as an input? I have a larger talbe with numbers (text file, whitespace seperated) which are ...
3k views

When can I assume that all decimal digits returned by Mathematica are provably correct?

How to Control the Precision and Accuracy of Numerical Results Arbitrary-Precision Numbers Mathematica works with exact numbers and with two different types of approximate numbers: machine-...
296 views

Finite precision - how to get rid of “near zeros” [duplicate]

I am performing a finite-precision operation on a matrix A which I know precisely; call the result B. The operation is taking ...
1k views

Expression of uncertainty in measurement.

I have a problem with writing a Mathematica function. I have been requested to show the results of my experiments with the measurement uncertainty (mu) like below: ...
4k views

How do I get Mathematica to show a number in non-exponential form? [duplicate]

Sometimes I make a calculation in Mathematica that produces a big number, which Mathematica shows like so: -1.52522*10^7 This is annoying to me, because I want ...
323 views

Is it possible to lower the bitwidth of (floating point) numbers?

The answer to this question will most probably be a definite no. Nevertheless, I would like to know whether it is possible to represent reals in the memory on less than the standard 32 or 64 bits (...
837 views

How can I change the default output number form to accounting form?

By default, large numbers are displayed in scientific form in output like 1.2345 x 10^8 in Mathematica 8.0.4, but I would prefer having numbers in accounting form ...
844 views

Number with no decimal mark

I'm using Mathematica to create some images and labeling them after a simple calculation done previously. As the name of the file depends on the result, I want to show it with no decimal separator (...
2k views

Number format in Legend Labels

I would like to use the usual (new and nice) BarLegend[] with something like BarLegend[{"LakeColors", 1/10000 {-2, 2}}] which ...
751 views

Fast Karatsuba Squaring, how to?

I want to improve timing of squaring for big numbers. So I asked What is the fastest way to split a number into parts and What is the most efficient way to add zeros to end of a number with several ...
401 views

What is the most efficient way to add zeros to end of a number?

Beside *10^n, is there a faster way to add thousands of zeros to end of a number? Updated Timings: ...
699 views

What is the fastest way to split a number into parts?

I have very large numbers (million digits). number = A*10^partlen + B As of now, I split the numbers by this way: ...
4k views

Convert a string to hex number?

How can I convert a string containing a hex number such as "6b" to a hex digit that mathematica can use to do math with? I have tried using ...
771 views

hexList[] returns a list of decimal numbers

Sorry for not being clear about this question earlier. I appreciate the answers I got, but the edits I made should make the question more understandable. I have been working with hex in Mathematica,...
3k views

Change number from real to integer [duplicate]

Possible Duplicate: Is this the most efficient way to round approximate integers to integers while leaving other Reals untouched? Please consider the following: ...
896 views

Representation of negative exponents [duplicate]

Possible Duplicate: Way to improve “show me this decimal number to M places, don't use scientific notation”? How can I expand e.g. number 1.*10^-8 so that there would be no ...
3k views

Converting numbers to integers

I've read the available documentation but I still haven't found an NumberForm -> Integer function yet. No result in this site's search, either. Does it exist? ...
1k views

decompose a number (less than 255) in a sum of powers of 2

Is there a built in function that would take a number and decompose it into a sum of powers of 2? The numbers will be non negative less than 256. For what it's worth I'm trying to understand a paper ...