# Questions tagged [number-representation]

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

29 questions with no upvoted or accepted answers
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### How would one add Hyperreals as a new type to Mathematica?

Hyperreals are an extension to the real numbers; they formalise the concepts of infinities and infinitestimals as numbers, rather than the named limit points outside of the system of reals and form ...
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### 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 ...
• 1,053
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### Why does an integer index inside a symbol become real when entering a ChebyshevT function with floating point arithmetic?

When I enter an indexed symbol into a ChebyshevT function with integer arithmetic like this: ChebyshevT[1, 3 * a[4]] I get the expected result: ...
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### How does Mathematica evaluate N[π, 30] == π?

I want to know how N[π, 30] == π works. The result is True. I wonder whether the exact number ...
186 views

### RealDigits and functional style

So while thinking about Replacing numbers of which you only know certain digits I have faced, again, a problem that I find hard to extract from RealDigits' output ...
• 137k
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### Check the data of representations of Lie groups

Is there a way in Mathematica to check the data of representation of Lie groups? For example, the number of generators. the rank (or the dimension) of the representation matrices. and a list of all ...
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### Rationalize error

The docs state that "Rationalize[x,dx] yields the rational number with smallest denominator that lies within dx of x." However, testing this out it appears to be false. ...
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### On numbers with N digits after comma in Mathematica

Consider a table tabb={{1.233546576,2.454546565},{22334.46687875465,6787233.3565665655}} I want to convert it into a table where all the numbers are only with 4 ...
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I'm trying to pad some binary and hexadecimal numbers using PaddedForm, and also to separate the digits into blocks of 4. For example, I'd like a number like ...
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### Question to developers: what are the actual or potential difficulties in implementing split-complex unity $j$ out of the box?

I wonder, what are some real or potential and purely theoretic difficulties you may face if you decided to implement the split-complex unity $j$ such that $j^2=1$ along with already existing complex ...
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1 vote
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### Extracting digits of a real number with RealDigits produces unexpected result

I have a list of real numbers, each of which has two decimal places. I'm trying to extract the second digit after the decimal point. The function I'm using is ...
• 1,291
1 vote
113 views

### Implementing the Binary GCD algorithm in Mathematica

Well, I have $n\in\mathbb{N}$ and I want to transform $n$ to a binary number which can be done using FromDigits[IntegerDigits[n, 2]]. I want to compute the ...
• 1,941
1 vote
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### How to Shape Text?

Imagine I have a certain number 23819657294172004194219023914217958273128471531429470113 If I convert it to a string with ...
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1 vote
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### How does this FromDigit module work?

I am entering the following input: ...
• 181
1 vote
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### Why does this reduce evaluate with exact numbers but not numbers specified to 20/50/200 decimals of precision?

Consider the following lines of code: ...
• 809
1 vote
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### 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 ...
54 views

### Combining numbers with fractional powers together

I get lots of numerical answers that have integers raised to fractional powers multiplying each other. A simple example: 2^(1/3) 3^(2/3) which is of course 18^(1/3). How do I get Mathematica to do ...
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### When there is decimal number in N[], how can ensure digits more than machine precision?

We know that N[3/7,100] will keep 100 digits after decimal point. But N[3.1/7,100] will Keep only machine precision fewer ...
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### Alternative for PowerRepresentations[n, x, 1]

I am looking for numbers $n$ that can be written as the sum of other numbers. So: PowersRepresentations[n, x, 1]. But is there a faster way of finding these numbers?...
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### How to copy and paste numbers with "" mark and use them in calculations, without using N or setting precision every time

Suppose we have run a calculation and get a number like 2.758952615889003 If we then copy-paste this number and do a calculation like ...
• 809
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### Correct way to format numbers

I have defined the following function: randvec[mag_]:= mag Normalize[Table[RandomReal[], {j, 1, 4}]] I would like to format the numbers in the list so that they ...
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### How to control the visible area (up and down the line) in NumberLinePlot?

How can you control the up and down line visible part of the graph? The target if view arrosw and text below the line (purple arrow) and if it´s posible make great the upper area ...
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### Solving a system of linear equations in Mathematica regarding the errors of different methods

I have a system of equations, i.e. 0.62243x + 0.51824y = 0.70524 0.71497x + 0.59496y = 0.80996 I have 3 ways to solve this system (there are more but I am ...
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### Decimal representation in Mathematica 10

I am using a slider to assign the value for a dynamic variable x, and want to display the value of y=10^Dynamic@x in decimal ...
• 101
Considering a fraction: val = "F \!$$\*FractionBox[\(1$$, $$1$$]\)"; I extract the part of interest: ...