# Questions tagged [arbitrary-precision]

Questions on the arbitrary precision capabilities of Mathematica.

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### Arbitrary precision workflow

Please, consider the following MWE representing my code: ...
• 181
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### Plot freezes with arbitrary precision complex evaluations

I find that Plot has some strange behavior. a = {{-5.3553 I, 0.15893 }, {2.3053, 0.014253}}; Det[a] // Abs gives ...
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### NDSolve with integrated event, discrete variable and arbitrary-precision arithmetic gives error

I'm trying to solve an ODE numerically with NDSolve but get an unexpected error message (ExperimentalNumericalFunction::nlnum1),...
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### Is there a way to convert a high precision value to its digits?

Is there a way to convert a number like 2.532638417287037060215921976686465786639617879720.124930050805514*^-12 to a high precision integer? Mathematica gives me only 20 digits with ...
214 views

### Calculating the angle between vectors returns small complex number instead of zero

I am calculating the angle between vectors $$cos(\theta{_a}{_b}) = \frac{a^T b}{||a|| ||b||}$$ In mathematica I am coding ...
149 views

### How to get correct numerical result without lots of digit precisions?

I am wondering if it is possible to get the correct numerical result without computing with a lot of precisions in expressions. as a simple example suppose in the middle of some of my numerical code ...
257 views

### How to prevent Mathematica from rounding some PDF values to 0?

Dear Mathematica community, I'm having a problem with the PDF function for the hypoexponential distribution. Specifically, Mathematica returns 0 as soon as the value is very small. Below is an example:...
57 views

### ToString[SetPrecision[x,1.2]] doesn't work as expected

2nd Code Block demonstrates failure in comment of output ...
31 views

### Issues with ConvexOptimization and SetPrecision

I am completely new to Mathematica (second day), so do not expect things to look polished. I am trying to perform a ConvexOptimization over a List/Array (dimensionality ...
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When I evaluate x = 1.0000000000000000001 (* Precision of 20 digits *) Mathematica returns ...
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### long division acurate answer on dividing long numbers [closed]

ok but first of all if i have the huge number to be divided what will i have to use for the division to be accurate long division or some other formula square root or 2 this is to calculate music ...
1 vote
57 views

### Finding the position of maximal value when dealing with precision numbers [closed]

In for example this answer a solution is given to find the position of a maximal value. However, this solutions seems to run into trouble when dealing with precision numbers. Take the following ...
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111 views

### Rational numbers in NDSolve

Is it possible to use NDSolve with Rational numbers instead of Real? I use all rational ...
• 141
2k views

### How to force Mathematica to do infinite-precision calculations?

Consider the following calculation: 1234*5678*90.12 The result is: 6.31439*10^8 However, I want to get a precise result. Of ...
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### Precision in Graph methods

It appears that GraphDistance, GraphDistanceMatrix, FindShortestPath, etc. all work with ...
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### How to use Equal for close arbitrary precision numbers to be considered the same?

I am trying to add a comparator function in a larger piece of code which can equate two arbitrary precision numbers and yields True if they are approximately close. ...
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1 vote
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### Difficulty when trying to find roots to high accuracy

I'm working with the logistic map $f(x,\lambda)=4\lambda x(1-x)$, and iterations of the logistic map $f^{(2^n)}(x,\lambda)=f^{(2^{n-1})}(f^{(2^{n-1})}(x,\lambda),\lambda)$. There are some special ...
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1 vote
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### Can I change the default behavior so that "0.1" is interpreted as "1/10" automatically?

Consider the function f[a_] := NIntegrate[Sqrt[a + Log[x]], {x, 1, 10}, WorkingPrecision -> 30]. With this definition, I cannot call ...
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### Increase precision of ConvexHullMesh

I want to generate a set of equations for all planes in the convex hull as specified in this question. The problem is that the generated set of equations don't correctly cover all the points. I run a ...
1 vote
175 views

### FindMaximum does not use requested WorkingPrecision

I think that there is a bug in the way FindMaximum handles WorkingPrecision for constrained problems. Has anyone encountered a similar problem before? Is there a work around? Here is an example in ...
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### LinearSolve in arbitrary precision has a sudden change in performance as the size of a problem is gradually increased

It is expected that calculations in arbitrary precision are much slower than in machine precision. However, LinearSolve has an unexpected behavior: there is a ...
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1 vote
156 views

### Does SetPrecision[x, Infinity] expose the internal exact number in the approximated number?

What I already know (maybe) : My theory about Mathematica's way of implementing approximated number An number approX with arbitrary precision ...
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### How to initialize arbitrary precision?

How do I calculate $$\frac{1}{{\frac{1}{7 \times 10^7}- \frac{8\times10^{17}\times 3.1\times 10^7}{6.7 \times 10^{-11}\times \left(1.9 \times 10^{27}\right)^2} }}\tag{1}$$ To arbitrary precision? I ...
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### Creating an interpolation matrix efficiently

I would like to know if there is a fast way to create the following matrix (note that the matrix is defined with arbitrary precision): ...
• 585
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### Dealing with zero at high precision

I am using mathematica to deal with rational functions, $p(x)/q(x)$, where the polynomials, $p,q$ have a high degree and coefficients with high order of precision, e.g: ...
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54 views

### Set Underflow precision in Mathematica 12 same as version 11.x [duplicate]

It seems like Mathematica version 12 sets arbitrary underflow precision depending on the function, but I would like the underflow precision to be same as what was for previous version of Mathematica ...
48 views

### What is the limit of digits to show in the conversion of an exact number to an Arbitrary Precision Number?

By executing something like N[π, c] what is the maximum positive integer value c can have until the output is compromised by ...
130 views

### 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 ...
198 views

### Linear Algebra in Arbitrary Precision - SLOW

I am trying to implement an arbitrary precision algorithm, but I am not very familiar with Mathematica or arbitrary precision arithmetic. I was able to implement it but surprised by how much slower it ...
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1 vote
65 views

### Changing machine precision notebook-wide leads to peculiarities

For a project of mine it is preferrable to set notebook precision globally. I have done so by using the answer in Global precision setting. The idea is to dynamically create a ...
• 177
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### Why this very simple problem turns to "Indeterminate"?

Why the following calculation gives Indeterminate value? ...
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### Preventing Mathematica from considering small values to be equal to zero [duplicate]

In my calculations I have a variable (say z) which can be an argument of Log, say, z Log[z]. ...
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1 vote
98 views

### Number definition and approximation

I run these lines: a = 0.833 SetPrecision[a, 20] and this is the output: 0.833 0.83299999999999996270 I expected to ...
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### DumpSave and precision of interpolation data

Consider the following prec = 32; x = N[Range[0, 1, 1/10], prec]; f = Interpolation[Transpose@{x, x}]; Then ...
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1 vote
760 views

### How can I suppress the warning "precision may be lost"?

When I import data from a .dat file, V11.3 emits the message: is too small to represent as a normalized machine number; precision may be lost. How can I close the ...
• 617
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### Truncate a number in mathematica

I want to truncate a simple number to n decimal digits. For example, 2/3. I used f[x_, n_] := N[IntegerPart[x 10^n]/10^n] but I get ...
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### How to get the correct result in a simple operation in Mathematica

I have the following values for x[[i]], y[[i]] and A[[i,j]]: ...
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### Simple division with high precision in Mathematica [closed]

I want to do a simple division i.e. 0.70524/0.51824 . What I want is to find the result of the roundation of this division for precision from 1 to 19 decimal digits....
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### Arbitrary Precision, Nearly-Singular Matrices, and LinearSolve

I have been trying to solve a nonlinear eigenvalue problem, $\mathbf{M}(\lambda) \mathbf{v} = 0$, in Mathematica using Newton's method. The core of the algorithm relies upon an inverse iteration, ...
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611 views

### Why does N not upgrade precision? [duplicate]

Precision[N[1.0, 20]] Precision[N[1, 20]] MachinePrecision 20. It would be so much more intuitive and less error prone, if <...
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255 views

### Plot3D discrepancy between MMA 10 and 11.3 - possible small numbers issue

I'm having some troubles with the following code I wrote in MMA 10 some time ago: ...
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226 views

### Early vs. late application of arbitrary precision

The following arbitrary-precision computations, in which arbitrary precision is applied early (to the inputs), both work as expected: ...
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