Questions tagged [arbitrary-precision]

Questions on the arbitrary precision capabilities of Mathematica.

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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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Confusion about precision [duplicate]

When I evaluate x = 1.0000000000000000001 (* Precision of 20 digits *) Mathematica returns ...
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-3 votes
1 answer
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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 ...
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1 vote
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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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Rational numbers in NDSolve

Is it possible to use NDSolve with Rational numbers instead of Real? I use all rational ...
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6 votes
2 answers
628 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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3 votes
1 answer
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Precision in Graph methods

It appears that GraphDistance, GraphDistanceMatrix, FindShortestPath, etc. all work with ...
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127 views

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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General:munfl error problem

I have the following function, that is the result of The integration between x and some upper limit of a positive function, thus should be positive $f(x,vE) = \frac{e^{-1140.09 x} \left(e^{67945.5 \...
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3 votes
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How to deal with too small numbers

When dealing with a code that produces too small numbers (in a complicated way) like 0.33691 4.015757066049965*10^-330 I get the following warning General::munfl: ...
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1 vote
1 answer
80 views

InverseFunction: Precision problem

I define a function SS[t] as an inverse function: ...
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2 votes
2 answers
120 views

Most efficient strategy for integrating over removable poles?

I am finding many situations where I have to numerically integrate some function $f(x)$ of the form: $$f(x)=f_{s}(x)-ax^{-n},$$ where $f_s$ is a special function with a finite-order pole that is ...
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Shouldn't NIntegrate return a number whose Precision is PrecisionGoal, not WorkingPrecision?

I know that Mathematica has great built-in precision tracking, so when you do calculations with arbitrary-precision numbers, Mathematica keeps track of the precision on the result. Given this careful ...
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Use Check in a While loop without wasting the calculation

I am trying to generate and solve a matrix that tends towards being singular using variable arbitrary precision to ensure accuracy. Consider, for example, a matrix with tunable singularity: ...
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Solving linear systems efficiently

In certain calculation I encountered a system of linear equations in 144 variables, and it takes hours to compute. Most probably the reason is that coefficients are really huge integers (about $10^{50}...
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2 votes
1 answer
118 views

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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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 ...
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1 vote
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121 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
2 answers
137 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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1 answer
49 views

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): ...
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2 votes
1 answer
73 views

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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2 votes
0 answers
53 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 ...
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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 ...
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4 votes
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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 ...
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5 votes
1 answer
142 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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39 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 ...
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1 answer
78 views

Why this very simple problem turns to "Indeterminate"?

Why the following calculation gives Indeterminate value? ...
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1 answer
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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
1 answer
91 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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5 votes
0 answers
56 views

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
1 answer
509 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 ...
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2 answers
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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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1 answer
69 views

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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9 votes
1 answer
207 views

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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5 votes
2 answers
501 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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9 votes
1 answer
232 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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5 votes
2 answers
210 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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8 votes
1 answer
824 views

What is wrong with importing Real32 or Real64?

Those who visit the chat might have seen the question of varkor. I'm posting it here in the hope that I have missed something. Assume you have a real number ...
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6 votes
1 answer
284 views

Mathematica precision common problems

When I do something a little bit more complicated than standard documentation examples, I often hit precision problem. Or I accidentally disprove Riemann hypothesis Like this ...
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1 vote
1 answer
197 views

Interpolation function precision in multi dimentional case

I have this interpolation example ...
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3 votes
1 answer
286 views

Can NDEigensystem use arbitrary precision arithmetic?

Consider the following computation of an eigenfunction of 1D Laplacian on the interval of $[0,\pi]$: ...
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7 votes
2 answers
2k views

Fast integer square-root

I'm looking for the highest-performance method of calculating integer square roots in Mathematica of very big arbitrary-precision numbers. As an example testcase, I use: ...
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2 votes
1 answer
178 views

plot of polynomial expression failed [duplicate]

I want to plot a polynomial expression for {a,0,1}: ...
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1 vote
1 answer
112 views

Rigorous error bounds for `NIntegrate`

Suppose I want to numerically evaluate an integral of the form $$\int_{-\infty} ^\infty f(x) \mathrm{d}x $$ with error not exceeding some positive bound $\epsilon$. Is there a way to do this using <...
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  • 1,028
6 votes
4 answers
448 views

How do I convert an inexact number smaller than $MinMachineNumber to machine-precision?

I was trying to convert some arbitrary-precision numbers to machine-precision numbers using N[myNumber,MachinePrecision]. But, although my test number did lose some ...
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  • 6,902
0 votes
0 answers
58 views

Arbitrary precision calculation makes my computer hang

I have this code list = Accumulate@Tan[N[Range[10^8]]]; // AbsoluteTiming and the timing is slightly more than two seconds. Now if I try to compute this ...
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