# Questions tagged [arbitrary-precision]

Questions on the arbitrary precision capabilities of Mathematica.

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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: ...
39 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 ...
40 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 ...
118 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 ...
72 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 ...
32 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 ...
59 views

### Why this very simple problem turns to “Indeterminate”?

Why the following calculation gives Indeterminate value? ...
54 views

### 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]. ...
78 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 ...
47 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 ...
121 views

### How can I suppress the warning $\mathrm{\it precision\ may\ be\ lost}$?

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 ...
318 views

### 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 ...
56 views

### 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]]: ...
46 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....
92 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, ...
371 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 <...
166 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: ...
139 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: ...
447 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 ...
220 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 ...
84 views

### Interpolation function precision in multi dimentional case

I have this interpolation example ...
182 views

### Can NDEigensystem use arbitrary precision arithmetic?

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

### plot of polynomial expression failed [duplicate]

I want to plot a polynomial expression for {a,0,1}: ...
79 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 <...
284 views

I have encountered weird buggy behavior of EllipticK with arbitrary precision input and when $MinPrecision is set. Consider the following code: ... 2answers 443 views ### Why does SetPrecision not apply to 0? Is there a rationale why SetPrecision works on integers except for 0? SetPrecision[1,5] 1.0000 ... 1answer 711 views ### Why does 1 - Exp[-10.0^12] cause an out-of-memory error? I would like to understand why evaluation of the expression 1 - Exp[-10.0^12] causes an out-of-memory error and how can I prevent such errors when calculating ... 1answer 76 views ### Why does SetPrecision drop “unknown” digits if precision requested is Infinity but retain them if it's finite? I was trying to reset the imprecision record of a number like 0.00760222661227556321.025 by calling SetPrecision with second ... 0answers 225 views ### Bug? Numerical calculation error with FullSimplify and arbitrary precision Bug introduced after 5.2, fixed in 8.0, reintroduced in 9.0 and persisting through 11.3 Is this a bug? If I do FullSimplify[n E^(0`10 n)] then it returns <... 2answers 275 views ### Integrate over sharp peak [closed] Hi I have a function that has a sharp spike. I need to NIntegrate over the peak but it seems that NIntegrate does not handle it well. Actually as far as I can tell, even the evaluation of the ... 0answers 120 views ### Does Mathematica implement its own methods of tracking precision? [closed] I know that for arbitrary precision arithmetic Mathematica uses GMP. But apart from just providing arbitrary precision, Mathematica also does precision tracking for its arbitrary-precision numbers, so ... 1answer 191 views ### Arbitrary-Precision Arithmetic behaves unexpectedly I want to understand how small numerical errors propagate through a computation and may drastically change the final result. To this end, I consider a toy world in which every number is limited to ... 1answer 83 views ### Finding the probability of one or more very unlikely successes in an enormous number of Bernoulli trials I'm trying to find an upper bound on the complexity of a self-replicating matter pattern in order for it to be at all probable for it to spontaneously occur in the universe. The idea being, if some ... 1answer 151 views ### Specify a decimal value as exact I would like to specify that a number is exact, even though it contains a decimal point. For example, I would like to be able to write some variation of 3.4 and ... 1answer 213 views ### How to disable roundoff error tracking in arbitrary precision arithmetic? In my calculations I need some larger precision. But due to the fact that I iteratively refine the results to compensate for rounding errors accumulated in previous iteration, Mathematica's arbitraty ... 0answers 71 views ### Why is distributing the definitions of a list of arbitrary precision numbers so slow? For a parallel application I need to make a large list of numbers available to the parallel kernels, which I do using DistributeDefinitions. I have noticed that this is much slower when the numbers ... 0answers 74 views ### Matrix ODE gives badly-behaved numerical solution [duplicate] I am trying to solve matrix ODE: ... 2answers 150 views ### Why do I get number with Precision larger than error estimate? I'm trying to integrate a large function like this ... 1answer 127 views ### Why does this expression involving HypergeometricU and$MinPrecision crash?

Bug introduced in 10.0 and fixed in 11.0 Can somebody help me understand why the following code snippet cause the Mathematica kernel to crash (without producing any further error messages)? ...
208 views

### $N[a,50]-N[a,10]=0$ why? and what's the rationale behind?

Let $a=\sqrt{3}$. What's the point of having In[102]:= N[Sqrt[3],100]-N[Sqrt[3],10] Out[102]= 0.*10^-10 ? Let's imagine I wanted to get the difference between ...