Questions tagged [arbitrary-precision]
Questions on the arbitrary precision capabilities of Mathematica.
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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 2.5326384172870370602159219766864657866396178797`20.124930050805514*^-12 to a high precision integer?
Mathematica gives me only 20 digits with ...
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4
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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
...
- 133
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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 ...
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2
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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:...
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ToString[SetPrecision[x,1.2]] doesn't work as expected
2nd Code Block demonstrates failure in comment of output
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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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1
answer
76
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Confusion about precision [duplicate]
When I evaluate
x = 1.0000000000000000001 (* Precision of 20 digits *)
Mathematica returns
...
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1
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107
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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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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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2
answers
1k
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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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answer
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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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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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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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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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1
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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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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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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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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):
...
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2
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1
answer
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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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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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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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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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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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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
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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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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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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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2
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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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1
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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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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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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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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
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268
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Interpolation function precision in multi dimentional case
I have this interpolation example
...
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1
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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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