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Search took 0.14 seconds. Search: Posts Made By: alpertron
Forum: Miscellaneous Math 2021-01-24, 16:14
Replies: 2
Views: 376
Posted By alpertron
I've just tested the first sentence written by...

I've just tested the first sentence written by the OP with values of x up to 10 million using the following line in PARI-GP:

for (x=2,10000000,n=x^3-x-1;if (Mod(x,n)^n==Mod(x,n) &&...
Forum: Programming 2020-12-25, 19:05
Replies: 37
Views: 10,676
Posted By alpertron
You are right. But the Eisenstein criterion...

You are right. But the Eisenstein criterion cannot be used for all polynomials.

There is still more room for optimization.
Forum: Programming 2020-12-25, 18:21
Replies: 37
Views: 10,676
Posted By alpertron
I've just added FFT for modular polynomial...

I've just added FFT for modular polynomial multiplications when the modulus is small. This enables faster factoring when trying to factor integer polynomials, especially when the number of modular...
Forum: Programming 2020-12-13, 21:06
Replies: 37
Views: 10,676
Posted By alpertron
I've just added TeX output to my polynomial...

I've just added TeX output to my polynomial factorization calculator located at https://www.alpertron.com.ar/POLFACT.HTM

For example, the roots of x17 + 1 are:

\begin{array}{l}...
Forum: Programming 2020-11-30, 17:15
Replies: 37
Views: 10,676
Posted By alpertron
I should add TEX output to my calculators when...

I should add TEX output to my calculators when requested by user. That would be an interesting addition to the programs.
Forum: Programming 2020-11-30, 15:47
Replies: 37
Views: 10,676
Posted By alpertron
There is a copy error. Using your input I get: ...

There is a copy error. Using your input I get:


x1 to x3 = 0
r = (19 + 3 * 33^(1/2))^(1/3)
s = (19 - 3 * 33^(1/2))^(1/3)
x4 = 1 + r + s
x5 = 1 - (r + s) / 2 + (i/2) * (r - s) * 3^(1/2)
x6 =...
Forum: Programming 2020-11-28, 23:13
Replies: 37
Views: 10,676
Posted By alpertron
I fixed the LLL routine and optimized the Hensel...

I fixed the LLL routine and optimized the Hensel Lifting. Now the factorization of polynomials of degree less than 1000 with small coefficients can be done in seconds.
Forum: Data 2020-11-26, 02:28
Replies: 6
Views: 1,148
Posted By alpertron
Thanks. So this was a false alarm.

Thanks. So this was a false alarm.
Forum: Data 2020-11-26, 01:06
Replies: 6
Views: 1,148
Posted By alpertron
Too few factors found in 600M to 620M

I've just looked at https://www.mersenne.ca/status/tf/0/1/2/60000 and I found that there should be some hardware error:

21192 factors in the range 600M-610M today in the 72-bit range: only 3...
Forum: Number Theory Discussion Group 2020-10-17, 02:44
Replies: 3
Views: 889
Posted By alpertron
Computing the Jacobi symbol is a lot faster than...

Computing the Jacobi symbol is a lot faster than modular exponentiation.

This is the source code I wrote in C language based on Crandall's and Pomerance's Prime Number book:


// Calculate...
Forum: Programming 2020-10-04, 21:20
Replies: 37
Views: 10,676
Posted By alpertron
When the irreducible polynomial has degree >= 5,...

When the irreducible polynomial has degree >= 5, now my code performs the factorization of this polynomials with prime modulus up to 100.

If the conditions of Keith Conrad's paper that you can...
Forum: FermatSearch 2020-10-03, 18:15
Replies: 65
Views: 6,212
Posted By alpertron
Before even thinking on performing the primality...

Before even thinking on performing the primality check of F33, a lot more trial factoring is needed and then someone has to run P-1.
Forum: Programming 2020-10-02, 19:42
Replies: 37
Views: 10,676
Posted By alpertron
All these examples are working now. Thanks for...

All these examples are working now. Thanks for finding the errors.

Please refresh the page to get the current version.
Forum: Programming 2020-10-02, 01:18
Replies: 37
Views: 10,676
Posted By alpertron
I fixed this error. Please refresh the page and...

I fixed this error. Please refresh the page and retry.


Since the application works with integer polynomials, the slash operator performs the division disregarding the remainder.

This means...
Forum: Programming 2020-10-01, 18:32
Replies: 37
Views: 10,676
Posted By alpertron
I've just fixed this error. Please refresh the...

I've just fixed this error. Please refresh the page so the Web page is dated 1 October 2020 and try again.
Forum: Programming 2020-09-30, 03:40
Replies: 37
Views: 10,676
Posted By alpertron
Now the response of the Web application is...

Now the response of the Web application is shorter for polynomials of the form x5+n (n = integer).
Forum: Programming 2020-09-30, 02:53
Replies: 37
Views: 10,676
Posted By alpertron
The values found by the solver are correct as you...

The values found by the solver are correct as you can see by unsetting pretty print, and then factoring it again.

This is the output of the calculator.


R1 = 0
R2 = (15625)^(1/5)
R3 = 0
R4...
Forum: Programming 2020-09-27, 22:47
Replies: 37
Views: 10,676
Posted By alpertron
Hello folks, I have added more features to...

Hello folks,

I have added more features to this calculator at https://www.alpertron.com.ar/POLFACT.HTM

Now it quickly factors integer polynomials with degree up to 1000 using Van Hoeij...
Forum: Factoring 2020-09-25, 03:28
Replies: 40
Views: 13,763
Posted By alpertron
I've just updated the page...

I've just updated the page https://www.alpertron.com.ar/BRILLIANT3.HTM with your results. Thanks a lot.
Forum: Factoring 2020-09-19, 00:24
Replies: 40
Views: 13,763
Posted By alpertron
I've just added the discoveries posted to this...

I've just added the discoveries posted to this thread to https://www.alpertron.com.ar/BRILLIANT.HTM and also fixed the errors detected at https://www.alpertron.com.ar/BRILLIANT2.HTM
Forum: Factoring 2020-09-13, 17:02
Replies: 40
Views: 13,763
Posted By alpertron
At this moment I'm making changes to my...

At this moment I'm making changes to my calculator that factors and finds the roots of polynomials (you can see it at https://www.alpertron.com.ar/POLFACT.HTM). After that, I will update the page of...
Forum: Lounge 2020-08-26, 14:44
Replies: 48
Views: 9,258
Posted By alpertron
In Argentina merchants are required to indicate...

In Argentina merchants are required to indicate the price per kg or liter, so this cheat cannot be done.
Forum: Data 2020-07-11, 19:34
Replies: 347
Views: 48,095
Posted By alpertron
After running my Nvidia GTX 950 for 30 days, I...

After running my Nvidia GTX 950 for 30 days, I was able to find more than 60 factors in the ranges 71->72 bits, 72->73 bits and partially in 73->74 bits, reducing the number of unfactored Mersenne...
Forum: Factoring 2020-06-15, 15:28
Replies: 22
Views: 7,233
Posted By alpertron
Your code takes too long for changing...

Your code takes too long for changing polynomials. But that step should be very fast (that is why SIQS is named in that way). Probably you are using very few primes in the construction of your...
Forum: Msieve 2020-04-25, 14:13
Replies: 11
Views: 5,576
Posted By alpertron
WebAssembly threads requires SharedArrayBuffer....

WebAssembly threads requires SharedArrayBuffer. This was implemented on major browsers but since Spectre and Meltdown attacks were found in January 2018, the feature was disabled in both Chrome and...
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