20191115, 02:40  #12 
Aug 2002
Buenos Aires, Argentina
3^{2}×149 Posts 
I've fixed several errors, including the number of digits in groups, a fix on biquadratic equations, now it works on Web browsers that do not support WebAssembly and other minor errors.
With respect to the equation mentioned by Dr Sardonicus, I fixed a few errors, but the support from the application is incomplete when the Galois group has order 5. I will continue working on this. 
20191115, 20:13  #13 
∂^{2}ω=0
Sep 2002
República de California
37×313 Posts 
Thanks, Dario! That works even on my old FFforMacOS10.6.8.
Was it much work to remove the WebAs dependence? I always say, if you can gain a lot of portability without having to expend inordinate effort, it's worth doing. But then again, I'm an oldtimer  I realize much of the New Economy is based on domain fragmentation, getting folks to pay multiple times for what is basically the same thing. :) 
20191115, 21:07  #14  
Aug 2002
Buenos Aires, Argentina
3^{2}×149 Posts 
Quote:
All my Web applications use WebAssembly because it runs 2 to 3 times faster than asm.js. This is important when you try to factor a big polynomial (or big number in https://www.alpertron.com.ar/ECM.HTM). Last fiddled with by alpertron on 20191115 at 21:18 Reason: typo 

20200927, 22:47  #15 
Aug 2002
Buenos Aires, Argentina
3^{2}·149 Posts 
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 algorithm (which includes LLL), but notice that with some big polynomials it is possible to get an out of memory bounds so the factorization cannot complete. Then it shows the roots of polynomials with degree up to 5 with radicals and trigonometric functions. Notice that the roots of most fifthdegree polynomials cannot be expressed with radicals or trigonometric functions. It also shows the roots of cyclotomic polynomials (x^n  1 and their divisors) and polynomials of the form ax^n + b and ax^(2n) + bx + c. For example, one of the roots of x^51  1 found by this calculator is: x44 = cos(80*pi/51) + i * sin(80*pi/51) = (1/32)*(1+17^(1/2)(342*17^(1/2))^(1/2)+2*(17+3*17^(1/2)+(170+38*17^(1/2))^(1/2))^(1/2)) + (1/16)*(3)^(1/2)*(342*17^(1/2)2*(342*17^(1/2))^(1/2)+4*(17+3*17^(1/2)(170+38*17^(1/2))^(1/2))^(1/2))^(1/2)(i/32)*(3)^(1/2)*(1+17^(1/2)(342*17^(1/2))^(1/2)+2*(17+3*17^(1/2)+(170+38*17^(1/2))^(1/2))^(1/2))(i/16)*(342*17^(1/2)2*(342*17^(1/2))^(1/2)+4*(17+3*17^(1/2)(170+38*17^(1/2))^(1/2))^(1/2))^(1/2) I have also added compatibility with screen readers so more people can access it. I tested it with NVDA and Narrator on Windows and Talkback on Android. Please let me know if you find some error. 
20200929, 16:02  #16 
Feb 2017
Nowhere
23×181 Posts 

20200930, 02:53  #17 
Aug 2002
Buenos Aires, Argentina
3^{2}·149 Posts 
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. Code:
R1 = 0 R2 = (15625)^(1/5) R3 = 0 R4 = 0 S1 = (1+5^(1/2))*(R1 + R4) + (15^(1/2))*(R2 + R3) S2 = (1+5^(1/2))*(R2 + R3) + (15^(1/2))*(R1 + R4) T1 = (10 + 2 * 5^(1/2))^(1/2)*(R4  R1) + (10  2 * 5^(1/2))^(1/2)*(R3  R2) T2 = (10 + 2 * 5^(1/2))^(1/2)*(R3  R2) + (10  2 * 5^(1/2))^(1/2)*(R4  R1) x1 = (R1 + R2 + R3 + R4) / 5 x2 = (S1 + i * T1) / 20 x3 = (S1  i * T1) / 20 x4 = (S2 + i * T2) / 20 x5 = (S2  i * T2) / 20 Code:
%1 = I (23:47) gp > R1 = 0 %2 = 0 (23:47) gp > R2 = (15625)^(1/5) %3 = 6.8986483073060741619503173210800884643 (23:47) gp > R3 = 0 %4 = 0 (23:47) gp > R4 = 0 %5 = 0 (23:47) gp > S1 = (1+5^(1/2))*(R1 + R4) + (15^(1/2))*(R2 + R3) %6 = 22.324494875306315076216696369277540320 (23:47) gp > S2 = (1+5^(1/2))*(R2 + R3) + (15^(1/2))*(R1 + R4) %7 = 8.5271982606941667523160617271173633913 <^(1/2))^(1/2)*(R4  R1) + (10  2 * 5^(1/2))^(1/2)*(R3  R2) %8 = 16.219694943147773999539440789223925778 <^(1/2))^(1/2)*(R3  R2) + (10  2 * 5^(1/2))^(1/2)*(R4  R1) %9 = 26.244017705167891715114016211195788877 (23:47) gp > x1 = (R1 + R2 + R3 + R4) / 5 %10 = 1.3797296614612148323900634642160176929 (23:47) gp > x2 = (S1 + i * T1) / 20 %11 = 1.1162247437653157538108348184638770160  0.81098474715738869997697203946119628889*I (23:47) gp > x3 = (S1  i * T1) / 20 %12 = 1.1162247437653157538108348184638770160 + 0.81098474715738869997697203946119628889*I (23:47) gp > x4 = (S2 + i * T2) / 20 %13 = 0.42635991303470833761580308635586816957  1.3122008852583945857557008105597894439*I (23:47) gp > x5 = (S2  i * T2) / 20 %14 = 0.42635991303470833761580308635586816957 + 1.3122008852583945857557008105597894439*I (23:47) gp > f(x)=x^55 %15 = (x)>x^55 (23:48) gp > f(%11) %16 = 2.350988701644575016 E38 + 4.701977403289150032 E38*I (23:48) gp > f(%12) %17 = 2.350988701644575016 E38  4.701977403289150032 E38*I (23:48) gp > f(%13) %18 = 2.350988701644575016 E38  2.938735877055718770 E38*I (23:48) gp > f(%14) %19 = 2.350988701644575016 E38 + 2.938735877055718770 E38*I (23:48) gp > f(%10) %20 = 4.701977403289150032 E38 
20200930, 03:40  #18 
Aug 2002
Buenos Aires, Argentina
3^{2}×149 Posts 
Now the response of the Web application is shorter for polynomials of the form x^{5}+n (n = integer).

20201001, 12:39  #19 
Feb 2017
Nowhere
23×181 Posts 
My mistake, I was merely having trouble reading the output. New version with sine/cosine renderings of roots of unity is much easier on my dim old eyes, thanks!

20201001, 12:59  #20  
Apr 2012
2^{2}·7·13 Posts 
Quote:
Cheers. Last fiddled with by jwaltos on 20201001 at 13:03 

20201001, 15:24  #21  
"Robert Gerbicz"
Oct 2005
Hungary
1,429 Posts 
Quote:
it shows: Your polynomial −1 Clearly wrong. 

20201001, 18:32  #22 
Aug 2002
Buenos Aires, Argentina
1341_{10} Posts 

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