20191112, 20:32  #1 
Aug 2002
Buenos Aires, Argentina
10100101000_{2} Posts 
Calculator that can factor and find exact roots of polynomials
Hello folks,
I have uploaded to https://www.alpertron.com.ar/POLFACT.HTM a calculator that can factor polynomials over the integers or modulo a power of a prime. It also can find exact roots of polynomials expressed with radical expressions. At this moment the roots are shown only if the degree of the irreducible factor of the input polynomial is <= 5. It also indicates when the quintic equation cannot be expressed as radical expressions. Please let me know if there is any error. 
20191112, 21:22  #2 
∂^{2}ω=0
Sep 2002
República de California
2C31_{16} Posts 
I opened a new tab in my FF session, went to your page, enabled JS in NoScript, and, with a view toward polyfactoring x^41 as a little test, entered 41 and clicked 'factor'. I notice that whether I click 'evaluate' or 'factor', both those buttons go gray together, and "Factoring polynomial..." appears. Waited a full minute before killing it ... no result.

20191112, 21:31  #3 
Aug 2002
Buenos Aires, Argentina
2^{3}×3×5×11 Posts 
I started Firefox 70.0.1 on Windows 10, entered .41 so it showed x^41 in the polynomial box, then I pressed the Factor button. The output with Pretty Print disabled is:
Code:
x^4 − 1 Irreducible polynomial factors: x − 1 x + 1 x^2 + 1 Roots: x1 = 1 x2 = 1 x3 =  1 *i x4 = 1 *i Time elapsed: 0d 0h 0m 0.0s 
20191112, 22:11  #4  
∂^{2}ω=0
Sep 2002
República de California
3^{3}·419 Posts 
Quote:


20191112, 22:16  #5  
Aug 2002
Buenos Aires, Argentina
2^{3}×3×5×11 Posts 
Quote:
With respect to the second part, my code does not know what operating system is running. It uses Javascript and WebAssembly. Maybe you have not enabled WebAssembly in your plugin. Last fiddled with by alpertron on 20191112 at 22:24 

20191113, 11:32  #6 
Aug 2002
Buenos Aires, Argentina
2^{3}·3·5·11 Posts 
I installed the NoScript extension to Firefox on Windows 10, and the Javascript was disabled when I loaded the calculator. After selecting "Temp TRUSTED" for my Web site, it worked OK and I could see the responses from the application.

20191113, 17:02  #7 
Feb 2017
Nowhere
7^{2}×67 Posts 
I tried the minimum polynomial for ,
x^5 + x^4  4*x^3  3*x^2 + 3*x+ 1 and the answer was a bit hard to read. I'm not sure whether it was right. 
20191113, 20:13  #8 
∂^{2}ω=0
Sep 2002
República de California
3^{3}·419 Posts 
Exactly what I did using both FF and PaleMoon on my Mac. My next thought was that perhaps the versions of those browsers I'm running on that older legacy system (which has OS X frozen at 10.6.8 because my codebuild flow is set up for that, and upgrading would break stuff) can't handle something in your JS, but retrying under Ubuntu 19 running on my Intel NUC, which is 45 years old gives the same failure. Oh, well.

20191113, 20:15  #9  
Aug 2002
Buenos Aires, Argentina
2^{3}×3×5×11 Posts 
Quote:
Another error is that the digits in group is not working. The program always shows groups of 6 digits. I will work on that. 

20191113, 20:17  #10  
Aug 2002
Buenos Aires, Argentina
2^{3}·3·5·11 Posts 
Quote:


20191113, 22:48  #11  
Feb 2017
Nowhere
7^{2}×67 Posts 
Quote:
It is somewhat similar to the minimum polynomial x^3  3*x  1 for , which the calculator expresses in terms of cosines. Obviously, it "knows" the trigonometric solution for the casus irreducibilis of the cubic. 

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