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Greatest common divisor wrong result #4094

Open rtoy opened 1 month ago

rtoy commented 1 month ago

Imported from SourceForge on 2024-07-09 11:20:50 Created by rayon340 on 2023-12-28 17:10:23 Original: https://sourceforge.net/p/maxima/bugs/4231

Dear everyone, hi. I have tried to calculate the greatest common divisor of the three following monomials:

12a^3b^2c^2, 6a^2b^3c^3, 3a^2b^2c^3.

In order to do this I have written:

gcd(12a^3b^2c^2, 6a^2b^3c^3, 3a^2b^2*c^3);

but Maxima gives me the result "6a^2b^2c^2" instead of "3a^2b^2c^2". What is the point?

rtoy commented 1 month ago

Imported from SourceForge on 2024-07-09 11:20:52 Created by rtoy on 2023-12-28 17:21:34 Original: https://sourceforge.net/p/maxima/bugs/4231/#e575

I think you're using gcd wrong. The manual for gcd (via "? gcd") says:

-- Function: gcd (, , , ...) Returns the greatest common divisor of and . The flag

so it only takes two polynomials. It doesn't describe what x_1 is, though and I don't really know either.

rtoy commented 1 month ago

Imported from SourceForge on 2024-07-09 11:20:55 Created by macrakis on 2023-12-28 17:34:11 Original: https://sourceforge.net/p/maxima/bugs/4231/#6a60

As Ray says, gcdtakes two polynomials. Arguments x_1, x_2, etc. specify the variable ordering (cf. ratvars and divide, which also takes x_n arguments). I agree that the doc should be explicit about this.

For the gcd of more than two polynomials, here's an easy approach:

xreduce('gcd,[12*a^3*b^2*c^2, 6*a^2*b^3*c^3,3*a^2*b^2*c^3]);
     => 3*a^2*b^2*c^2
rtoy commented 1 month ago

Imported from SourceForge on 2024-07-09 11:20:59 Created by rayon340 on 2023-12-28 17:41:19 Original: https://sourceforge.net/p/maxima/bugs/4231/#daf7

Ok, many thanks to both of you. So I can either use nested gcd calls

gcd(12a^3b^2c^2, gcd(6a^2b^3c^3, 3a^2b^2c^3))

or use the xreduce function with gcd. I think it could be more intuitive to let gcd function to take more than two polynomials.

Best regards.

rtoy commented 1 month ago

Imported from SourceForge on 2024-07-09 11:21:02 Created by macrakis on 2023-12-28 19:34:19 Original: https://sourceforge.net/p/maxima/bugs/4231/#daf7/0433

I understand your point. But that leaves the question of how to specify variable order.

Fateman, can you supply an example where the result is non-trivially different with different variable order? (not just x-y vs y-x).

On Thu, Dec 28, 2023 at 12:41 PM Emanuele Giusti via Maxima-bugs < maxima-bugs@lists.sourceforge.net> wrote:

Ok, many thanks to both of you. So I can either use nested gcd calls

gcd(12a^3b^2c^2, gcd(6a^2b^3c^3, 3a^2b^2c^3))

or use the xreduce function with gcd. I think it could be more intuitive to let gcd function to take more than two polynomials.

Best regards.

[bugs:#4231] https://sourceforge.net/p/maxima/bugs/4231/ Greatest common divisor wrong result

Status: not-a-bug Group: None Labels: greatest common divisor gcd Created: Thu Dec 28, 2023 05:10 PM UTC by Emanuele Giusti Last Updated: Thu Dec 28, 2023 05:34 PM UTC Owner: nobody

Dear everyone, hi. I have tried to calculate the greatest common divisor of the three following monomials:

12a^3b^2c^2, 6a^2b^3c^3, 3a^2b^2c^3.

In order to do this I have written:

gcd(12a^3b^2c^2, 6a^2b^3c^3, 3a^2b^2*c^3);

but Maxima gives me the result "6a^2b^2c^2" instead of "3a^2b^2 c^2". What is the point?

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rtoy commented 1 month ago

Imported from SourceForge on 2024-07-09 11:21:06 Created by rayon340 on 2023-12-28 19:55:17 Original: https://sourceforge.net/p/maxima/bugs/4231/#daf7/0433/5ecf

Hi. I do not understand what you mean and I do not understand the meaning of the word "Fateman". I am not an english native speaker. The dictionary does not provide any translation for that word. I am a new Maxima user. I do not want to make a controversy. Of course Maxima has an algorithm to calculate the gcd of two polynomials; maybe it could be possible to extend the funtionality of that algorithm to deal with more than two polynomials. For me it is fine to use the two solutions you have provided to me, what I have said is only a suggestion.

rtoy commented 1 month ago

Imported from SourceForge on 2024-07-09 11:21:09 Created by rtoy on 2023-12-29 00:39:39 Original: https://sourceforge.net/p/maxima/bugs/4231/#daf7/0433/5ecf/6592

I think what Stavros is saying is that if you change gcd to have more then two polynomials then how do you know what the last polynomial is and where the x_1 argument begins. That is, gcd has no way of knowing if you want gcd(p1,p2,p3, x1) to do 3 polynomials or if p3 is another ratvar polynomial for ordering.

"Fateman" is a reference to Richard Fateman, one of the original Macsyma authors who still contributes to Maxima.

rtoy commented 1 month ago

Imported from SourceForge on 2024-07-09 11:21:13 Created by macrakis on 2023-12-29 15:37:17 Original: https://sourceforge.net/p/maxima/bugs/4231/#daf7/0630

You can also package the functionality so that it's easy to use:

gcdn([l]) := xreduce('gcd, l)$

It is rare that you'll need to specify the main variable -- which as far as I can tell only determines whether there is a factor of -1:

makelist( gcd (x^2-y^2, x-y,x), gcd,'[ez,subres,red,spmod]); => [x - y, x - y, x - y, x - y]

makelist( gcd (x^2-y^2, x-y,y), gcd,'[ez,subres,red,spmod]); => [y - x, y - x, y - x, y - x]

and the exact form of the result:

qq; 2 2 2 2 2 2 y z - x z - y z + x z + x y - x y rr; (y - z) (z - x)

gcd(qq,rr,x,y,z); 2 z + ((- y) - x) z + x y gcd(qq,rr,x,z,y); 2 (- z ) + y (z - x) + x z gcd(qq,rr,y,x,z); 2 z + ((- y) - x) z + x y gcd(qq,rr,y,z,x); 2 (- z ) + x (z - y) + y z gcd(qq,rr,z,x,y); 2 z - x z + y (x - z) gcd(qq,rr,z,y,x); 2 z - y z + x (y - z)

On Thu, Dec 28, 2023 at 12:41 PM Emanuele Giusti < rayon340@users.sourceforge.net> wrote:

Ok, many thanks to both of you. So I can either use nested gcd calls

gcd(12a^3b^2c^2, gcd(6a^2b^3c^3, 3a^2b^2c^3))

or use the xreduce function with gcd. I think it could be more intuitive to let gcd function to take more than two polynomials.

Best regards.

[bugs:#4231] https://sourceforge.net/p/maxima/bugs/4231/ Greatest common divisor wrong result

Status: not-a-bug Group: None Labels: greatest common divisor gcd Created: Thu Dec 28, 2023 05:10 PM UTC by Emanuele Giusti Last Updated: Thu Dec 28, 2023 05:34 PM UTC Owner: nobody

Dear everyone, hi. I have tried to calculate the greatest common divisor of the three following monomials:

12a^3b^2c^2, 6a^2b^3c^3, 3a^2b^2c^3.

In order to do this I have written:

gcd(12a^3b^2c^2, 6a^2b^3c^3, 3a^2b^2*c^3);

but Maxima gives me the result "6a^2b^2c^2" instead of "3a^2b^2 c^2". What is the point?

Sent from sourceforge.net because you indicated interest in https://sourceforge.net/p/maxima/bugs/4231/

To unsubscribe from further messages, please visit https://sourceforge.net/auth/subscriptions/

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rtoy commented 1 month ago

Imported from SourceForge on 2024-07-09 11:21:17 Created by fateman on 2023-12-29 23:04:27 Original: https://sourceforge.net/p/maxima/bugs/4231/#298f

see gcd ( (x+y+1)^2, (x+y+1)^3,x,y); vs gcd((x+y+1)^2,(x+y+1)^3, y,x);
to see what the extra arguments do. Richard Fateman ;)

rtoy commented 1 month ago

Imported from SourceForge on 2024-07-09 11:21:20 Created by macrakis on 2023-12-30 00:00:53 Original: https://sourceforge.net/p/maxima/bugs/4231/#2cb3

Here is a minimum example of the sign of the result being different because of variable ordering:

gcd(x-y,y-x,x) => x - y
gcd(x-y,y-x,y) => y - x