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Bug in spmod gcd algorithm for polynomials #1345

Open rtoy opened 3 months ago

rtoy commented 3 months ago

Imported from SourceForge on 2024-07-04 09:54:22 Created by mgerbershagen on 2021-08-21 12:55:40 Original: https://sourceforge.net/p/maxima/bugs/3832

The following input

trigsimp(trigexpand(1/(16*(a^8*m^4*cos(theta)^4+2*a^6*m^4*r^2*cos(theta)^2+a^4*m^4*r^4)*sin(theta)^8+8*(a^10*m^2*r^2*cos(theta)^10+2*(2*a^8*m^2*r^4-a^8*m^3*r^2)*cos(theta)^8+6*(a^6*m^2*r^6-a^6*m^3*r^4)*cos(theta)^6+2*(2*a^4*m^2*r^8-3*a^4*m^3*r^6)*cos(theta)^4+(a^2*m^2*r^10-2*a^2*m^3*r^8)*cos(theta)^2)*sin(theta)^4+a^12*r^4*cos(theta)^16+2*(3*a^10*r^6-2*a^10*m*r^4)*cos(theta)^14+(15*a^8*r^8-20*a^8*m*r^6+4*a^8*m^2*r^4)*cos(theta)^12+4*(5*a^6*r^10-10*a^6*m*r^8+4*a^6*m^2*r^6)*cos(theta)^10+(15*a^4*r^12-40*a^4*m*r^10+24*a^4*m^2*r^8)*cos(theta)^8+2*(3*a^2*r^14-10*a^2*m*r^12+8*a^2*m^2*r^10)*cos(theta)^6+(r^16-4*m*r^14+4*m^2*r^12)*cos(theta)^4)+1/(4*((a^6*m^2*r^2-2*a^6*m^3+a^8*m^2)*cos(theta)^4+2*(a^4*m^2*r^4+(a^6*m^2-2*a^4*m^3)*r^2)*cos(theta)^2+a^2*m^2*r^6+(a^4*m^2-2*a^2*m^3)*r^4)*sin(theta)^4+(a^8*r^4+(a^10-2*a^8*m)*r^2)*cos(theta)^10+2*(2*a^6*r^6+(2*a^8-5*a^6*m)*r^4-(a^8*m-2*a^6*m^2)*r^2)*cos(theta)^8+6*(a^4*r^8+(a^6-3*a^4*m)*r^6-(a^6*m-2*a^4*m^2)*r^4)*cos(theta)^6+2*(2*a^2*r^10+(2*a^4-7*a^2*m)*r^8-3*(a^4*m-2*a^2*m^2)*r^6)*cos(theta)^4+(r^12+(a^2-4*m)*r^10-2*(a^2*m-2*m^2)*r^8)*cos(theta)^2)));

gives an error

PQUOTIENT: Quotient by a polynomial of higher degree (case 2a)
 -- an error. To debug this try: debugmode(true);

I have traced this down to a bug in the zgcd function which computes the gcd of

sin(theta)^4*(cos(theta)^4*(r^2*m^2*a^6*4+(m^3*a^6*(-8)+m^2*a^8*4))+cos(theta)^2*(r^4*m^2*a^4*8+r^2*(m^3*a^4*(-16)+m^2*a^6*8))+(r^6*m^2*a^2*4+r^4*(m^3*a^2*(-8)+m^2*a^4*4)))+(cos(theta)^10*(r^4*a^8*1+r^2*(m*a^8*(-2)+a^10*1))+cos(theta)^8*(r^6*a^6*4+r^4*(m*a^6*(-10)+a^8*4)+r^2*(m^2*a^6*4+m*a^8*(-2)))+cos(theta)^6*(r^8*a^4*6+r^6*(m*a^4*(-18)+a^6*6)+r^4*(m^2*a^4*12+m*a^6*(-6)))+cos(theta)^4*(r^10*a^2*4+r^8*(m*a^2*(-14)+a^4*4)+r^6*(m^2*a^2*12+m*a^4*(-6)))+cos(theta)^2*(r^12*1+r^10*(m*(-4)+a^2*1)+r^8*(m^2*4+m*a^2*(-2))))

and

sin(theta)^8*(cos(theta)^4*m^4*a^8*16+cos(theta)^2*r^2*m^4*a^6*32+r^4*m^4*a^4*16)+sin(theta)^4*(cos(theta)^10*r^2*m^2*a^10*8+cos(theta)^8*(r^4*m^2*a^8*32+r^2*m^3*a^8*(-16))+cos(theta)^6*(r^6*m^2*a^6*48+r^4*m^3*a^6*(-48))+cos(theta)^4*(r^8*m^2*a^4*32+r^6*m^3*a^4*(-48))+cos(theta)^2*(r^10*m^2*a^2*8+r^8*m^3*a^2*(-16)))+(cos(theta)^16*r^4*a^12*1+cos(theta)^14*(r^6*a^10*6+r^4*m*a^10*(-4))+cos(theta)^12*(r^8*a^8*15+r^6*m*a^8*(-20)+r^4*m^2*a^8*4)+cos(theta)^10*(r^10*a^6*20+r^8*m*a^6*(-40)+r^6*m^2*a^6*16)+cos(theta)^8*(r^12*a^4*15+r^10*m*a^4*(-40)+r^8*m^2*a^4*24)+cos(theta)^6*(r^14*a^2*6+r^12*m*a^2*(-20)+r^10*m^2*a^2*16)+cos(theta)^4*(r^16*1+r^14*m*(-4)+r^12*m^2*4))

to be

sin(theta)^4*(cos(theta)^4*(r^2*m^2*a^6*4+(m^3*a^6*(-8)+m^2*a^8*4))+cos(theta)^2*(r^4*m^2*a^4*8+r^2*(m^3*a^4*(-16)+m^2*a^6*8))+(r^6*m^2*a^2*4+r^4*(m^3*a^2*(-8)+m^2*a^4*4)))+(cos(theta)^10*(r^4*a^8*1+r^2*(m*a^8*(-2)+a^10*1))+cos(theta)^8*(r^6*a^6*4+r^4*(m*a^6*(-10)+a^8*4)+r^2*(m^2*a^6*4+m*a^8*(-2)))+cos(theta)^6*(r^8*a^4*6+r^6*(m*a^4*(-18)+a^6*6)+r^4*(m^2*a^4*12+m*a^6*(-6)))+cos(theta)^4*(r^10*a^2*4+r^8*(m*a^2*(-14)+a^4*4)+r^6*(m^2*a^2*12+m*a^4*(-6)))+cos(theta)^2*(r^12*1+r^10*(m*(-4)+a^2*1)+r^8*(m^2*4+m*a^2*(-2))))

Other gcd algorithms seem to work fine, for instance the oldgcd function gives

sin(theta)^4*(cos(theta)^4*m^2*a^6*4+cos(theta)^2*r^2*m^2*a^4*8+r^4*m^2*a^2*4)+(cos(theta)^10*r^2*a^8*1+cos(theta)^8*(r^4*a^6*4+r^2*m*a^6*(-2))+cos(theta)^6*(r^6*a^4*6+r^4*m*a^4*(-6))+cos(theta)^4*(r^8*a^2*4+r^6*m*a^2*(-6))+cos(theta)^2*(r^10*1+r^8*m*(-2)))

Unfortunately, I haven't been able to reduce the example to a simpler one.

rtoy commented 3 months ago

Imported from SourceForge on 2024-07-04 09:54:23 Created by robert_dodier on 2022-06-25 16:51:11 Original: https://sourceforge.net/p/maxima/bugs/3832/#58b4

This bug appears to be fixed by commit 73105cf (from merge request #25), but before closing this bug report, I'd like to put together some test cases. If anyone has some test cases, they could post them here, otherwise, I'll put something together.

rtoy commented 3 months ago

Imported from SourceForge on 2024-07-04 09:54:27 Created by robert_dodier on 2022-06-25 16:52:57 Original: https://sourceforge.net/p/maxima/bugs/3832/#fc63