assert( gcd(2*3*5,2*3*7,2*5*7) == 2 ) assert( gcd(2*3*5,2*3*7,2*5*7,3*5*7) == 1 ) assert( gcd(1000:2) == 2 ) assert( gcd splice(1000:2,3) == 1 ) assert( gcd {} == 0 ) assert( gcd 2 == 2 ) assert( lcm(2,3,5,7) == 210 ) assert( lcm(1000:2) == 2 ) assert( lcm(0, 0) == 0 ) assert( lcm(0/1, 0/1) == 0 ) assert( lcm {} == 1 ) assert( lcm 2 == 2 ) R = ZZ/32003[x,y] f = (x+y)^3*(x-y^2) g = (x+y)^2*(x^3-x*y+y^3)^4 assert ( gcd(f,g) == (x+y)^2 ) assert ( lcm(0_R, 0_R) == 0 ) assert ( gcd f == f ) assert ( lcm f == f ) GF 729[x, y, z] assert( gcd((x^5+y^3+a+1)*(y-1),(x^5+y^3+a+1)*(z+1)) == x^5+y^3+a+1 ) GF 25[x, y, z] assert( gcd(z-a,z^2-a^2) == z-a ) assert( gcd((x^5+y^3+a+1)*(y-1),(x^5+y^3+a+1)*(z+1)) == x^5+y^3+a+1 ) assert( 1 == gcd(x^5+x-3,x^6-a*x-1) ) assert( gcd((x^3+x-a)*(x^5+x-3),(x^3+x-a)*(x^6-a*x-1)) == x^3+x-a ) R = GF 25[x] -- one of the book chapters depends on this feature assert(gcd((x^3+x-a)*(x^5+x-1),(x^3+x-a)*(x^6-a*x-1)) == x^3+x-a) R = GF 25[x,y] -- one of the book chapters depends on this feature assert(gcd((x^3+x-a)*(x^5+x-1),(x^3+x-a)*(x^6-a*x-1)) == x^3+x-a) R = (GF 25)[x,y] assert(gcd((x^3+y-a)*(y^5+x-1),(x^3+y-a)*(x^6-a*x-1)) == x^3+y-a) R = ZZ[x] assert( gcd(6*x, 4*x) == 2*x ) R = QQ[x] assert( gcd(6*x, 4*x) == x ) R = ZZ[x,y] d = 5*x^2*y+7*x^3-y^4 f = (3*x^3-x*y+y^2) * d g = (3*x^3+x*y+y^2) * d h = gcd(f,g) assert(h == -d) R = QQ[x,y] d = 5*x^2*y+7*x^3-1/11*y^4 f = (3*x^3-x*y+y^2) * d g = (3*x^3+x*y+y^2) * d h = gcd(f,g) assert(h == -11* d) R = ZZ/101[x] d = x^3+x-2; f = d*(x^5+x-1); g = d*(x^6-x-1); assert(gcd(f,g) == d) w = gcdCoefficients(f,g) assert( w#0 == d) -- "factory" used to return 24*d here. It's good that it returns d now assert( w#0 == f * w#1 + g * w#2 ) R = GF 25[x] d = x^3+x-a; f = d*(x^5+x-1); g = d*(x^6-a*x-1); assert(gcd(f,g) == d) w = gcdCoefficients(f,g) assert( w#0 == f * w#1 + g * w#2 ) assert( w#0 % d == 0 ) -- test the two gcd's are associated; the precise (unit) factor varies assert( d % w#0 == 0 ) -- actually, we'd like w#0 == d. I wonder why factory doesn't ensure that? R = QQ[x]; R2=R[t]; assert ( gcd(t^2-x^2,t^3-x^3) == t-x ) debug Core R = QQ[x,y] f = 1+x^2 g = 1+x^3 rawGCD( raw ( f ), raw ( g )) rawGCD( raw ( 1/2*f ), raw ( 1/3*g )) rawExtendedGCD( raw ( f ), raw ( g )) rawExtendedGCD( raw ( 1/2*f ), raw ( 1/3*g )) end -- Local Variables: -- compile-command: "make -C $M2BUILDDIR/Macaulay2/packages/Macaulay2Doc/test gcd.out" -- End:

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