restart; currentdir(); with(PolynomialTools): #with(LinearAlgebra): with(ListTools):

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read(recden); monic:=proc(a) #monic makes rpolys monic if getpoly(a)=0 then a else mulrpoly(invrpoly(lcrpoly(a)),a); fi; end proc: read "MRES.mpl"; #Example 1: M1:=z1^2-2: #Minimal polynomial of sqrt(2) M2:=z2^2-7: #Minimal polynomial of sqrt(7) f1:=rpoly((z1 + 60)*x^3+y*z2-z1,[x,y,z2,z1],[M1,M2]); f2:=rpoly(263*x+4*y*z1,[x,y,z2,z1],[M1,M2]);

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#MRS returns the resultant of f1 and f2 w.r.t. variable x and the number of pri MRS(f1,f2,x,nextprime(2^8)); #When we chose a small prime, the chance of hitting lc-bad, det-bad, and ZD primes increases.

p=257 is a ZD prime ZD=POLYNOMIAL([257, [z1], [[242, 0, 214, 0, 1]]],[111, 120, 1]) p=263 is an lc-bad prime polynomial case

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MRS(f1,f2,x,nextprime(2^30)); #We chose a large prime

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MRS(f1,f2,y,nextprime(2^8));

p=263 is an lc-bad prime polynomial case

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MRS(f1,f2,y,nextprime(2^30));

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#Example 2: M1:=z1^2-2: M2:=z2^2-3: M3:=z3^2-5: M4:=z4^2-7: f1:=rpoly(randpoly([x,y,z4,z3,z2,z1],degree=3),[x,y,z4,z3,z2,z1],[M1,M2,M3,M4]); f2:=rpoly(randpoly([x,y,z4,z3,z2,z1],degree=2),[x,y,z4,z3,z2,z1],[M1,M2,M3,M4]);

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untrace(MRS); MRS(f1,f2,y,nextprime(2^10));

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