R = ZZ/101[a,r..z] f = a * id_(R^1) g = a^2* id_(R^1) assert( degree f == {1} ) assert isHomogeneous f assert( degree g == {2} ) assert isHomogeneous g h = g // f assert( degree h == {1} ) assert isHomogeneous h chk = (f,g) -> assert( target f == target g and (h := f//g; target h == source g and source h == source f and f % g + g * h == f )) M = R^2 N = R^3 chk(map(M,N,0),map(M,M,1)) chk(map(M,M,1),map(M,N,0)) chk(map(M,M,{{r,s},{t,u}}),map(M,N,{{r,s,t},{u,v,w}})) f = map(R^2,,{{x},{y}}) g = map(R^2,,{{x},{z}}) (q,r) = quotientRemainder(f,g) assert( g*q+r == f ) assert( degree g == {0} ) assert( degree q == {0} ) assert( degree f == {0} ) R = ZZ[x,d,WeylAlgebra=>{x=>d}] f = matrix{{x*d,d*x,x,d}} g = matrix{{x,d}} (q,r) = quotientRemainder(f,g) assert(g*q+r == f) g = matrix{{x}} (q,r) = quotientRemainder(f,g) assert(g*q+r == f) g = matrix{{d}} (q,r) = quotientRemainder(f,g) assert(g*q+r == f) a =-1.428571429e-01 lift(a,QQ) assert( instance(oo,QQ) and a === promote(oo,RR) ) a = 4.537815126e-01 lift(a,QQ) assert( instance(oo,QQ) and a === promote(oo,RR) ) a = 5.923344948e-02 lift(a,QQ) assert( instance(oo,QQ) and a === promote(oo,RR) ) a = -7.481504637e-02 lift(a,QQ) assert( instance(oo,QQ) and a === promote(oo,RR) ) a = -1.984139325e-01 lift(a,QQ) assert( instance(oo,QQ) and a === promote(oo,RR) ) -- from github issue #194 R=QQ[x,Inverses=>true,MonomialOrder=>RevLex] assert not liftable(x-1,QQ) end -- Local Variables: -- compile-command: "make -C $M2BUILDDIR/Macaulay2/packages/Macaulay2Doc/test lift.out" -- End:

Simpan