Artifact 127eaf992939f5f1506363d54e1afa92f19ac1674489ee54d56f16d5cd1c8d7e:
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r37/packages/groebner/ideals.rlg
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[f2fda60abd]
at
2011-09-02 18:13:33
on branch master
— Some historical releases purely for archival purposes
git-svn-id: https://svn.code.sf.net/p/reduce-algebra/code/trunk/historical@1375 2bfe0521-f11c-4a00-b80e-6202646ff360 (user: arthurcnorman@users.sourceforge.net, size: 1846) [annotate] [blame] [check-ins using] [more...]
Mon Jan 4 00:02:39 MET 1999 REDUCE 3.7, 15-Jan-99 ... 1: 1: 2: 2: 2: 2: 2: 2: 2: 2: 2: 3: 3: I_setting(x,y,z); torder revgradlex; {{},lex} u := I(x*z-y**2, x**3-y*z); 2 3 u := i(x*z - y ,x - y*z) y member I(x,y^2); 0 x member I(x,y^2); 1 I(x,y^2) subset I(x,y); 1 % yes I(x,y) subset I(x,y^2); 0 % no % examples taken from Cox, Little, O'Shea: "Ideals, Varieties and Algorithms" q1 := u .: I(x); 3 2 2 2 q1 := i(x - y*z,x *y - z , - x*z + y ) % quotient ideal q2 := u .+ I(x^2 * y - z^2); 3 2 2 2 q2 := i(x - y*z,x *y - z , - x*z + y ) % sum ideal if q1 .= q2 then write "same ideal"; same ideal % test equality intersection(u,I(y)); 3 2 2 2 2 3 i(x *y - y *z,x *y - y*z , - x*y*z + y ) % ideal intersection u .: I(y); 3 2 2 2 i(x - y*z,x *y - z , - x*z + y ) u .: I(x,y); 3 2 2 2 i(x - y*z,x *y - z , - x*z + y ) %----------------------------------------------------- u1 := I(x,y^2); 2 u1 := i(x,y ) u1u1:= u1 .* u1; 4 2 2 u1u1 := i(y ,x*y ,x ) % square ideal u0 :=I(x,y); u0 := i(x,y) % test equality/inclusion for u1,u1u1,u0 u1 .= u1u1; 0 % no u1 subset u1u1; 0 % no u1u1 subset u1; 1 % yes u1 .= u0; 0 % no u1 subset u0; 1 % yes intersection (I(x) , I(x^2,x*y,y^2)) .= intersection(I(x) , I(x^2,y)); 1 end; 4: 4: 4: 4: 4: 4: 4: 4: 4: Time for test: 70 ms 5: 5: Quitting Mon Jan 4 00:02:44 MET 1999