Mathematica 2.0 for SPARC Copyright 1988-91 Wolfram Research, Inc. -- X11 windows graphics initialized -- In[1]:= < 3 - 3 x - 2 x + 6 x - y - x y + 2 x y, 2 x + 3 x + x y + x y} In[8]:= Basis[G,V] 2 5 11 x 4 x 5 y 7 x y Spoly[g2,g1] = - + ---- - ---- - --- - ----- 3 9 3 9 9 2 6 3 x 2 x 2 y Spoly[g3,g1] = -(-) - --- + ---- + --- 7 7 7 7 Spoly[g3,g2] = 0 2 3 -30 x 30 x 12 x Spoly[g4,g1] = ----- - ----- + ----- 7 7 7 Spoly[g4,g2] = 0 Spoly[g4,g3] = 0 Spoly[g5,g1] = 0 Spoly[g5,g2] = 0 Spoly[g5,g3] = 0 Spoly[g5,g4] = 0 Spoly[g6,g1] = 0 Spoly[g6,g2] = 0 Spoly[g6,g3] = 0 Spoly[g6,g4] = 0 Spoly[g6,g5] = 0 Almost done...Performing Final Reduction. 5.66667 Second 2 3 x 2 -5 x 5 x 3 Out[8]= {-3 - --- + x + y, ---- - ---- + x } 2 2 2 In[9]:= H = {2 - 3*x + y^2, -6 + 4*y - 3*y^2 + 4*y^3 + y^5} 0.0166667 Second 2 2 3 5 Out[9]= {2 - 3 x + y , -6 + 4 y - 3 y + 4 y + y } In[10]:= Basis[H,V] 2 Spoly[g2,g1] = -9 x + 9 x y 2 3 Spoly[g3,g1] = -2 x + 3 x - x y Spoly[g3,g2] = 0 Spoly[g4,g1] = 0 2 3 4 5 Spoly[g4,g2] = -12 x + 9 x - 24 x + 54 x - 27 x 3 4 Spoly[g4,g3] = x + 2 x - 3 x Spoly[g5,g1] = 0 Spoly[g5,g2] = 0 Spoly[g5,g3] = 0 Spoly[g5,g4] = 0 Spoly[g6,g1] = 0 Spoly[g6,g2] = 0 Spoly[g6,g3] = 0 Spoly[g6,g4] = 0 Spoly[g6,g5] = 0 Almost done...Performing Final Reduction. 4.81667 Second 3 2 2 3 -x 2 x 4 Out[10]= {2 - 3 x + y , 2 x - 3 x + x y, -- - ---- + x } 3 3 In[11]:= R = {-1 + (5*x)/3 + 3*x^2 + y/3 + (2*x*y)/3 + x^2*y, -15/7 - (11*x)/7 + (12*x^2)/7 + (5*y)/7 + x*y, -3/5 - (4*x)/5 + (6*x^2)/5 + y/5 + x*y} 0.0166667 Second 2 5 x 2 y 2 x y 2 15 11 x 12 x 5 y Out[11]= {-1 + --- + 3 x + - + ----- + x y, -(--) - ---- + ----- + --- + x y, 3 3 3 7 7 7 7 2 3 4 x 6 x y > -(-) - --- + ---- + - + x y} 5 5 5 5 In[12]:= Basis[R,V] 2 3 54 183 x 228 x 12 x 18 y Spoly[g2,g1] = -- - ----- - ------ + ----- - ---- 49 49 49 7 49 3 2 6 x Spoly[g3,g1] = -3 x - 3 x + ---- 5 Spoly[g3,g2] = 0 Spoly[g4,g1] = 0 Spoly[g4,g2] = 0 Spoly[g4,g3] = 0 Spoly[g5,g1] = 0 Spoly[g5,g2] = 0 Spoly[g5,g3] = 0 Spoly[g5,g4] = 0 Almost done...Performing Final Reduction. 3.31667 Second 2 3 x 2 -5 x 5 x 3 Out[12]= {-3 - --- + x + y, ---- - ---- + x } 2 2 2 In[13]:= K = {-x^2 + x^2*y, -x^2 + x^3 + y, 2 - x*y + x*y^2} 0. Second 2 2 2 3 2 Out[13]= {-x + x y, -x + x + y, 2 - x y + x y } In[14]:= Basis[K,V] 2 4 5 Spoly[g2,g1] = x - x + x Spoly[g3,g1] = 2 x Spoly[g3,g2] = 2 Spoly[g4,g1] = 0 Spoly[g4,g2] = 0 Spoly[g4,g3] = 0 Spoly[g5,g1] = 0 Spoly[g5,g2] = 0 Spoly[g5,g3] = 0 Spoly[g5,g4] = 0 Spoly[g6,g1] = 0 Spoly[g6,g2] = 0 Spoly[g6,g3] = 0 Spoly[g6,g4] = 0 Spoly[g6,g5] = 0 Almost done...Performing Final Reduction. 2.61667 Second Out[14]= {1} In[15]:= L = {1/4 - x + y^2*z + 4*z^2, 1/2 + x*y^2 + 2*z, -y^2 - z/2 + x*z^2} 0. Second 1 2 2 1 2 2 z 2 Out[15]= {- - x + y z + 4 z , - + x y + 2 z, -y - - + x z } 4 2 2 In[16]:= Basis[L,U] 2 2 4 2 4 1 x y x y x y x y Spoly[g2,g1] = -(-) + - + -- - ---- + ---- - ----- 8 4 16 4 8 4 2 2 2 4 1 x x 31 y 3 x y x y Spoly[g3,g1] = -- + -- + -- - ----- + ------ + ---- 16 16 4 32 16 16 Spoly[g3,g2] = 0 Spoly[g4,g1] = 0 Spoly[g4,g2] = 0 2 2 2 2 2 6 49 99 x 95 x 767 y 63 x y 31 x y 4 y Spoly[g4,g3] = -- + ---- + ----- - ------ + ------- - -------- + 16 y - -- 16 32 8 16 8 8 2 2 2 2 2 1 3 x x 3 2 9 x y 3 x y Spoly[g5,g1] = -(-) + --- - -- + x + 2 y - ------ + ------- 4 8 4 2 4 2 3 4 2 2 34 14 x 215 x 44 x 8 x 476 y 263 x y 4 Spoly[g5,g2] = -(--) - ---- - ------ + ----- + ---- + ------ - -------- - 4 y 3 3 6 3 3 3 3 Spoly[g5,g3] = 0 Spoly[g5,g4] = 0 Spoly[g6,g1] = 0 Spoly[g6,g2] = 0 2 3 4 5 2 7037 2263 x 4991 x 45229 x 341 x 31 x 23963 y Spoly[g6,g3] = ---- - ------ + ------- - -------- - ------ - ----- - -------- + 288 64 288 576 24 12 144 2 16523 x y > ---------- 48 Spoly[g6,g4] = 0 Spoly[g6,g5] = 0 Spoly[g7,g1] = 0 Spoly[g7,g2] = 0 Spoly[g7,g3] = 0 Spoly[g7,g4] = 0 Spoly[g7,g5] = 0 Spoly[g7,g6] = 0 Spoly[g8,g1] = 0 2 3 4 297833 469247 x 481837 x 251555 x 1399 x Spoly[g8,g2] = -(------) + -------- - --------- - --------- - ------- + 86346 57564 172692 172692 57564 5 6 2 106 x 4 x 497 y > ------ - ---- + ------ 14391 9 43173 Spoly[g8,g3] = 0 Spoly[g8,g4] = 0 Spoly[g8,g5] = 0 Spoly[g8,g6] = 0 Spoly[g8,g7] = 0 Spoly[g9,g1] = 0 2 3 4 5 6 7 10 133 x 57 x 25 x 2 x x 4 x 8 x Spoly[g9,g2] = --- - ----- + ----- - ----- - ---- - ---- + ---- - ---- 533 1599 533 1066 123 3198 1599 1599 Spoly[g9,g3] = 0 Spoly[g9,g4] = 0 Spoly[g9,g5] = 0 Spoly[g9,g6] = 0 Spoly[g9,g7] = 0 Spoly[g9,g8] = 0 Spoly[g10,g1] = 0 Spoly[g10,g2] = 0 Spoly[g10,g3] = 0 Spoly[g10,g4] = 0 Spoly[g10,g5] = 0 Spoly[g10,g6] = 0 Spoly[g10,g7] = 0 Spoly[g10,g8] = 0 Spoly[g10,g9] = 0 Spoly[g11,g1] = 0 Spoly[g11,g2] = 0 Spoly[g11,g3] = 0 Spoly[g11,g4] = 0 Spoly[g11,g5] = 0 Spoly[g11,g6] = 0 Spoly[g11,g7] = 0 Spoly[g11,g8] = 0 Spoly[g11,g9] = 0 Spoly[g11,g10] = 0 Almost done...Performing Final Reduction. 74.8333 Second 2 3 4 5 6 144407 85042 x 232833 x 61031 x 2111 x 75 x 4638 x Out[16]= {------ - ------- + --------- + -------- + ------- - ----- + ------- + 1988 497 3976 1988 3976 497 497 2 3 4 5 297833 1407741 x 481837 x 251555 x 4197 x 318 x > z, -(------) + --------- - --------- - --------- - ------- + ------ - 994 1988 1988 1988 1988 497 6 2 3 4 5 6 19188 x 2 15 133 x 171 x 75 x 13 x x x 7 > -------- + y , -(--) + ----- - ------ + ----- + ----- + -- - -- + x } 497 4 8 8 16 4 16 2 In[17]:=