Annotation of OpenXM_contrib2/asir2000/lib/bgk, Revision 1.1.1.1
1.1 noro 1: /* $OpenXM: OpenXM/src/asir99/lib/bgk,v 1.1.1.1 1999/11/10 08:12:30 noro Exp $ */
2: /* examples for groebner basis computations by Boege, Gebauer, Kredel */
3:
4: /* $(hairer,runge-kutta 1,05.11.83)
5: d=q
6: r=d(c2,c3,b3,b2,b1,a21,a32,a31)
7: opt=10 */
8: Hairer1 = [
9: [a31,a32,a21,b1,b2,b3,c3,c2],[
10: (+c2-a21),
11: (+c3-a31-a32),
12: (+b1+b2+b3-1),
13: (+b2*c2+b3*c3-1/2),
14: (+b2*c2^2+b3*c3^2-1/3),
15: (+b3*a32*c2-1/6)
16: ]]$
17:
18: /*$(hairer,runge-kutta*2,05.11.1983)
19: d=q
20: r=d(c2,c3,c4,b4,b3,b2,b1,a21,a31,a32,a41,a42,a43)
21: opt=10*/
22: Hairer2 = [
23: /* [a43,a42,a41,a32,a31,a21,b1,b2,b3,b4,c4,c3,c2],[ */
24: [a21,a31,a41,b1,b2,a42,a32,a43,b3,b4,c4,c3,c2],[
25: (+b1+b2+b3+b4-1),
26: (+b2*c2+b3*c3+b4*c4-1/2),
27: (+b2*c2^2+b3*c3^2+b4*c4^2-1/3),
28: (+b3*a32*c2+b4*a42*c2+b4*a43*c3-1/6),
29: (+b2*c2^3+b3*c3^3+b4*c4^3-1/4),
30: (+b3*c3*a32*c2+b4*c4*a42*c2+b4*c4*a43*c3-1/8),
31: (+b3*a32*c2^2+b4*a42*c2^2+b4*a43*c3^2-1/12),
32: (+b4*a43*a32*c2-1/24),
33: (+c2-a21),
34: (+c3-a31-a32),
35: (+c4-a41-a42-a43)
36: ]]$
37:
38:
39: /*$(hairer,runge-kutta 3,10.11.1983)
40: d=q
41: r=d(c2,c3,c4,c5,b2,b3,b4,b5,a32,a42,a43,a52,a53,a54)
42: opt=g10*/
43: Hairer3 = [
44: /* [a54,a53,a52,a43,a42,a32,b5,b4,b3,b2,c5,c4,c3,c2], */
45: [b2,b3,b4,b5,a52,a53,a42,a54,a32,a43,c5,c4,c3,c2],
46: [
47: (+b2*c2+b3*c3+b4*c4+b5*c5-1/2),
48: (+b2*c2^2+b3*c3^2+b4*c4^2+b5*c5^2-1/3),
49: (+b3*a32*c2+b4*a42*c2+b4*a43*c3+b5*a52*c2+b5*a53*c3+b5*a54*c4-1/6),
50: (+b2*c2^3+b3*c3^3+b4*c4^3+b5*c5^3-1/4),
51: (+b3*c3*a32*c2+b4*c4*a42*c2+b4*c4*a43*c3+b5*c5*a52*c2+b5*c5*a53*c3+b5*c5*a54*c4-1/8),
52: (+b3*a32*c2^2+b4*a42*c2^2+b4*a43*c3^2+b5*a52*c2^2+b5*a53*c3^2+b5*a54*c4^2-1/12),
53: (+b4*a43*a32*c2+b5*a53*a32*c2+b5*a54*a42*c2+b5*a54*a43*c3-1/24),
54: (+b2*c2^4+b3*c3^4+b4*c4^4+b5*c5^4-1/5),
55: (+b3*c3^2*a32*c2+b4*c4^2*a42*c2+b4*c4^2*a43*c3+b5*c5^2*a52*c2+b5*c5^2*a53*c3+b5*c5^2*a54*c4-1/10),
56: (+b3*c2^2*a32*c3+b4*c2^2*a42*c4+b4*c3^2*a43*c4+b5*c2^2*a52*c2+b5*c3^2*a53*c5+b5*c4^2*a54*c5-1/15),
57: (+b4*c4*a43*a32*c2+b5*c5*a53*a32*c2+b5*c5*a54*a42*c2+b5*c5*a54*a43*c3-1/30),
58: (+b3*a32^2*c2^2+b4*a42^2*c2^2+2*b4*a42*c2*a43*c3+b4*a43^2*c3^2+b5*a52^2*c2^2+b5*a53^2*c3^2+b5*a54^2*c4^2+2*b5*a52*c2*a53*c3+2*b5*a52*c2*a54*c4+2*b5*a53*c3*a54*c4-1/20),
59: (+b3*a32*c2^3+b4*a42*c2^3+b4*a43*c3^3+b5*a52*c2^3+b5*a53*c3^3+b5*a54*c4^3-1/20),
60: (+b4*a43*c3*a32*c2+b5*a53*c3*a32*c2+b5*a54*c4*a42*c2+b5*a54*c4*a43*c3-1/40),
61: (+b4*a43*a32*c2^2+b5*a53*a32*c2^2+b5*a54*a42*c2^2+b5*a54*a43*c3^2-1/60),
62: (+b5*a54*a43*a32*c2-1/120)
63: ]]$
64:
65: /*$(hairer,runge-kutta 4,p=5 s=6,20.12.1983)
66: d=q
67: r=d(c2,c3,c4,c5,c6,b2,b3,b4,b5,b6,a32,a42,a43,a52,a53,
68: a54,a62,a63,a64,a65)
69: opt=oil*/
70: Hairer4 = [
71: [a65,a64,a63,a62,a54,a53,a52,a43,a42,a32,b6,b5,b4,b3,b2,c6,c5,c4,c3,c2,c51],[
72: (+b2*c2+b3*c3+b4*c4+b5*c5+b6*c6-1/2),
73: (+b2*c2^2+b3*c3^2+b4*c4^2+b5*c5^2+b6*c6^2-1/3),
74: (+b3*a32*c2+b4*a42*c2+b4*a43*c3+b5*a52*c2+b5*a53*c3+b6*a62*c2+b6*a63*c3+b6*a64*c4+b6*a65*c5+b5*a54*c4-1/6),
75: (+b2*c2^3+b3*c3^3+b4*c4^3+b5*c51^3+b6*c6^3-1/4),
76: (+b3*c3*a32*c2+b4*c4*a42*c2+b4*c4*a43*c3+b5*c5*a52*c2+b6*c6*a62*c2+b6*c6*a63*c3+b6*c6*a64*c4+b6*c6*a65*c5+b5*c5*a53*c3+b5*c5*a54*c4-1/8),
77: (+b3*a32*c2^2+b4*a42*c2^2+b4*a43*c3^2+b5*a52*c2^2+b6*a62*c2^2+b6*a63*c3^2+b6*a64*c4^2+b6*a65*c5^2+b5*a53*c3^2+b5*a54*c4^2-1/12),
78: (+b4*a43*a32*c2+b5*a53*a32*c2+b5*a54*a42*c2+b5*a54*a43*c3+b6*a63*a32*c2+b6*a64*a42*c2+b6*a64*a43*c3+b6*a65*a52*c2+b6*a65*a53*c3+b6*a65*a54*c4-1/24),
79: (+b2*c2^4+b3*c3^4+b4*c4^4+b5*c5^4+b6*c6^4-1/5),
80: (+b3*c3^2*a32*c2+b4*c4^2*a42*c2+b4*c4^2*a43*c3+b5*c5^2*a52*c2+b5*c5^2*a53*c3+b5*c5^2*a54*c4+b6*c6^2*a62*c2+b6*c6^2*a63*c3+b6*c6^2*a64*c4+b6*c6^2*a65*c5-1/10),
81: (+b3*c2^2*a32*c3+b4*c2^2*a42*c4+b4*c3^2*a43*c4+b5*c2^2*a52*c5+b5*c3^2*a53*c5+b5*c4^2*a54*c5+b6*c2^2*a62*c6+b6*c3^2*a63*c6+b6*c4^2*a64*c6+b6*c5^2*a65*c6-1/15),
82: (+b4*c4*a43*a32*c2+b5*c5*a53*a32*c2+b5*c5*a54*a42*c2+b5*c5*a54*a43*c3+b6*c6*a63*a32*c2+b6*c6*a64*a42*c2+b6*c6*a64*a43*c2+b6*c6*a65*a52*c2+b6*c6*a65*a53*c3+b6*c6*a65*a54*c4-1/30),
83: (+b3*a32^2*c2^2+b4*a42^2*c2^2+2*b4*a42*c2*a43*c3+b4*a43^2*c3^2+b5*a52^2*c2^2+b5*a53^2*c3^2+b5*a54^2*c4^2+2*b5*a52*c2*a53*c3+2*b5*a52*c2*a54*c4+2*b5*a53*c3*a54*c4+b6*a62^2*c2^2+b6*a63^2*c3^2+b6*a64^2*c4^2+b6*a65^2*c5^2+2*b6*a62*c2*a63*c3+2*b6*a62*c2*a64*c4+2*b6*a62*c2*a65*c5+2*b6*a63*c3*a64*c4+2*b6*a63*c3*a65*c5+2*b6*a64*c4*a65*c5-1/20),
84: (+b3*a32*c2^3+b4*a42*c2^3+b4*a43*c3^3+b5*a52*c2^3+b5*a53*c3^3+b5*a54*c4^3+b6*a62*c2^3+b6*a63*c3^3+b6*a64*c4^3+b6*a65*c5^3-1/20),
85: (+b4*a43*c3*a32*c2+b5*a53*c3*a32*c2+b5*a54*c4*a42*c2+b5*a54*c4*a43*c3+b6*a63*c3*a32*c2+b6*a64*c4*a42*c2+b6*a64*c4*a43*c3+b6*a65*c5*a52*c2+b6*a65*c5*a53*c3+b6*a65*c5*a54*c4-1/40),
86: (+b4*a43*a32*c2^2+b5*a53*a32*c2^2+b5*a54*a42*c2^2+b5*a54*a43*c3^2+b6*a63*a32*c2^2+b6*a63*a42*c2^2+b6*a64*a43*c3^2+b6*a65*a52*c2^2+b6*a65*a53*c3^2+b6*a65*a54*c4^2-1/60),
87: (+b5*a54*a43*a32*c2+b6*a64*a43*a32*c2+b6*a65*a53*a32*c2+b6*a65*a54*a42*c2+b6*a65*a54*a43*c3-1/20)
88: ]]$
89:
90: /*$(butcher,runge-kutta,20 1 1984 s=3 pt=4)
91: d=q
92: r=d(b,c2,c3,a,b3,b2,a32,b1)
93: opt=liope10*/
94: Butcher = [
95: [b1,a32,b2,b3,a,c3,c2,b],[
96: (b1+b2+b3
97: -(a+b)),
98: (b2*c2+b3*c3
99: -(1/2+1/2*b+b^2-a*b)),
100: (b2*c2^2+b3*c3^2
101: -(a*(1/3+b^2)-4/3*b-b^2-b^3)),
102: (b3*a32*c2
103: -(a*(1/6+1/2*b+b^2)-2/3*b-b^2-b^3)),
104: (b2*c2^3+b3*c3^3
105: -(1/4+1/4*b+5/2*b^2+3/2*b^3+b^4
106: -a*(b+b^3))),
107: (b3*c3*a32*c2
108: -(1/8+3/8*b+7/4*b^2+3/2*b^3+b^4
109: -a*(1/2*b+1/2*b^2+b^3))),
110: (b3*a32*c2^2
111: -(1/12+1/12*b+7/6*b^2+3/2*b^3+b^4
112: -a*(2/3*b+b^2+b^3))),
113: (1/24+7/24*b+13/12*b^2+3/2*b^3+b^4
114: -a*(1/3*b+b^2+b^3))
115: ]]$
116:
117: /*$(gerdt,10.10.84)
118: d=q
119: r=d(l1,l2,l3,l4,l5,l6,l7)
120: opt=oil pe10*/
121: Gerdt = [
122: [l7,l6,l5,l4,l3,l2,l1],[
123: (l1*(l4-1/2*l5+l6)),
124: ((2/7*l1^2-l4)*(-10*l1+5*l2-l3)),
125: ((2/7*l1^2-l4)*(3*l4-l5+l6)),
126: ((-2*l1^2+l1*l2+2*l1*l3-l2^2-7*l5+21*l6) *(-3*l1+2*l2)+21*(7*l7-2*l1*l4+3/7*l1^3)),
127: ((-2*l1^2+l1*l2+2*l1*l3-l2^2-7*l5+21*l6) *(2*l4-2*l5)+(7*l7-2*l1*l4+3/7*l1^3) *(-45*l1+15*l2-3*l3)),
128: (2*(-2*l1^2+l1*l2+2*l1*l3-l2^2-7*l5+21*l6) *l7+(7*l7-2*l1*l4+3/7*l1^3)* (12*l4-3*l5+2*l6)),
129: ((l1*(5*l1-3*l2+l3))* (2*l2-l1) +7*(l1*(2*l6-4*l4))),
130: ((l1*(5*l1-3*l2+l3))* l3+7*(l1*(2*l6-4*l4))),
131: ((l1*(5*l1-3*l2+l3))* (-2*l4-2*l5)+(l1*(2*l6-4*l4))* (2*l2-8*l1)+84*1/2*l1*l7),
132: ((l1*(5*l1-3*l2+l3))* (8/3*l5+6*l6)+(l1*(2*l6-4*l4))* (11*l1-17/3*l2+5/3*l3)-168*1/2*l1*l7),
133: (15*l7* (l1*(5*l1-3*l2+l3)) +(l1*(2*l6-4*l4))*(5*l4-2*l5) +1/2*l1*l7*(-120*l1+30*l2-6*l3)),
134: (-3*(l1*(5*l1-3*l2+l3))* l7+(l1*(2*l6-4*l4))* (-1/2*l4+1/4*l5-1/2*l6)+1/2*l1*l7* (24*l1-6*l2)),
135: (3*(l1*(2*l6-4*l4))* l7+1/2*l1*l7* (40*l4-8*l5+4*l6))
136: ]]$
137:
138:
139: /*$(raksanyi 1,1983 rational*functions.)
140: d=f(a1,a2,a3,a4)
141: r=(x1,x2,x3,x4)
142: opt=oil*/
143: Raksanyi = [
144: [x4,x3,x2,x1],[
145: (x4-(a4-a2)),
146: (x1+x2+x3+x4-(a1+a3+a4)),
147: (x1*x3+x1*x4+x2*x3+x3*x4-(a1*a4+a1*a3+a3*a4)),
148: (x1*x3*x4-(a1*a3*a4))
149: ]]$
150:
151:
152: /*$(rose,general equilibrium model,1984)
153: d=q
154: r=d(u3,u4,a46)
155: opt=iog*/
156: Rose = [
157: [u3,u4,a46],[
158: /*[a46,u4,u3],[*/
159: (u4^4-20/7*a46^2),
160: (a46^2*u3^4+7/10*a46*u3^4+7/48*u3^4-50/27
161: *a46^2-35/27*a46-49/216),
162: (a46^5*u4^3+7/5*a46^4*u4^3+609/1000*a46^3
163: *u4^3+49/1250*a46^2*u4^3-27391/800000*a46*u4^3
164: -1029/160000*u4^3+3/7*a46^5*u3*u4^2+3/5*a46^6
165: *u3*u4^2+63/200*a46^3*u3*u4^2+147/2000*a46^2
166: *u3*u4^2+4137/800000*a46*u3*u4^2-7/20*a46^4
167: *u3^2*u4-77/125*a46^3*u3^2*u4-23863/60000*a46^2
168: *u3^2*u4-1078/9375*a46*u3^2*u4-24353/1920000
169: *u3^2*u4-3/20*a46^4*u3^3-21/100*a46^3*u3^3
170: -91/800*a46^2*u3^3-5887/200000*a46*u3^3
171: -343/128000*u3^3)
172: ]]$
173:
174:
175:
176: /*$(university of waterloo,19.03,1984)
177: d=q
178: r=d(a0,a2,a3,a4,a5,b0,b1,b2,b3,b4,b5,c0,c1,c2,c3,c4,c5)
179: opt=oil*pe10*/
180: Waterloo = [
181: [c5,c4,c3,c2,c1,c0,b5,b4,b3,b2,b1,b0,a5,a4,a3,a2,a0],[
182: (a4*b4),
183: (a5*b1+b5+a4*b3+a3*b4),
184: (a2*b2),
185: (a5*b5),
186: (a0*b2+b2+a4*b2+a2*b4+c2+a2*b0+a2*b1),
187: (a0*b0+a0*b1+a0*b4+a3*b2+b0+b1+b4+a4*b0 +a4*b1 +a2*b5+a4*b4+c1+c4+a5*b2+a2*b3+c0),
188: (a3*b0+a0*b3+a0*b5+a5*b0+b3+b5+a5*b4+a4*b3+ a4*b5+a3*b4+a5*b1+a3*b1+c3+c5-1),
189: (a5*b3+a5*b5+a3*b5+a3*b3),
190: (a5*b3+2*a5*b5+a3*b5),
191: (a0*b5+a5*b0+a3*b4+2*a5*b4+a5*b1+b5+a4*b3 +2*a4*b5+c5),
192: (a4*b0+2*a4*b4+a2*b5+b4+a4*b1+a5*b2+a0*b4 +c4),
193: (a2*b4+a4*b2),
194: (a4*b5+a5*b4),
195: (2*a3*b3+a5*b3+a3*b5),
196: (c3+a0*b3+2*b3+b5+a4*b3+a3*b0+2*a3*b1+ a5*b1+a3*b4),
197: (c1+a0*b1+2*b1+a4*b1+a2*b3+b0+a3*b2+b4),
198: (a2*b1+b2),
199: (a5*b3+a3*b5),
200: (b4+a4*b1)
201: ]]$
202:
203:
204: /*$(trinks 1,ideal a. 09.12.1983)
205: d=q
206: r=d(b,s,t,z,p,w)
207: opt=1*/
208: Trinks1 = [
209: /*[z,t,w,b,p,s],[*/
210: [w,p,z,t,s,b],[
211: (+45*p+35*s-165*b-36),
212: (+35*p+40*z+25*t-27*s),
213: (+15*w+25*p*s+30*z-18*t-165*b^2),
214: (-9*w+15*p*t+20*z*s),
215: (w*p+2*z*t-11*b^3),
216: (99*w-11*s*b+3*b^2)
217: ]]$
218:
219:
220: /*$(trinks 2,ideal p=a+f7lr.10.12.1983)
221: d=q
222: r=d(b,s,t,z,p,w)
223: opt=il*/
224: Trinks2 = [
225: [w,p,z,t,s,b],[
226: +45*p+35*s-165*b-36,
227: +35*p+40*z+25*t-27*s,
228: +15*w+25*p*s+30*z-18*t-165*b^2,
229: -9*w+15*p*t+20*z*s,
230: w*p+2*z*t-11*b^3,
231: 99*w-11*s*b+3*b^2,
232: b^2+33/50*b+2673/10000
233: ]]$
234:
235: Ge = [
236: [x,y,z,t,u,v,w],[
237: (w*(t-1/2*z+y)),
238: ((2/7*w^2-t)*(-10*w+5*v-u)),
239: ((2/7*w^2-t)*(3*t-z+y)),
240: ((-2*w^2+w*v+2*w*u-v^2-7*z+21*y) *(-3*w+2*v)+21*(7*x-2*w*t+3/7*w^3)),
241: ((-2*w^2+w*v+2*w*u-v^2-7*z+21*y) *(2*t-2*z)+(7*x-2*w*t+3/7*w^3) *(-45*w+15*v-3*u)),
242: (2*(-2*w^2+w*v+2*w*u-v^2-7*z+21*y) *x+(7*x-2*w*t+3/7*w^3)* (12*t-3*z+2*y)),
243: ((w*(5*w-3*v+u))* (2*v-w) +7*(w*(2*y-4*t))),
244: ((w*(5*w-3*v+u))* u+7*(w*(2*y-4*t))),
245: ((w*(5*w-3*v+u))* (-2*t-2*z)+(w*(2*y-4*t))* (2*v-8*w)+84*1/2*w*x),
246: ((w*(5*w-3*v+u))* (8/3*z+6*y)+(w*(2*y-4*t))* (11*w-17/3*v+5/3*u)-168*1/2*w*x),
247: (15*x* (w*(5*w-3*v+u)) +(w*(2*y-4*t))*(5*t-2*z) +1/2*w*x*(-120*w+30*v-6*u)),
248: (-3*(w*(5*w-3*v+u))* x+(w*(2*y-4*t))* (-1/2*t+1/4*z-1/2*y)+1/2*w*x* (24*w-6*v)),
249: (3*(w*(2*y-4*t))* x+1/2*w*x* (40*t-8*z+4*y))
250: ]]$
251: end$
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