Annotation of OpenXM_contrib2/asir2000/lib/bgk, Revision 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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