Re: Why does Solve give me no solutions for this in Version 8.0.1?
- To: mathgroup at smc.vnet.net
- Subject: [mg119969] Re: Why does Solve give me no solutions for this in Version 8.0.1?
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Sat, 2 Jul 2011 05:01:59 -0400 (EDT)
$Version 8.0 for Mac OS X x86 (64-bit) (February 23, 2011) ClearAll[a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s]; vars={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s}; eqns={ Total[vars]-190==0, a+b+c-38==0, a+d+h-38==0, a+e+j+o+s-38==0, b+e+i+m-38==0, b+f+k+p-38==0, c+f+j+n+q-38==0, c+g+l-38==0, d+e+f+g-38==0, d+i+n+r-38==0, g+k+o+r-38==0, h+i+j+k+l-38==0, h+m+q-38==0, l+p+s-38==0, m+n+o+p-38==0, q+r+s-38==0}; soln1=Solve[eqns,vars][[1]] Solve::svars: Equations may not give solutions for all "solve" variables. >> {c->38-a-b,g->38-d-e-f,h->38-a-d,k->38-b-e-f-i-j,l->-38+a+b+d+e+f,m->38-b-e-i,n->38-d-e-f-i-j,o->-38+b+d+e+f+i,p->e+i+j,q->-38+a+b+d+e+i,r->e+f+j,s->76-a-b-d-2 e-f-i-j} And@@(eqns/.soln1) True soln2=Reduce[eqns,vars]//ToRules {c->38-a-b,g->38-d-e-f,h->38-a-d,k->38-b-e-f-i-j,l->-38+a+b+d+e+f,m->38-b-e-i,n->38-d-e-f-i-j,o->-38+b+d+e+f+i,p->e+i+j,q->-38+a+b+d+e+i,r->e+f+j,s->76-a-b-d-2 e-f-i-j} soln1===soln2 True Bob Hanlon ---- Phil J Taylor <xptaylor at gmail.com> wrote: ============= This system of equations for the Magic Hexagon is indeterminate. Solve still provides useful information in Version 6.0 ClearAll[a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s]; eqns = { a + b + c + d + e + f + g + h + i + j + k + l + m + n + o + p + q + r + s - 190 == 0, a + b + c - 38 == 0, a + d + h - 38 == 0, a + e + j + o + s - 38 == 0, b + e + i + m - 38 == 0, b + f + k + p - 38 == 0, c + f + j + n + q - 38 == 0, c + g + l - 38 == 0, d + e + f + g - 38 == 0, d + i + n + r - 38 == 0, g + k + o + r - 38 == 0, h + i + j + k + l - 38 == 0, h + m + q - 38 == 0, l + p + s - 38 == 0, m + n + o + p - 38 == 0, q + r + s - 38 == 0 }; Join[ Solve[eqns, b], Solve[eqns, d], Solve[eqns, g], Solve[eqns, m], Solve[eqns, p], Solve[eqns, j], Solve[eqns, r], Solve[eqns, e], Solve[eqns, f], Solve[eqns, i], Solve[eqns, k], Solve[eqns, n], Solve[eqns, o], Solve[eqns, a], Solve[eqns, c], Solve[eqns, h], Solve[eqns, l], Solve[eqns, q], Solve[eqns, s]] Out[1]: {{b -> j + n + o}, {d -> j + k + o}, {g -> i + j + n}, {m -> f + j + k}, {p -> e + i + j}, {j -> -38 + d + g + r}, {r -> -38 + h + l + m + p}, {e -> -38 + h + k + q + r}, {f -> -38 + i + l + r + s}, {i -> -38 + f + p + q + s}, {k -> -38 + e + m + q + s}, {n -> -38 + g + h + k + l}, {o -> -38 + d + h + i + l}, {a -> -38 + i + m + n + q + r}, {c -> -38 + k + o + p + r + s}, {h -> -38 + n + o + p + r + s}, {l -> -38 + m + n + o + q + r}, {q -> -38 + g + k + l + o + p}, {s -> -38 + d + h + i + m + n}} Version 8.0.1 returns {}.