maxima - 最大值：从方程中消除变量

Question

给定K个变量中的N个方程，Maxima 可以在KJ变量中生成NJ方程吗？

SOLVE 和 ELIMINATE 似乎无能为力，正要伸手去拿笔和纸。

标签： maximaequation-solving

Answer 1

(%i1) elim ([a = x + y, b = y + z, c = z + x, a = b * c], [a, b, c]);
(%o1)     elim([a = y + x, b = z + y, c = z + x, a = b c], [a, b, c])
(%i2) load (to_poly);
(%o2)  ~/maxima-5.44.0/share/to_poly_solve/to_poly.lisp
(%i3) elim ([a = x + y, b = y + z, c = z + x, a = b * c], [a, b, c]);
         2
(%o3) [[z  + (y + x) z + (x - 1) y - x], 
                                     [b z - y + b x - x, z + x - c, y + x - a]]
(%i4) solve (first (%o3), x);
                                     2
                                    z  + y z - y
(%o4)                        [x = - ------------]
                                     z + y - 1