What is the best way to identify a multivariate change of variables for an expression? Consider the followin: ``` >>> c 3*y**4 + 6*y**3*z + 42*y**3 - 9*y**2*z**2 + 126*y**2*z + 148*y**2 - 12*y*z**3 + 589*y*z + 7*y + 12*z**4 - 168*z**3 + 586*z**2 + 14*z + 2 >>> factor(c-2) (y + 2*z)*(y - z + 7)*(3*y**2 + 3*y*z + 21*y - 6*z**2 + 42*z + 1) >>> factor(_.args[-1]-1) 3*(y + 2*z)*(y - z + 7) >>> (x*(3*x+1)+2).subs(x,(y + 2*z)*(y - z + 7)).expand() == c True ```
This is a bit like `horner` (but `horner` gives something else in this cse): ``` >>> horner(c) y*(y*(y*(3*y + 6*z + 42) + z*(126 - 9*z) + 148) + z*(589 - 12*z**2) + 7) + z*(z*(z*(12*z - 168) + 586) + 14) + 2 ``` It is also a bit like `decompose` (but `decompose` doesn't work on multivariates). The ability to identify this multivariate generator allows for a straightforward solution to the quartic in `y`: ``` >>> inv = solve(x - (y + 2*z)*(y - z + 7),y) >>> xs = solve(x*(3*x+1)+2,x) >>> ys = [i.subs(x, xi) for i in inv for xi in xs] >>> ys [-z/2 - sqrt(9*z**2 - 42*z + 145/3 - 2*sqrt(23)*I/3)/2 - 7/2, -z/2 - sqrt(9*z**2 - 42*z + 145/3 + 2*sqrt(23)*I/3)/2 - 7/2, -z/2 + sqrt(9*z**2 - 42*z + 145/3 - 2 *sqrt(23)*I/3)/2 - 7/2, -z/2 + sqrt(9*z**2 - 42*z + 145/3 + 2*sqrt(23)*I/3)/2 - 7/2] ``` Without identifying the generator the equation can also be solved ``` >>> sol=solve(c,y) >>> sol [sqrt(3)*(-sqrt(3)*z - sqrt(27*z**2 - 126*z + 145 - 2*sqrt(23)*I) - 7*sqrt(3))/6 , sqrt(3)*(-sqrt(3)*z + sqrt(27*z**2 - 126*z + 145 - 2*sqrt(23)*I) - 7*sqrt(3))/ 6, sqrt(3)*(-sqrt(3)*z - sqrt(27*z**2 - 126*z + 145 + 2*sqrt(23)*I) - 7*sqrt(3)) /6, sqrt(3)*(-sqrt(3)*z + sqrt(27*z**2 - 126*z + 145 + 2*sqrt(23)*I) - 7*sqrt(3) )/6] ``` The solutions are the same (but in different form). e.g. for `z = 3` ``` >>> [i.subs(z, 3).n(2) for i in sol] [-6.0 + 0.4*I, -4.0 - 0.4*I, -6.0 - 0.4*I, -4.0 + 0.4*I] >>> [i.subs(z, 3).n(2) for i in ys] [-6.0 + 0.4*I, -6.0 - 0.4*I, -4.0 - 0.4*I, -4.0 + 0.4*I] ``` /c -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/a63b0136-6860-4312-b9a2-4380dc627f85n%40googlegroups.com.
