Algsys fails to solve this triangular system:
(%i1) eq : [q1^4+2,2*q2*q1^2-2,8*q3*q1^3+(12*q2^2+5)*q1^2-8*q2];
(%o1) [q1^4+2,2*q1^2*q2-2,8*q1^3*q3+q1^2*(12*q2^2+5)-8*q2]
(%i2) algsys(eq,[q1,q2,q3]);
(%o2) []
Changing order of the unknowns allows algsys to solve:
(%i3) algsys(eq,[q3,q2,q1]);
(%o3) [[q3=(3*(-1)^(1/4))/(8*2^(1/4)),q2=%i/sqrt(2), ...]
I'll file a bug report. But maybe somebody knows something
about this bug.
Barton