# Last modified on Tue Jan 25 18:54:16 PST 1994 by heydon

# This file is designed to test how the non-linear numeric solver performs
# when the input system contains a subsystem that is linear is a subset of the
# unknowns, but non-linear for the rest of the constraints. The question is
# whether the solver will converge on the exact solution for the linearly
# constrained variables immediately or not.

# Here is the linear subsystem:
#    y = x + 2
#    y = -1 * x
# This system has the solution x = -1, y = 1.
2 2 1
x ~ 0
y
y = PLUS(x, 2)
y = TIMES(-1, x)

# Now we add an additional constraint:
#    d^2 = (x - 3)^2 + (y - 4)^2
# We must introduce locals to express this constraint in normal form.
8 8 6
d ~ 10
x ~ 0
y
dx
dy
dxx
dyy
dd
y = PLUS(x, 2)
dx = PLUS(x, -3)
dy = PLUS(y, -4)
dxx = TIMES(dx, dx)
dyy = TIMES(dy, dy)
dd = PLUS(dxx, dyy)
dd = TIMES(d, d)
y = TIMES(-1, x)

3 3 2
x ~ 0
y
z
z = TIMES(x, 2)
y = PLUS(x, 2)
y = TIMES(-1, x)

3 3 2
x ~ 0
y
z
y = PLUS(x, 2)
z = TIMES(x, y)
y = TIMES(-1, x)

3 3 1
x ~ 0
z ~ 2
y
y = TIMES(z, z)
y = PLUS(x, 2)
y = TIMES(-1, x)

6 5 4
x ~ 1
a ~ 2
y
b
aa
aaa
y = PLUS(x, 2)
aa = TIMES(a, a)
aaa = TIMES(a, aa)
b = PLUS(aaa, x)
y = TIMES(-1, x)