The examples in this subsection have been used for testing purposes by Richard Lang.


Solve the following equations in x ...

No.1 3*x - 1 - (5*x - (2 - 4*x)) = -11

This equation apparently is a linear one.
No.2 (x - 5)*(10 - x) = (3 - x)*(2 + x) + 2*(x + 20)

This equation turns out to be linear, too.
No.3 (2*x + 5)^2 + (3*x + 4)^2 = (13*x + 2)*(x + 1) + 2*(15 + 14*x)
No.4 (2*x+1)^3 + (x+1)^3 = (2*x+1)^2 * 2*x + (x+2)^3 + x^2
No.5 (6*x - 9) * (5*x+7) - (4*x+7) * (3*x - 6) = 429

An equation solver also has to cope with digressive equations correctly, too:

No.6 1 = 0
No.7 0 = 0

This result is under consideration.

The following equations systematically cover the types of equation as  presently implemented. They are provided a certain method (in the specification hidden from the user; nevertheless you can view is in the 'Calchead' of the calculations root).

No.8 2 + (-1)*x + x^2 = 0
No.9 -2 + x + x^2 = 0
No.10 x +  x^2 = 0
No.11 -1 + x + 2*x^2 = 0

In all algebra systems term are ordered like this, in contrary to traditional customs in calculating by hand.  ISAC  uses the order above due to the same compellent technical reasons as algebra systems.
No.12 -2 + x + x^2 = 0
No.13 -8 + 2*x^2 = 0
No.14 -4 + x^2 = 0
No.15 2*x + 2*x^2 = 0
No.16 x + 2*x^2 = 0

And this example does not specify a certain method (in the hidden specification provided with the example) -- ISACs hierarchy of problems refines the type of the equation, and the type found assigns the appropriate method for solving.

No.17 3*x - 1 - (5*x - (2 - 4*x)) = -11