**A complex polynomial system**- is denoted by the dimension followed by as many complex multivariate polynomials as the dimension. The dimension is a positive natural number.
**A complex multivariate polynomial**- is denoted as a sequence of terms,
separated by
`+`and terminated by the semicolon`;`. The brackets`(`and`)`must be used to isolate a sequence of terms as a factor in a complex multivariate polynomial. **A term**- can be either a coefficient or a coefficient,
followed by
`*`and a monomial. If in the latter case the coefficient equals one, then it may be omitted. **A coefficient**- may be denoted as an integer, a rational, a floating-point or a complex number.
**A monomial**- is a sequence of powers of unknowns,
separated by
`*`. The power operator is represented by`**`or .It must be followed by a positive natural number. If the power equals one, then it may be omitted. **An unknown**- can be denoted by at most five
characters. The first character must be a letter and the other two characters
must be different from
`+`,`-`,`*`,`,``/`,`;`,`(`and`)`. The letter*i*means , whence it does not represent an unknown. The number of unknowns may not exceed the declared dimension.

Some examples of valid notations of complex multivariate polynomials:

x**2*y + 1/2*z*y**2 - 2*z + y**3 + x - 1E9/-8.E-6* y + 3; x^2*y + z*y^2 - 2*z + y^3 + x - y + 3; (1.01 + 2.8*i)*x1**2*x2 + x3**2*x1 - 3*x1 + 2*x2*x3 - 3; (x1^2*x2 + x3^2*x1 - 3*x1 + 2*x2*x3 - 3)*x2**2*(x2-1+i);

Some notes concerning the internal representation:

- Graded lexicographical ordering is used for the monomials.
- The internal order of the unknowns is determined by the order
in which they occur in the polynomial system.
For example, if
`x2`is read before`x1`, then the powers of x2 will come first in the representation of the support sets and mixed subdivision. - The continuation parameter is represented by
*t*. Although*t*is not a reserved symbol, it is better not to use it to represent unknowns, to avoid confusion.

An input file to phc must begin with a polynomial system in the appropriate format. As example, consider the intersection of a circle with a parabola:

2 x**2 + 4*y**2 - 4; 2*y**2 - x;