1. Input formats

A lot of examples are contained in the database of Demo systems, which can be downloaded in zipped and tarred format from the above web site.

The input file starts with the number of equations and (optionally, but necessary in case of an unequal number) the number of unknowns. For example, the polynomial system of Bertrand Haas (which provided a counterexample for the conjecture of Koushnirenko) is represented as follows

   2
     x**108 + 1.1*y**54 - 1.1*y;
     y**108 + 1.1*x**54 - 1.1*x;

For future use, we save this system in the file haas. Observe that the = 0 is replaced by a semicolon. The exponentiation may also be denoted by a hat instead of a double asterix.

Symbols that are forbidden to denote names of variables are i and I, because they both represent $\sqrt{-1}$. Also forbidden are e and E because they are used in the scientific notation of floating-point numbers, like 0.01 = 1.0e-2 = 1.0E-2.

The equations defining the adjacent $2 \times 2$-minors of a general $2 \times 4$-matrix are represented as

   3 8
    x11*x22 - x21*x12;
    x12*x23 - x22*x13;
    x13*x24 - x23*x14;

thus as 3 polynomials in the 8 undeterminates of a general $2 \times 4$-matrix. We save this file as adjmin4.

The program also accepts polynomials in factored form, for example,

   5
    (a-1)*(b-5)*(c-9)*(d-13) - 21;
    (a-2)*(b-6)*(c-10)*(f-17) - 22;
    (a-3)*(b-7)*(d-14)*(f-18) - 23;
    (a-4)*(c-11)*(d-15)*(f-19) - 24;
    (b-8)*(c-12)*(d-16)*(f-20) - 25;

is a valid input file for PHC. Note that we replaced the logical e variable by f. We save this input in the file with name multilin.