# Package sat/SAT.ConvertToCNF

## SAT.ConvertToCNF

Converts a given quadratic (cubic) system of polynomial equations (SPE) over GF(2) to CNF. Writes the CNF to a temporary file whose path is returned.

### Syntax

```SAT.ConvertToCNF(SPE:LIST, CuttingNumber:INT, QStrategy:INT, CStrategy:INT):STRING
```

### Description

This function starts the conversion algorithm.

• @param SPE: A List containing the polynomial equations of the system.

• @param CuttingNumber: Maximal support-length of the linear polynomials when their corresponding CNF is written to the file. Could be 3 - 6.

• @param QStrategy: Strategy for quadratic substitution. 0 - Standard; 1 - Linear Partner; 2 - Adv. Lin. Partner;

• @param CStrategy: Strategy for cubic substitution. 0 - Standard; 1 - Quadratic Partner;

• @return The path of the file where the output was written to.

#### Example

```-- quadratic system:
Use S ::= ZZ/(2)[x[1..3]];
F1 := x*x + x*x + x*x + x;
F2 := x + 1;
F3 := x*x + x;
SPE := [F1,F2,F3];
CNFPath := SAT.ConvertToCNF(SPE,4,0,0);
SolPath := SAT.LaunchCryptoMiniSat(CNFPath);
SAT.GetResult(SolPath,S);
--Result: [0,1,0] Test with: Eval(SPE,[0,1,0]);
```

#### Example

```-- cubic system:
Use S ::= ZZ/(2)[x[1..3]];
F1 := x*x*x + x*x + x*x + x + x +1;
F2 := x*x*x + x*x + x*x + x + x;
F3 := x*x + x*x + x;
SPE := [F1,F2,F3];
CNFPath := SAT.ConvertToCNF(SPE,4,1,0);
SolPath := SAT.LaunchCryptoMiniSat(CNFPath);
SAT.GetResult(SolPath,S);
--Result: [0,0,1] Test with: Eval(SPE,[0,0,1]);
```