### 4 Implemented packages

#### 4.1 MPFR

##### 4.1-1 IsMPFRFloat

`‣ TYPE_MPFR` | ( global variable ) |

The category of floating-point numbers.

Note that they are treated as commutative and scalar, but are not necessarily associative.

#### 4.2 MPFI

##### 4.2-1 IsMPFIFloat

`‣ TYPE_MPFI` | ( global variable ) |

The category of intervals of floating-point numbers.

Note that they are treated as commutative and scalar, but are not necessarily associative.

#### 4.3 MPC

##### 4.3-1 IsMPCFloat

`‣ TYPE_MPC` | ( global variable ) |

The category of intervals of floating-point numbers.

Note that they are treated as commutative and scalar, but are not necessarily associative.

#### 4.4 CXSC

##### 4.4-1 IsCXSCReal

`‣ IsCXSCComplex` | ( filter ) |

`‣ IsCXSCInterval` | ( filter ) |

`‣ TYPE_CXSC_RP` | ( global variable ) |

`‣ TYPE_CXSC_CP` | ( global variable ) |

`‣ TYPE_CXSC_RI` | ( global variable ) |

`‣ TYPE_CXSC_CI` | ( global variable ) |

The category of floating-point numbers.

Note that they are treated as commutative and scalar, but are not necessarily associative.

#### 4.5 FPLLL

##### 4.5-1 FPLLLReducedBasis

`‣ FPLLLReducedBasis` ( `m` ) | ( operation ) |

Returns: A matrix spanning the same lattice as `m`.

This function implements the LLL (Lenstra-Lenstra-Lovász) lattice reduction algorithm via the external library **fplll**.

The result is guaranteed to be optimal up to 1%.

##### 4.5-2 FPLLLShortestVector

`‣ FPLLLShortestVector` ( `m` ) | ( operation ) |

Returns: A short vector in the lattice spanned by `m`.

This function implements the LLL (Lenstra-Lenstra-Lovász) lattice reduction algorithm via the external library **fplll**, and then computes a short vector in this lattice.

The result is guaranteed to be optimal up to 1%.