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### 4 Implemented packages

#### 4.1 MPFR

##### 4.1-1 IsMPFRFloat
 ‣ IsMPFRFloat ( filter )
 ‣ 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
 ‣ IsMPFIFloat ( filter )
 ‣ 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
 ‣ IsMPCFloat ( filter )
 ‣ 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
 ‣ IsCXSCReal ( filter )
 ‣ IsCXSCComplex ( filter )
 ‣ IsCXSCInterval ( filter )
 ‣ IsCXSCBox ( 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%.

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