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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 )
 `‣ CXSCFloatsFamily` ( global variable )
 `‣ 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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