GAP (FLOAT) - Chapter 4: Implemented packages

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4 Implemented packages
4.1 MPFR
4.1-1 IsMPFRFloat
4.2 MPFI
4.2-1 IsMPFIFloat
4.3 MPC
4.3-1 IsMPCFloat
4.4 CXSC
4.4-1 IsCXSCReal
4.5 FPLLL
4.5-1 FPLLLReducedBasis
4.5-2 FPLLLShortestVector

### 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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