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IntegerRelations

  

LinearDependency

  

find an integer dependence (relation)

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

LinearDependency(v,opts)

Parameters

v

-

list or Vector of (complex) floating-point numbers

opts

-

(optional); equation of the form method=LLL or method=PSLQ specifying the algorithm used

Description

• 

The LinearDependency(v,opts) command finds an integer relation between the numbers in v - if they are linearly dependent. Given a list (or a Vector) of n real or complex numbers, LinearDependency outputs a list (or a Vector) u of n integers such that i=1nuivi is close to zero.

• 

By default, Bailey and Ferguson's PSLQ (Partial Sum of Least Squares) algorithm is used.

• 

The optional argument method=LLL specifies that the LLL (Lenstra-Lenstra-Lovasz) lattice basis reduction algorithm be used.

Examples

withIntegerRelations:

r2+3

r:=2+3

(1)

vexpandseqri,i=0..4

v:=1,2+3,5+223,112+93,49+2023

(2)

vevalfv,12

v:=1.,3.14626436994,9.89897948556,31.1448064542,97.9897948556

(3)

vevalfv

v:=1.,3.146264370,9.898979486,31.14480645,97.98979486

(4)

uLinearDependencyv

u:=1,0,10,0,1

(5)

adduivi,i=1..5

0.

(6)

madduizi1,i=1..5

m:=z410z2+1

(7)

simplifymz=r|mz=r

0

(8)

r1+213

r:=1+21/3

(9)

vVectorexpandseqri,i=0..4,12

v:=11+21/31+221/3+22/31+321/3+322/37+221/3+622/3

(10)

vevalfv,12:vevalfv

v:=1.1.629960525+1.091123636I1.466220524+3.556976909I1.491220003+7.397559819I10.50228211+10.43062509I

(11)

uLinearDependencyv,method=LLL

u:=12641

(12)

adduivi,i=1..5

0.1.10-8I

(13)

madduizi1,i=1..5

m:=z44z3+6z22z1

(14)

simplifymz=r|mz=r

0

(15)

solvem=0,z

1,21/3+1,1221/312I321/3+1,1221/3+12I321/3+1

(16)

evalcr

1221/3+12I321/3+1

(17)

See Also

identify

IntegerRelations

IntegerRelations[LLL]

IntegerRelations[PSLQ]

 


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