Homogeneous Diophantine - Maple Help
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NumberTheory

  

HomogeneousDiophantine

  

solution to Minkowski's linear forms

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

HomogeneousDiophantine(ineqs, xvars, yvars)

HomogeneousDiophantine(real_cfs, real_errors)

HomogeneousDiophantine(padic_cfs, adicities, padic_errors)

HomogeneousDiophantine(real_cfs, real_errors, padic_cfs, adicities, padic_errors)

Parameters

ineqs

-

inequality or set of inequalities with abs or valuep

xvars

-

name or set of names

yvars

-

name or set of names

real_cfs, padic_cfs

-

convertible to a Matrix of real numbers

adicities

-

convertible to a Vector of prime numbers

real_errors

-

convertible to a Vector of real numbers

padic_errors

-

convertible to a Vector of positive integers

Description

• 

The HomogeneousDiophantine function finds a solution  over the integers to a set of inequalities of the form

  

or   

  

where  is the p-adic valuation.

• 

The inequalities can be described explicitly, corresponding to the first calling sequence, or implicitly, corresponding to the other calling sequences.

• 

If the first calling sequence is used, then the return value is of the form

• 

If the other calling sequences are used, then the return value is a two-element list corresponding to the x values and the y values,

Examples

(1)

(2)

An equivalent matrix form calling sequence is:

(3)

The solutions may be different but both are valid.

Both abs and valuep may be used in the same system.

(4)

The error list for the p-adic cases are negatives of the exponents on the adicities.

(5)

Compatibility

• 

The NumberTheory[HomogeneousDiophantine] command was introduced in Maple 2016.

• 

For more information on Maple 2016 changes, see Updates in Maple 2016.

See Also

isolve

NumberTheory

NumberTheory[InhomogeneousDiophantine]

padic[valuep]

 


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