Home - News ( United States | United Kingdom | Italy | Germany ) - Football scores

Showing content from http://reference.wolfram.com/language/ref/FindIntegerNullVector.html below:

FindIntegerNullVector—Wolfram Language Documentation

We deliver solutions for the AI era—combining symbolic computation, data-driven insights and deep technology expertise.

• Data & Computational Intelligence
• Model-Based Design
• Algorithm Development
• Wolfram|Alpha for Business
• Blockchain Technology
• Education Technology
• Quantum Computation

WolframConsulting.com

• See Also
  • Rationalize
  • RootApproximant
  • LatticeReduce
  • FindSequenceFunction
  • FindInstance
• Related Guides
  • Number Recognition

Exact input:

Inexact input:

Exact input with norm bound:

There is no null vector with norm less than or equal to 2:

This finds an integer null vector for a vector of exact real numbers:

This proves that there is no null vector with norm less than or equal to 8:

For a bound close to the norm of a null vector you may not get proof that no null vector exists:

The returned null vector does not satisfy the norm bound:

FindIntegerNullVector cannot prove that numbers are linearly independent over the integers:

It can prove that there is no integer null vector with norm less than or equal to a given bound:

For inexact input, the relation is true up to the precision of the input:

No null vector exists for the given norm bound:

Here no null vector is found, but nonexistence of a null vector is proven only for a smaller norm bound:

This finds a null vector for a 20-digit approximation of :

The result is not a null vector for the exact vector :

A null vector found for a higher-precision approximation of is also a null vector for :

This gives a Gaussian integer null vector for a vector of exact complex numbers:

This finds a Gaussian integer null vector for a vector of approximate complex numbers:

By default, PossibleZeroQ with Method->"ExactAlgebraics" is used to prove relations:

This uses exact methods to prove the relation:

This uses a high-precision numeric test instead:

Find coefficients of the minimal polynomial of an algebraic number:

This finds the minimal polynomial using symbolic methods:

Find a relation between transcendental numbers:

Find the coefficients in Machin's formula for computing approximations of :

FindIntegerNullVector returns an integer null vector for the given vector:

An integer null vector is a nontrivial integer solution of a homogeneous linear equation:

Use FindInstance to find solutions of equations:

Find coefficients of the minimal polynomial of an algebraic number using its approximation:

Use RootApproximant to find an algebraic number using its approximation:

The precision of an approximation may not be sufficient to find a relation between numbers:

Using a higher-precision approximation, you get a true relation:

Numeric zero testing used for nonalgebraic numbers may allow results that are not null vectors:

This gives the precision used in zero testing when no symbolic zero-testing method applies:

With a higher zero-testing precision, FindIntegerNullVector correctly rejects the vector:

Reset the system option to the original value:

RetroSearch is an open source project built by @garambo | Open a GitHub Issue

Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo

HTML: 3.2 | Encoding: UTF-8 | Version: 0.7.4