Macaulay2 » Documentation
Packages » ExampleSystems :: wright
next | previous | forward | backward | up | index | toc

# wright -- system of A.H. Wright

- Usage:
    `wright(kk)`
- Inputs:
  - kk, a ring, the coefficient ring
- Outputs:
  - a list, of the polynomials in the system

## Description

This system was solved in May 2020, using solveSystem in Macaulay2 v1.15 with an Intel(R) Core(TM) i5-5250U CPU at 1.60GHz.

There were 32 solutions found in 0.0944 seconds (with a Bezout bound of 32).

Reference: "Computation of all solutions to a system of polynomial equations" by M. Kojima and S. Mizuno (pages 131-157), "Finding all solutions to a system of polynomial equations" by A.H. Wright (pages 125-133), and "A simple homotopy method for determining all isolated solutions to polynomial systems" by W. Zulehner (pages 167-177).

See also: http://homepages.math.uic.edu/~jan/Demo/wright.html.

    i1 : wright(QQ)

           2                                 2                                 2
    o1 = {x  - x  + x  + x  + x  + x  - 10, x  + x  - x  + x  + x  + x  - 10, x
           1    1    2    3    4    5        2    1    2    3    4    5        3
         ------------------------------------------------------------------------
                                         2                                 2
         + x  + x  - x  + x  + x  - 10, x  + x  + x  + x  - x  + x  - 10, x  + x
            1    2    3    4    5        4    1    2    3    4    5        5    1
         ------------------------------------------------------------------------
         + x  + x  + x  - x  - 10}
            2    3    4    5

    o1 : List

## Ways to use wright:

- `wright(Ring)`

## For the programmer

The object wright is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/ExampleSystems/wright.m2:45:0.