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# fp Plugin 10.1

1. last year

### Dana B

4 Dec 2018 Xojo Inc Austin, Texas

Announcing fp Plugin 10.1 from Bob Delaney.

Using the fp multi-precision engine, fp Plugin 10.1 for Xojo has eight data types:
BigInteger
BigFloat
BigComplex
BigFraction
BigPoly
BigFloatMatrix
BigComplexMatrix
BigFractionMatrix
All types have unlimited precision.

fp Plugin allows a developer to construct Xojo programs which can handle the eight data types much like doubles and integers are handled. To a large extent the plugin's data types can be freely used with the +, -, *, and / operators, and can be used in comparisons. And some of Xojo's functions have been overloaded to take the plugin's data types, where it makes sense to do so.

Version 10.1 adds the ability to calculate the eigenvectors and eigenvalues of any square matrix at any chosen precision. It also can compute the rank of any matrix. The included TestBigFractionMatrix application uses these new functions. For example, the matrix:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
gives this output:

eigenvalue = 36.20937271229855
algebraic multiplicity = 1
geometric multiplicity = 1
eigenvector(s) =
1
2.310468635614927
3.620937271229855
4.931405906844782

eigenvalue = 0
algebraic multiplicity = 2
geometric multiplicity = 2
eigenvector(s) =
1
0
-3
2

0
1
-2
1

eigenvalue = -2.209372712298546
algebraic multiplicity = 1
geometric multiplicity = 1
eigenvector(s) =
1
0.3895313643850727

• 0.2209372712298546
• 0.8314059068447819

The matrix
1 2 4
0 1 3
0 0 1
gives the output:

eigenvalue = 1
algebraic multiplicity = 3
geometric multiplicity = 1
eigenvector(s) =
1
0
0

So there were three eigenvalues of 1, but only one eigenvector.

fp Plugin is compiled for Mac, Windows, and Linux for both 32 and 64 bit applications.
fp Plugin is freeware with an easy-to-meet license. It is unconditionally available for any use, but is without warranty.