Roots of a cubic polynomial: Difference between revisions
J draft
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=={{header|J}}==
Using J's [[j:Vocabulary/pdot|polynomial primitive]] for most of the heavy lifting here. Also using J's [[j:Vocabulary/dot|generalized determinant]] to find the characteristic polynomial (first turning each element of the matrix into a polynomial then finding the determinant of the result):
Implementation:
<syntaxhighlight lang=J>
NB. matrix characteristic polynomial
mcp=: {{ ;pdf/ .ppr y,each -=i.#y }}
pdf=: -/@,:L:0 NB. polynomial difference
ppr=: +//.@(*/)L:0 NB. polynomial product
proots=: 1 {:: p. NB. polynomial roots
task=: {{
poly=. mcp y
roots=. proots poly
errors=. poly p."1 0 roots
lines=. (,:'matrix: '),&.|:&": y
lp=. 'coefficients: ',":poly
lr=. 'roots: ',":roots
le=. 'errors: ',":errors
lines,lp,lr,:le
}}</syntaxhighlight>
Task examples:
<syntaxhighlight lang=J>
task 1 _1,0 1 1,:0 0 1
matrix: 1 _1 0
0 1 1
0 0 1
coefficients: 1 _3 3 _1
roots: 1 1 1
errors: 0 0 0
task _2 _4 2,_2 1 2,:4 2 5
matrix: _2 _4 2
_2 1 2
4 2 5
coefficients: _90 27 4 _1
roots: 6 _5 3
errors: 0 0 0
task 1 _1,0 1 _1,:0 0 1
matrix: 1 _1 0
0 1 _1
0 0 1
coefficients: 1 _3 3 _1
roots: 1 1 1
errors: 0 0 0
task 2 0,0 _1,:0 0 _1
matrix: 2 0 0
0 _1 0
0 0 _1
coefficients: 2 3 0 _1
roots: 2 _1 _1
errors: 0 0 0
task 2 0,0 3 4,:0 4 9
matrix: 2 0 0
0 3 4
0 4 9
coefficients: 22 _35 14 _1
roots: 11 2 1
errors: 0 0 0
task 1 0,0,.+.1ad_45 1ad45
matrix: 1 0 0
0 0.707107 _0.707107
0 0.707107 0.707107
coefficients: 1 _2.41421 2.41421 _1
roots: 1 0.707107j0.707107 0.707107j_0.707107
errors: 0 4.44089e_15j_1.77636e_15 4.44089e_15j1.77636e_15</syntaxhighlight>
We could instead use [[j:Vocabulary/LAPACK|lapack]]. The lapack approach would be more stable for very large matrices, but that's not an issue here.
=={{header|Julia}}==
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