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order_two.go
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order_two.go
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package polynomials
import (
"math/big"
"github.com/gbdubs/maybebig/maybebig"
"github.com/gbdubs/polynomials/bigcomplex"
"github.com/gbdubs/polynomials/maybebigcomplex"
)
func SecondOrder(a, b, c *bigcomplex.BigComplex) []*bigcomplex.BigComplex {
if a.IsZero() {
return FirstOrder(b, c)
}
disc := sub(sq(b), mul(mul(a, c), bigcomplex.FromInt(4)))
negOne := bigcomplex.FromInt(-1)
two := bigcomplex.FromInt(2)
if disc.IsZero() {
return []*bigcomplex.BigComplex{div(mul(negOne, b), mul(two, a))}
}
root := disc.Sqrt()
result := []*bigcomplex.BigComplex{
div(sub(mul(negOne, b), root), mul(two, a)),
div(add(mul(negOne, b), root), mul(two, a)),
}
return bigcomplex.Unique(result)
}
func SecondOrderMB(a, b, c *maybebigcomplex.BigComplex) []*maybebigcomplex.BigComplex {
if a.IsZero() {
return FirstOrderMB(b, c)
}
disc := subMB(sqMB(b), mulMB(mulMB(a, c), maybebigcomplex.FromInt(4)))
negOne := maybebigcomplex.FromInt(-1)
two := maybebigcomplex.FromInt(2)
if disc.IsZero() {
return []*maybebigcomplex.BigComplex{divMB(mulMB(negOne, b), mulMB(two, a))}
}
root := disc.Sqrt()
result := []*maybebigcomplex.BigComplex{
divMB(subMB(mulMB(negOne, b), root), mulMB(two, a)),
divMB(addMB(mulMB(negOne, b), root), mulMB(two, a)),
}
return maybebigcomplex.Unique(result)
}
func SecondOrderComplex128(a, b, c complex128) []complex128 {
return ToComplex128s(
SecondOrder(
FromComplex128UseWithCaution(a),
FromComplex128UseWithCaution(b),
FromComplex128UseWithCaution(c)))
}
func SecondOrderReal(a, b, c *big.Float) []*big.Float {
return RealComponents(
FilterToReals(
SecondOrder(
&bigcomplex.BigComplex{Real: newFloat().Set(a), Imag: newFloat()},
&bigcomplex.BigComplex{Real: newFloat().Set(b), Imag: newFloat()},
&bigcomplex.BigComplex{Real: newFloat().Set(c), Imag: newFloat()})))
}
func SecondOrderRealMB(a, b, c *maybebig.Float) []*maybebig.Float {
return RealComponentsMB(
FilterToRealsMB(
SecondOrderMB(
&maybebigcomplex.BigComplex{Real: a, Imag: maybebig.NewFloatZ()},
&maybebigcomplex.BigComplex{Real: b, Imag: maybebig.NewFloatZ()},
&maybebigcomplex.BigComplex{Real: c, Imag: maybebig.NewFloatZ()})))
}
func SecondOrderRealFloat64(a, b, c float64) []float64 {
return Float64s(
RealComponents(
FilterToReals(
SecondOrder(
FromFloat64UseWithCaution(a),
FromFloat64UseWithCaution(b),
FromFloat64UseWithCaution(c)))))
}