Evaluate the polynomial at x.
Evaluate the polynomial at x.
Returns the coefficients in little-endian order.
Returns the coefficients in little-endian order. So, the i-th element is coeffsArray(i) * (x ** i).
Compose this polynomial with another.
Compose this polynomial with another.
Returns a map from exponent to coefficient of this polynomial.
Returns a map from exponent to coefficient of this polynomial.
Returns the degree of this polynomial.
Returns the degree of this polynomial.
This will flip/mirror the polynomial about the y-axis.
This will flip/mirror the polynomial about the y-axis. It is equivalent to
poly.compose(-Polynomial.x), but will likely be faster to calculate.
Traverses each term in this polynomial, in order of degree, lowest to highest (eg.
Traverses each term in this polynomial, in order of degree, lowest to
highest (eg. constant term would be first) and calls f with the degree
of term and its coefficient. This may skip zero terms, or it may not.
Traverses each non-zero term in this polynomial, in order of degree, lowest to highest (eg.
Traverses each non-zero term in this polynomial, in order of degree, lowest
to highest (eg. constant term would be first) and calls f with the degree
of term and its coefficient.
Returns true iff this polynomial is constant.
Returns true iff this polynomial is constant.
Returns true if this polynomial is ring.zero.
Returns true if this polynomial is ring.zero.
Returns the coefficient of max term of this polynomial.
Returns the coefficient of max term of this polynomial.
Returns the term of the highest degree in this polynomial.
Returns the term of the highest degree in this polynomial.
Returns the non-zero term of the minimum degree in this polynomial, unless it is zero.
Returns the non-zero term of the minimum degree in this polynomial, unless it is zero. If this polynomial is zero, then this returns a zero term.
Returns this polynomial as a monic polynomial, where the leading coefficient (ie.
Returns this polynomial as a monic polynomial, where the leading
coefficient (ie. maxOrderTermCoeff) is 1.
Returns the coefficient of the n-th degree term.
Returns the coefficient of the n-th degree term.
Returns the reciprocal of this polynomial.
Returns the reciprocal of this polynomial. Essentially, if this polynomial
is p with degree n, then returns a polynomial q(x) = x^n*p(1/x).
http://en.wikipedia.org/wiki/Reciprocal_polynomial
Returns a polynomial with the max term removed.
Returns a polynomial with the max term removed.
Removes all zero roots from this polynomial.
Removes all zero roots from this polynomial.
Returns the real roots of this polynomial.
Returns the real roots of this polynomial.
Depending on C, the finder argument may need to be passed "explicitly"
via an implicit conversion. This is because some types (eg BigDecimal,
Rational, etc) require an error bound, and so provide implicit
conversions to RootFinders from the error type. For instance,
BigDecimal requires either a scale or MathContext. So, we'd call this
method with poly.roots(MathContext.DECIMAL128), which would return a
Roots[BigDecimal whose roots are approximated to the precision specified
in DECIMAL128 and rounded appropriately.
On the other hand, a type like Double doesn't require an error bound and
so can be called without specifying the RootFinder.
a root finder to extract roots with
the real roots of this polynomial
Shift this polynomial along the x-axis by h, so that this(x + h) ==
this.shift(h).apply(x).
Shift this polynomial along the x-axis by h, so that this(x + h) ==
this.shift(h).apply(x). This is equivalent to calling
this.compose(Polynomial.x + h), but is likely to compute the shifted
polynomial much faster.
Returns the number of sign variations in the coefficients of this polynomial.
Returns the number of sign variations in the coefficients of this polynomial. Given 2 consecutive terms (ignoring 0 terms), a sign variation is indicated when the terms have differing signs.
Returns a list of non-zero terms.
Returns a list of non-zero terms.
Return an iterator of non-zero terms.
Return an iterator of non-zero terms.
This method is used to implement equals and hashCode.
NOTE: This method uses a (_ == 0) test to prune zero values. This makes sense in a context where Semiring[C] and Eq[C] are unavailable, but not other places.
Returns a polynmial that has a dense representation.
Returns a polynmial that has a dense representation.
Returns a polynomial that has a sparse representation.
Returns a polynomial that has a sparse representation.