- Companion
- class
Type members
Classlikes
An implementation of "A Separation Bound for Real Algebraic Expressions", by Burnikel, Funke, Mehlhorn, Schirra, and Schmitt. This provides a good ZeroBoundFunction for use in sign tests.
An implementation of "A Separation Bound for Real Algebraic Expressions", by Burnikel, Funke, Mehlhorn, Schirra, and Schmitt. This provides a good ZeroBoundFunction for use in sign tests.
Unlike the paper, we use log-arithmetic instead of working with exact, big integer values. This means our bound
isn't technically as good as it could be, but we save the cost of working with arithmetic. We also perform all log
arithmetic using Longs and check for overflow (throwing ArithmeticExceptions when detected). In practice we
shouldn't hit this limit, but in case we do, we prefer to throw over failing silently.
A bit bound represents either an upper or lower bound as some power of 2. Specifically, the bound is typically
either 2^bitBound or 2^-bitBound.
A bit bound represents either an upper or lower bound as some power of 2. Specifically, the bound is typically
either 2^bitBound or 2^-bitBound.
- Companion
- object
The Algebraic expression AST. Algebraic simply stores an expression tree representing all operations
performed on it. We then use this tree to deduce certain properties about the algebraic expression and use them to
perform exact sign tests, compute approximations, etc.
The Algebraic expression AST. Algebraic simply stores an expression tree representing all operations
performed on it. We then use this tree to deduce certain properties about the algebraic expression and use them to
perform exact sign tests, compute approximations, etc.
Generally, this should be regarded as an internal implementation detail of Algebraic.
- Companion
- object
An implementation of "A New Constructive Root Bound for Algebraic Expressions" by Chen Li & Chee Yap.
An implementation of "A New Constructive Root Bound for Algebraic Expressions" by Chen Li & Chee Yap.
A zero bound function, defined over an algebraic expression algebra.
A zero bound function, defined over an algebraic expression algebra.
Value members
Concrete methods
Returns an Algebraic expression equivalent to n, if n is finite. If n is either infinite or NaN, then an
IllegalArgumentException is thrown.
Returns an Algebraic expression equivalent to n, if n is finite. If n is either infinite or NaN, then an
IllegalArgumentException is thrown.
Returns an Algebraic expression equivalent to BigDecimal(n). If n is not parseable as a BigDecimal then an
exception is thrown.
Returns an Algebraic expression equivalent to BigDecimal(n). If n is not parseable as a BigDecimal then an
exception is thrown.
Returns a relative approximation of the n-th root of value, up to the number of digits specified by mc. This
only uses the rounding mode to chop-off the few remaining digits after the approximation, so may be inaccurate.
Returns a relative approximation of the n-th root of value, up to the number of digits specified by mc. This
only uses the rounding mode to chop-off the few remaining digits after the approximation, so may be inaccurate.
Returns an absolute approximation of the n-th root of value, up to scale digits past the decimal point. This
only uses the rounding mode to chop-off the few remaining digits after the approximation, so may be inaccurate.
Returns an absolute approximation of the n-th root of value, up to scale digits past the decimal point. This
only uses the rounding mode to chop-off the few remaining digits after the approximation, so may be inaccurate.
Returns a number that is approximately equal to x.pow(1/n). This number is useful as initial values in converging
n-root algorithms, but not as a general purpose n-root algorithm. There are no guarantees about the accuracy here.
Returns a number that is approximately equal to x.pow(1/n). This number is useful as initial values in converging
n-root algorithms, but not as a general purpose n-root algorithm. There are no guarantees about the accuracy here.
Returns an Algebraic expression whose value is equivalent to the i-th real root of the Polynomial poly. If
i is negative or does not an index a real root (eg the value is greater than or equal to the number of real
roots) then an ArithmeticException is thrown. Roots are indexed starting at 0. So if there are 3 roots, then they
are indexed as 0, 1, and 2.
Returns an Algebraic expression whose value is equivalent to the i-th real root of the Polynomial poly. If
i is negative or does not an index a real root (eg the value is greater than or equal to the number of real
roots) then an ArithmeticException is thrown. Roots are indexed starting at 0. So if there are 3 roots, then they
are indexed as 0, 1, and 2.
- Value Params
- i
the index (0-based) of the root
- poly
the polynomial containing at least i real roots
- Returns
an algebraic whose value is the i-th root of the polynomial
Returns all of the real roots of the given polynomial, in order from smallest to largest.
Returns all of the real roots of the given polynomial, in order from smallest to largest.
- Value Params
- poly
the polynomial to return the real roots of
- Returns
all the real roots of
poly
Returns an Algebraic whose value is the real root within (lb, ub). This is potentially unsafe, as we assume that exactly 1 real root lies within the interval, otherwise the results are undetermined.
Returns an Algebraic whose value is the real root within (lb, ub). This is potentially unsafe, as we assume that exactly 1 real root lies within the interval, otherwise the results are undetermined.
- Value Params
- i
the index of the root in the polynomial
- lb
the lower bound of the open interval containing the root
- poly
a polynomial with a real root within (lb, ub)
- ub
the upper bound of the open interval containing the root