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c

edu.cmu.cs.ls.keymaerax.tools.ext

RingsLibrary

class RingsLibrary extends AnyRef

A link to Rings library for its algebra tools

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Instance Constructors

  1. new RingsLibrary(terms: Traversable[Term])

Type Members

  1. case class ODE(time: Variable, state: Seq[Variable], const0: Seq[FuncOf], rhs: Seq[Term]) extends Product with Serializable

    encapsulates information relevant for working with ODEs with the Rings library

  2. type Ring = MultivariatePolynomial[Rational[BigInteger]]

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
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  2. final def ##(): Int
    Definition Classes
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  3. final def ==(arg0: Any): Boolean
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  4. final def asInstanceOf[T0]: T0
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  5. def clone(): AnyRef
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    protected[java.lang]
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    @native() @throws( ... )
  6. def distributive(t: Ring, xs: Seq[Term]): Map[List[Int], Term]

    a distributive representation w.r.t.

    a distributive representation w.r.t. Variables in xs

  7. final def eq(arg0: AnyRef): Boolean
    Definition Classes
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  8. def equals(arg0: Any): Boolean
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  9. def finalize(): Unit
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    @throws( classOf[java.lang.Throwable] )
  10. def fromRing(p: Ring): Term
  11. def fromRing(m: Monomial[Rational[BigInteger]]): Term
  12. final def getClass(): Class[_]
    Definition Classes
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    @native()
  13. def groebnerBasis(polynomials: List[Term]): List[Term]
  14. def hashCode(): Int
    Definition Classes
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    @native()
  15. def integrate(i: Int)(t: Ring): Ring

    integral/primitive of t w.r.t.

    integral/primitive of t w.r.t. Variable i

  16. def internalQuotientRemainder(a: Ring, b: Ring): Option[(Ring, Ring)]

    return None if b does not divide a, otherwise Some (quotient, remainder)

  17. final def isInstanceOf[T0]: Boolean
    Definition Classes
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  18. def lieDerivative(ode: (Variable) ⇒ Option[Ring])(t: Term): Ring

    compute the Lie Derivative

  19. val mapper: Map[NamedSymbol, String]
  20. val names: List[NamedSymbol]
  21. final def ne(arg0: AnyRef): Boolean
    Definition Classes
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  22. def normalizeLessEquals(qeTac: BelleExpr): DependentPositionTactic

    a<=b to 0<=a-b, with the standard representation of a-b (distributive and according to the variable order of ring, also distributes over conjunctions...

  23. final def notify(): Unit
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  24. final def notifyAll(): Unit
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    @native()
  25. def polynomialReduce(polynomial: Term, GB: List[Term]): (List[Term], Term)
  26. def quotientRemainder(term: Term, div: Term, x: Variable): (Term, Term)
  27. implicit val ring: MultivariateRing[Rational[BigInteger]]
  28. val ringsNames: List[(NamedSymbol, String)]
  29. def splitInternal(p: Ring, order: Int, vars: Seq[Int], drop: Seq[Int]): (Ring, Ring)

    split polynomial according to order w.r.t variables in list

  30. def substitutes(subst: (Variable) ⇒ Option[Ring])(t: Term): Ring

    Substitute into a polynomial: simultaneously replace Variables v

  31. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
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  32. def toHorner(t: Ring, xs: List[Ring]): Term

    rewrite t to Horner Form (w.r.t.

    rewrite t to Horner Form (w.r.t. "Variables" xs)

    we allow arbitrary terms as "variables" in order to factor out e.g., squares.

  33. def toRing(term: Term): Ring
  34. def toString(): String
    Definition Classes
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  35. val unmapper: Map[Int, Term]
  36. final def wait(): Unit
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  37. final def wait(arg0: Long, arg1: Int): Unit
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  38. final def wait(arg0: Long): Unit
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