trait OrderedRing extends Ring with RingWithOrder
Ordered rings are rings with ordering relation in which
addition, multiplication, and ordering are consistent:
leq(s, t) ==> leq(plus(s, a), plus(t, a)) and
leq(zero, s) & leq(zero, t) ==> leq(zero, mul(s, t)).
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Abstract Value Members
- abstract val dom: Sort
Domain of the ring
Domain of the ring
- Definition Classes
- PseudoRing
- abstract def int2ring(s: ITerm): ITerm
Conversion of an integer term to a ring term
Conversion of an integer term to a ring term
- Definition Classes
- PseudoRing
- abstract def leq(s: ITerm, t: ITerm): IFormula
Less-than-or-equal operator
Less-than-or-equal operator
- Definition Classes
- RingWithOrder
- abstract def lt(s: ITerm, t: ITerm): IFormula
Less-than operator
Less-than operator
- Definition Classes
- RingWithOrder
- abstract def minus(s: ITerm): ITerm
Additive inverses
Additive inverses
- Definition Classes
- PseudoRing
- abstract def mul(s: ITerm, t: ITerm): ITerm
Ring multiplication
Ring multiplication
- Definition Classes
- PseudoRing
- abstract def one: ITerm
The one element of this ring
The one element of this ring
- Definition Classes
- PseudoRing
- abstract def plus(s: ITerm, t: ITerm): ITerm
Ring addition
Ring addition
- Definition Classes
- PseudoRing
- abstract def zero: ITerm
The zero element of this ring
The zero element of this ring
- Definition Classes
- PseudoRing
Concrete Value Members
- final def !=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- final def ##: Int
- Definition Classes
- AnyRef → Any
- final def ==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- def additiveGroup: Group with Abelian with SymbolicTimes
Addition gives rise to an Abelian group
Addition gives rise to an Abelian group
- Definition Classes
- PseudoRing
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- def clone(): AnyRef
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.CloneNotSupportedException]) @HotSpotIntrinsicCandidate() @native()
- final def eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def equals(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef → Any
- def geq(s: ITerm, t: ITerm): IFormula
Greater-than-or-equal operator
Greater-than-or-equal operator
- Definition Classes
- RingWithOrder
- final def getClass(): Class[_ <: AnyRef]
- Definition Classes
- AnyRef → Any
- Annotations
- @HotSpotIntrinsicCandidate() @native()
- def gt(s: ITerm, t: ITerm): IFormula
Greater-than operator
Greater-than operator
- Definition Classes
- RingWithOrder
- def hashCode(): Int
- Definition Classes
- AnyRef → Any
- Annotations
- @HotSpotIntrinsicCandidate() @native()
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- def minus(s: ITerm, t: ITerm): ITerm
Difference between two terms
Difference between two terms
- Definition Classes
- PseudoRing
- def multiplicativeMonoid: Monoid
Multiplication gives rise to a monoid
Multiplication gives rise to a monoid
- Definition Classes
- Ring
- final def ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- final def notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @HotSpotIntrinsicCandidate() @native()
- final def notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @HotSpotIntrinsicCandidate() @native()
- def product(terms: ITerm*): ITerm
N-ary sums
N-ary sums
- Definition Classes
- PseudoRing
- def summation(terms: ITerm*): ITerm
N-ary sums
N-ary sums
- Definition Classes
- PseudoRing
- final def synchronized[T0](arg0: => T0): T0
- Definition Classes
- AnyRef
- def times(num: IdealInt, s: ITerm): ITerm
num * snum * s- Definition Classes
- PseudoRing
- def toString(): String
- Definition Classes
- PseudoRing → AnyRef → Any
- final def wait(arg0: Long, arg1: Int): Unit
- Definition Classes
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- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException]) @native()
- final def wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
Deprecated Value Members
- def finalize(): Unit
- Attributes
- protected[lang]
- Definition Classes
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- @throws(classOf[java.lang.Throwable]) @Deprecated
- Deprecated
(Since version 9)