Symbolic

java.lang.Object
- cetus.hir.SimpleExpression
- - cetus.hir.Symbolic

All Implemented Interfaces:

java.lang.Cloneable, java.lang.Comparable<SimpleExpression>, java.util.Comparator<SimpleExpression>
```
public class Symbolic
extends SimpleExpression
```
Class Symbolic provides static utility methods that simplifies expressions symbolically. This class holds only wrapper methods that utilizes the normalization functionalities in SimpleExpression.

Method Summary

Methods
Modifier and Type	Method and Description
`static Expression`	`add(Expression e1, Expression e2)` Returns addition of the two expressions with simplification.
`static Expression`	`addAll(java.util.List<Expression> exprs)` Returns an expression that adds all expressions in the given expression list.
`static Expression`	`and(Expression e1, Expression e2)` Returns and of two expressions with simplification.
`static Expression`	`decrement(Expression e)` Returns the given expression decremented by one.
`static Expression`	`divide(Expression e1, Expression e2)` Returns division of two expressions with simplification.
`static Expression`	`eq(Expression e1, Expression e2)` Returns comparison(==) of two expressions with simplification.
`static Expression`	`ge(Expression e1, Expression e2)` Returns comparison(greater equal) of two expressions with simplification.
`static Expression`	`getClosedFormSum(Identifier id, Expression lb, Expression ub, Expression e)` Returns the closed form of the given summation parameters, sum(e) s.t.
`static Expression`	`getClosedFormSum(Identifier id, Expression lb, Expression ub, Expression e, java.lang.Boolean divisible)` Computes and returns the closed form expression of the given expression, index, and bounds with the divisibility property of the given expression.
`static Expression`	`getCoefficient(Expression e, Identifier id)` Returns the symbolic coefficient of the given identifier in the expression.
`static java.util.List<Expression>`	`getCoefficient(Expression e, java.util.List<Identifier> ids)` Returns the list of coefficient with respect to the given set of identifiers.
`static long`	`getConstantCoefficient(Expression e)` Returns the constant term in the simplified expression.
`static Expression`	`getConstantCoefficient(Expression e, java.util.List<Identifier> ids)` Returns the constant term with respect to the given set of variables.
`static java.util.List<Expression>`	`getDenominators(Expression e)` Returns a list of denominators if the expression contains divisions.
`static java.util.List<Expression>`	`getFactors(Expression e)`
`static Expression`	`getLeastCommonDenominator(Expression e)`
`static java.util.List<Expression>`	`getPolynomialCoef(Expression e, Identifier id)` Returns a list of expressions which contains coefficients of n-th terms when the given id is the basis.
`static java.util.List<Expression>`	`getTerms(Expression e)` Returns a list of terms for expressions with addition.
`static java.util.List<Identifier>`	`getVariables(Expression e)` Returns the list of variables if the given expression is affine.
`static java.util.List<java.lang.Object>`	`getVariablesOnLHS(Expression e)` Returns a list of comparison expressions equivalent to the given expression.
`static Expression`	`gt(Expression e1, Expression e2)` Returns comparison(greater) of two expressions with simplification.
`static Expression`	`increment(Expression e)` Returns the given expression incremented by one.
`static boolean`	`isAffine(Expression e, java.util.List<Identifier> ids)` Checks if the given expression is an affine expression with respect to the given list of identifiers.
`static Expression`	`le(Expression e1, Expression e2)` Returns comparison(less equal) of two expressions with simplification.
`static Expression`	`lt(Expression e1, Expression e2)` Returns comparison(less) of two expressions with simplification.
`static Expression`	`mod(Expression e1, Expression e2)` Returns modulus of two expressions with simplification.
`static Expression`	`multiply(Expression e1, Expression e2)` Returns multiplication of two expressions with simplification.
`static Expression`	`multiplyAll(java.util.List<Expression> exprs)` Returns an expression that multiplies all expressions in the given expression list.
`static Expression`	`multiplyByLCM(Expression e)` Returns an expression multiplied by LCM of the denominators present in the terms in the specified expression.
`static Expression`	`ne(Expression e1, Expression e2)` Returns comparison(not equal) of two expressions with simplification.
`static Expression`	`negate(Expression e)` Returns negation of the given expression.
`static Expression`	`or(Expression e1, Expression e2)` Returns or of two expressions with simplification.
`static Expression`	`power(Expression e, int order)` Returns
`static Expression`	`simplify(Expression e)` Returns a simplified expression of the given expression with the default option which turns on every suboptions.
`static Expression`	`simplify(Expression e, int opt)` Returns a simplified expression of the given expression with the user-specified option.
`static Expression`	`simplifyDivisible(Expression e)` Returns a simplified expression assuming the given expression is divisible.
`static void`	`simplifyWithin(Traversable t)`
`static Expression`	`subtract(Expression e1, Expression e2)` Returns subtraction of two expressions with simplification.

Methods inherited from class cetus.hir.SimpleExpression
clone, compare, compareTo, equals, runtest, toString

Methods inherited from class java.lang.Object
getClass, hashCode, notify, notifyAll, wait, wait, wait

- Method Detail
  - simplify
```
public static Expression simplify(Expression e)
```
    Returns a simplified expression of the given expression with the default option which turns on every suboptions.
    
    Parameters:
    e - the given expression.
    
    Returns:
    the simplified expression.
  - simplify
```
public static Expression simplify(Expression e,
                  int opt)
```
    Returns a simplified expression of the given expression with the user-specified option.
    
    Parameters:
    e - the given expression.
    opt - the composable simplification option. e.g., Symbolic.FOLD, Symbolic.FOLD+Symbolic.FACTORIZE, ...
    
    Returns:
    the simplified expression.
  - add
```
public static Expression add(Expression e1,
             Expression e2)
```
    Returns addition of the two expressions with simplification.
  - subtract
```
public static Expression subtract(Expression e1,
                  Expression e2)
```
    Returns subtraction of two expressions with simplification.
  - multiply
```
public static Expression multiply(Expression e1,
                  Expression e2)
```
    Returns multiplication of two expressions with simplification.
  - divide
```
public static Expression divide(Expression e1,
                Expression e2)
```
    Returns division of two expressions with simplification.
  - mod
```
public static Expression mod(Expression e1,
             Expression e2)
```
    Returns modulus of two expressions with simplification.
  - and
```
public static Expression and(Expression e1,
             Expression e2)
```
    Returns and of two expressions with simplification.
  - or
```
public static Expression or(Expression e1,
            Expression e2)
```
    Returns or of two expressions with simplification.
  - eq
```
public static Expression eq(Expression e1,
            Expression e2)
```
    Returns comparison(==) of two expressions with simplification.
  - ne
```
public static Expression ne(Expression e1,
            Expression e2)
```
    Returns comparison(not equal) of two expressions with simplification.
  - le
```
public static Expression le(Expression e1,
            Expression e2)
```
    Returns comparison(less equal) of two expressions with simplification.
  - lt
```
public static Expression lt(Expression e1,
            Expression e2)
```
    Returns comparison(less) of two expressions with simplification.
  - ge
```
public static Expression ge(Expression e1,
            Expression e2)
```
    Returns comparison(greater equal) of two expressions with simplification.
  - gt
```
public static Expression gt(Expression e1,
            Expression e2)
```
    Returns comparison(greater) of two expressions with simplification.
  - negate
```
public static Expression negate(Expression e)
```
    Returns negation of the given expression.
  - power
```
public static Expression power(Expression e,
               int order)
```
    Returns
```
e
```
    's power to the
```
order
```
    with simplification.
  - increment
```
public static Expression increment(Expression e)
```
    Returns the given expression incremented by one.
  - decrement
```
public static Expression decrement(Expression e)
```
    Returns the given expression decremented by one.
  - getVariablesOnLHS
```
public static java.util.List<java.lang.Object> getVariablesOnLHS(Expression e)
```
    Returns a list of comparison expressions equivalent to the given expression. Each element in the returned list has an identifier on the right-hand side.
    
    Parameters:
    e - the given comparison expression.
    
    Returns:
    a list of equivalent/normalized comparison expressions.
  - getConstantCoefficient
```
public static long getConstantCoefficient(Expression e)
```
    Returns the constant term in the simplified expression.
    
    Parameters:
    e - the expression to be examined.
    
    Returns:
    the constant term in "long" type.
  - getConstantCoefficient
```
public static Expression getConstantCoefficient(Expression e,
                                java.util.List<Identifier> ids)
```
    Returns the constant term with respect to the given set of variables.
    
    Parameters:
    e - the expression to be examined.
    ids - the list of variables (identifiers).
    
    Returns:
    the symbolic constant term.
  - getCoefficient
```
public static Expression getCoefficient(Expression e,
                        Identifier id)
```
    Returns the symbolic coefficient of the given identifier in the expression.
    
    Parameters:
    e - the expression to be examined.
    id - the identifier.
    
    Returns:
    the symbolic coefficient of the identifier, null if the expression is too complicated.
  - getCoefficient
```
public static java.util.List<Expression> getCoefficient(Expression e,
                                        java.util.List<Identifier> ids)
```
    Returns the list of coefficient with respect to the given set of identifiers. The last element of the returned list is symbolic constant coefficient.
    
    Parameters:
    e - the expression to be examined.
    ids - the list of identifiers.
    
    Returns:
    the list of coefficients.
  - getVariables
```
public static java.util.List<Identifier> getVariables(Expression e)
```
    Returns the list of variables if the given expression is affine. This method replaces NormalExpression.getVariableList(e).
    
    Parameters:
    e - the expression to be examined.
    
    Returns:
    the list of variables if e is affine, null otherwise.
  - isAffine
```
public static boolean isAffine(Expression e,
               java.util.List<Identifier> ids)
```
    Checks if the given expression is an affine expression with respect to the given list of identifiers.
    
    Parameters:
    e - the expression to be examined.
    ids - the list of identifiers.
    
    Returns:
    true if it is affine, false otherwise.
  - getClosedFormSum
```
public static Expression getClosedFormSum(Identifier id,
                          Expression lb,
                          Expression ub,
                          Expression e)
```
    Returns the closed form of the given summation parameters, sum(e) s.t. 0<lb<=id<=ub. Computation is based on Bernoulli numbers. For now, assume the given constraints holds when this method is called. We can use range information to assure this assumption in the future.
    
    Parameters:
    id - the index variable.
    lb - the lower bound of id.
    ub - the upper bound of id.
    e - the given expression.
    
    Returns:
    the closed form of the given expression.
  - simplifyDivisible
```
public static Expression simplifyDivisible(Expression e)
```
    Returns a simplified expression assuming the given expression is divisible.
  - getClosedFormSum
```
public static Expression getClosedFormSum(Identifier id,
                          Expression lb,
                          Expression ub,
                          Expression e,
                          java.lang.Boolean divisible)
```
    Computes and returns the closed form expression of the given expression, index, and bounds with the divisibility property of the given expression.
  - getPolynomialCoef
```
public static java.util.List<Expression> getPolynomialCoef(Expression e,
                                           Identifier id)
```
    Returns a list of expressions which contains coefficients of n-th terms when the given id is the basis. e.g.) (2*i*i+1-i,i) returns [1, -1, 2].
    
    Parameters:
    e - the input expression.
    id - the basis variable.
    
    Returns:
    the list of coefficients.
  - getTerms
```
public static java.util.List<Expression> getTerms(Expression e)
```
    Returns a list of terms for expressions with addition. e.g., a+b*c --> {a, b*c}.
  - getFactors
```
public static java.util.List<Expression> getFactors(Expression e)
```
  - getDenominators
```
public static java.util.List<Expression> getDenominators(Expression e)
```
    Returns a list of denominators if the expression contains divisions. e.g., 2/a+b/c --> {a, c}.
  - addAll
```
public static Expression addAll(java.util.List<Expression> exprs)
```
    Returns an expression that adds all expressions in the given expression list.
  - multiplyAll
```
public static Expression multiplyAll(java.util.List<Expression> exprs)
```
    Returns an expression that multiplies all expressions in the given expression list.
  - multiplyByLCM
```
public static Expression multiplyByLCM(Expression e)
```
    Returns an expression multiplied by LCM of the denominators present in the terms in the specified expression.
  - getLeastCommonDenominator
```
public static Expression getLeastCommonDenominator(Expression e)
```
  - simplifyWithin
```
public static void simplifyWithin(Traversable t)
```

Class Symbolic

Method Summary

Methods inherited from class cetus.hir.SimpleExpression

Methods inherited from class java.lang.Object

Method Detail

simplify

simplify

add

subtract

multiply

divide

mod

and

or

eq

ne

le

lt

ge

gt

negate

power

increment

decrement

getVariablesOnLHS

getConstantCoefficient

getConstantCoefficient

getCoefficient

getCoefficient

getVariables

isAffine

getClosedFormSum

simplifyDivisible

getClosedFormSum

getPolynomialCoef

getTerms

getFactors

getDenominators

addAll

multiplyAll

multiplyByLCM

getLeastCommonDenominator

simplifyWithin