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Expr.java
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package symjava.symbolic;
import java.math.BigInteger;
import java.util.List;
import symjava.logic.And;
import symjava.logic.Not;
import symjava.logic.Or;
import symjava.logic.Xor;
import symjava.relational.Ge;
import symjava.relational.Relation;
import symjava.symbolic.utils.Utils;
abstract public class Expr implements Cloneable {
/**
* Label(or name) of an expression(Symbol, Func,...)
*/
protected String label = null;
/**
* A string used to sort terms in an expression
*/
protected String sortKey = null;
/**
* Number of operations for simplifying an expression
*/
public int simplifyOpNum = 0;
public boolean isSimplified = false;
public abstract Expr simplify();
public abstract boolean symEquals(Expr other);
/**
* Return the arguments of the expr
* @return
*/
public Expr[] args() { return new Expr[0]; }
/**
* Derivative of expr
* @param expr
* @return
*/
public abstract Expr diff(Expr expr);
/**
* Functional derivative of f with respect to df
* @param f
* @param df
* @return
*/
public Expr fdiff(Expr f, Expr df) {
if(!(f instanceof Func) || !(df instanceof Func))
throw new IllegalArgumentException();
Func F = (Func)f;
Symbol alpha = new Symbol("_alpha_");
Expr ff = this.subs(f, f.add(alpha.multiply(df)));
Expr dff = ff.diff(alpha);
if(Symbol.C0.symEquals(dff)) {
Func ret = new Func("0", F.args);
ret.expr = Symbol.C0;
return ret;
}
return dff.subs(alpha, 0).simplify();
}
/**
* Split the terms into a list for Add and Subtract
* @param outList
*/
public void flattenAdd(List<Expr> outList) {
outList.add(this);
};
/**
* Split the terms into a list for Multiply and Divide
* @param outList
*/
public void flattenMultiply(List<Expr> outList) {
outList.add(this);
}
/**
* Return true if the expression is an abstract thing.
* for example, a abstract function
* @return
*/
public boolean isAbstract() {
return false;
}
/**
* Return the string expression
*/
public String toString() {
return label;
}
/**
* Set the label(or name) of the expression
* @param label
* @return
*/
public Expr setLabel(String label) {
this.label = label;
return this;
}
/**
* Return the label(or name) of the expression
* @return
*/
public String getLabel() {
return label;
}
/**
* Set a string key for arranging terms in an expression
* @param sortKey
* @return
*/
public Expr setSortKey(String sortKey) {
this.sortKey = sortKey;
return this;
}
/**
* Get the string key used to arrange terms in an expression
* @param sortKey
* @return
*/
public String getSortKey() {
return sortKey;
}
/**
* Count number of operations for simplification
* @return
*/
public int getSimplifyOps() {
return simplifyOpNum;
}
public Expr setSimplifyOps(int n) {
//Make no sense, call setAsSimplified() explicitly
//if(n > simplifyOpNum)
// isSimplified = true;
simplifyOpNum = n;
return this;
}
public Expr incSimplifyOps(int n) {
simplifyOpNum += n;
isSimplified = true;
return this;
}
public Expr setAsSimplified() {
isSimplified = true;
return this;
}
/**
* Operator overload support:
* Expr a = 5;
*
* @param v
* @return
*/
public static Expr valueOf(int v) {
return new SymInteger(v);
}
public static Expr valueOf(long v) {
return new SymLong(v);
}
public static Expr valueOf(float v) {
return new SymFloat(v);
}
public static Expr valueOf(double v) {
return new SymDouble(v);
}
/**
* Operator overload support:
* a+b
* @param other
* @return
*/
public Expr add(Expr other) {
return Add.simplifiedIns(this, other);
}
public Expr add(int other) {
return Add.simplifiedIns(this, new SymInteger(other));
}
public Expr addRev(int other) {
return Add.simplifiedIns(new SymInteger(other), this);
}
public Expr add(long other) {
return Add.simplifiedIns(this, new SymLong(other));
}
public Expr addRev(long other) {
return Add.simplifiedIns(new SymLong(other), this);
}
public Expr add(float other) {
return Add.simplifiedIns(this, new SymFloat(other));
}
public Expr addRev(float other) {
return Add.simplifiedIns(new SymFloat(other), this);
}
public Expr add(double other) {
return Add.simplifiedIns(this, new SymDouble(other));
}
public Expr addRev(double other) {
return Add.simplifiedIns(new SymDouble(other), this);
}
/**
* Operator overload support:
* a-b
* @param other
* @return
*/
public Expr subtract(Expr other) {
return Subtract.simplifiedIns(this, other);
}
public Expr subtract(int other) {
return Subtract.simplifiedIns(this, new SymInteger(other));
}
public Expr subtractRev(int other) {
return Subtract.simplifiedIns(new SymInteger(other), this);
}
public Expr subtract(long other) {
return Subtract.simplifiedIns(this, new SymLong(other));
}
public Expr subtractRev(long other) {
return Subtract.simplifiedIns(new SymLong(other), this);
}
public Expr subtract(float other) {
return Subtract.simplifiedIns(this, new SymFloat(other));
}
public Expr subtractRev(float other) {
return Subtract.simplifiedIns(new SymFloat(other), this);
}
public Expr subtract(double other) {
return Subtract.simplifiedIns(this, new SymDouble(other));
}
public Expr subtractRev(double other) {
return Subtract.simplifiedIns(new SymDouble(other), this);
}
/**
* Operator overload support:
* a*b
* @param other
* @return
*/
public Expr multiply(Expr other) {
return Multiply.simplifiedIns(this, other);
}
public Expr multiply(int other) {
return Multiply.simplifiedIns(this, new SymInteger(other));
}
public Expr multiplyRev(int other) {
return Multiply.simplifiedIns(new SymInteger(other), this);
}
public Expr multiply(long other) {
return Multiply.simplifiedIns(this, new SymLong(other));
}
public Expr multiplyRev(long other) {
return Multiply.simplifiedIns(new SymLong(other), this);
}
public Expr multiply(float other) {
return Multiply.simplifiedIns(this, new SymFloat(other));
}
public Expr multiplyRev(float other) {
return Multiply.simplifiedIns(new SymFloat(other), this);
}
public Expr multiply(double other) {
return Multiply.simplifiedIns(this, new SymDouble(other));
}
public Expr multiplyRev(double other) {
return Multiply.simplifiedIns(new SymDouble(other), this);
}
/**
* Operator overload support:
* a/b
* @param other
* @return
*/
public Expr divide(Expr other) {
return Divide.simplifiedIns(this, other);
}
public Expr divide(int other) {
return Divide.simplifiedIns(this, new SymInteger(other));
}
public Expr divideRev(int other) {
return Divide.simplifiedIns(new SymInteger(other), this);
}
public Expr divide(long other) {
return Divide.simplifiedIns(this, new SymLong(other));
}
public Expr divideRev(long other) {
return Divide.simplifiedIns(new SymLong(other), this);
}
public Expr divide(float other) {
return Divide.simplifiedIns(this, new SymFloat(other));
}
public Expr divideRev(float other) {
return Divide.simplifiedIns(new SymFloat(other), this);
}
public Expr divide(double other) {
return Divide.simplifiedIns(this, new SymDouble(other));
}
public Expr divideRev(double other) {
return Divide.simplifiedIns(new SymDouble(other), this);
}
/**
* Operator overload support:
* -a
*
*/
public Expr negate() {
if(this instanceof SymReal<?>) {
SymReal<?> dd = (SymReal<?>)this;
double dv = dd.getValue().doubleValue();
if(dv == 0)
return Symbol.C0;
return new SymDouble(-dv);
}
return Negate.simplifiedIns(this);
};
/**
* x%y
* @return
*/
public Expr remainder(Expr other) {
return new Remainder(this, other);
}
/*
* !x
*/
public Expr not() {
return Not.simplifiedIns(this);
}
/**
* x&y
* @param other
* @return
*/
public Expr and(Expr other) {
return And.simplifiedIns(this, other);
}
/**
* x|y
* @param other
* @return
*/
public Expr or(Expr other) {
return Or.simplifiedIns(this, other);
}
/**
* x^y
* @param other
* @return
*/
public Expr xor(Expr other) {
return Xor.simplifiedIns(this, other);
}
// /**
// * TODO We cannot use the comparison operator overload in java-oo for our use case
// * @param other
// * @return
// */
// public int compareTo(Expr other) {
// if(Ge.stackTop == null)
// Ge.stackTop = Ge.apply(this, other); //fix: use push()
// else
// Ge.stackTop = Ge.apply(Ge.stackTop, other);
// return -1;
// }
/**
* Substitution
*
* @param from
* @param to
* @return
*/
public Expr subs(Expr from, Expr to) {
if(Utils.symCompare(this, from)) {
return to;
}
return this;
}
public Expr subs(Expr from, int to) {
return subs(from, new SymInteger(to));
}
public Expr subs(Expr from, long to) {
return subs(from, new SymLong(to));
}
public Expr subs(Expr from, float to) {
return subs(from, new SymFloat(to));
}
public Expr subs(Expr from, double to) {
return subs(from, new SymDouble(to));
}
protected Expr clone() {
try {
return (Expr) super.clone();
} catch (CloneNotSupportedException e) {
e.printStackTrace();
}
return null;
}
/**
* If the labels of two expressions are the same they are considered as
* the same symbolic expressions
*/
@Override
public int hashCode() {
return this.label.hashCode();
}
@Override
public boolean equals(Object obj) {
return this.label.equals(((Expr)obj).label);
}
}