Java Monomial类代码示例

import edu.jas.poly.Monomial; //导入依赖的package包/类
/**
 * Transforms a JAS polynomial to a Polynomial object.
 * 
 * @param j JAS polynomial
 * @return polynomial of Polynomial class
 */
private Polynomial jasToPoly(GenPolynomial<BigInteger> j)
{
	int numVariables = j.numberOfVariables();
	Polynomial result = new Polynomial(numVariables, j.length());
	for (Monomial<BigInteger> jasMono : j) {
		java.math.BigInteger coeff = (jasMono.coefficient()).getVal();
		ExpVector jasExpo = jasMono.exponent();
		ArrayList<Integer> expo = new ArrayList<Integer>();
		for (int var = 0; var < numVariables; var++) {
			expo.add((int)jasExpo.getVal(var));
		}
		result.addTerm(coeff, expo);
	}
	
	return result;
}
 

import edu.jas.poly.Monomial; //导入依赖的package包/类
/**
 * Get a UnivPowerSeries<C> from a GenPolynomial<C>.
 * @param a GenPolynomial<C>.
 * @return a UnivPowerSeries<C>.
 */
public UnivPowerSeries<C> fromPolynomial(GenPolynomial<C> a) {
    if (a == null || a.isZERO()) {
        return ZERO;
    }
    if (a.isONE()) {
        return ONE;
    }
    if (a.ring.nvar != 1) {
        throw new IllegalArgumentException("only for univariate polynomials");
    }
    HashMap<Integer, C> cache = new HashMap<Integer, C>(a.length());
    for (Monomial<C> m : a) {
        long e = m.exponent().getVal(0);
        cache.put((int) e, m.coefficient());
    }
    return new UnivPowerSeries<C>(this, new Coefficients<C>(cache) {


        @Override
        public C generate(int i) {
            // cached coefficients returned by get
            return coFac.getZERO();
        }
    });
}
 

import edu.jas.poly.Monomial; //导入依赖的package包/类
/**
 * Method bitHeight returns the bitlength of the greatest number occurring
 * during the computation of a Groebner base.
 */
public int bitHeight(List<GenPolynomial<BigRational>> list) {
    BigInteger denom = BigInteger.ONE;
    BigInteger num = BigInteger.ONE;
    for (GenPolynomial<BigRational> g : list) {
        for (Monomial<BigRational> m : g) {
            BigRational bi = m.coefficient();
            BigInteger i = bi.denominator().abs();
            BigInteger j = bi.numerator().abs();
            if (i.compareTo(denom) > 0)
                denom = i;
            if (j.compareTo(num) > 0)
                num = j;
        }
    }
    int erg;
    if (denom.compareTo(num) > 0) {
        erg = denom.bitLength();
    } else {
        erg = num.bitLength();
    }
    return erg;
}
 

import edu.jas.poly.Monomial; //导入依赖的package包/类
/**
 * Get the monomial list of a univariate polynomial with coefficients reduced by a modulo value.
 * 
 * @param polynomial
 * @param variable
 * @param termOrder
 *            the JAS term ordering
 * @param option
 *            the "Modulus" option
 * @return the list of monomials of the univariate polynomial.
 */
private static IAST monomialListModulus(IExpr polynomial, List<IExpr> variablesList, final TermOrder termOrder,
		IExpr option) throws JASConversionException {
	try {
		// found "Modulus" option => use ModIntegerRing
		ModLongRing modIntegerRing = JASModInteger.option2ModLongRing((ISignedNumber) option);
		JASModInteger jas = new JASModInteger(variablesList, modIntegerRing);
		GenPolynomial<ModLong> polyExpr = jas.expr2JAS(polynomial);
		IASTAppendable list = F.ListAlloc(polyExpr.length());
		for (Monomial<ModLong> monomial : polyExpr) {
			ModLong coeff = monomial.coefficient();
			ExpVector exp = monomial.exponent();
			IASTAppendable monomTimes = F.TimesAlloc(exp.length() + 1);
			jas.monomialToExpr(F.integer(coeff.getVal()), exp, monomTimes);
			list.append(monomTimes);
		}
		return list;
	} catch (ArithmeticException ae) {
		// toInt() conversion failed
		if (Config.DEBUG) {
			ae.printStackTrace();
		}
	}
	return F.NIL;
}
 

import edu.jas.poly.Monomial; //导入依赖的package包/类
/**
 * Check if the polynomial has maximum degree 2 in 1 variable and return the coefficients.
 * 
 * @param poly
 * @return <code>false</code> if the polynomials degree > 2 and number of variables <> 1
 */
public static boolean isQuadratic(GenPolynomial<BigRational> poly, BigRational[] result) {
	if (poly.degree() <= 2 && poly.numberOfVariables() == 1) {
		result[0] = BigRational.ZERO;
		result[1] = BigRational.ZERO;
		result[2] = BigRational.ZERO;
		for (Monomial<BigRational> monomial : poly) {
			BigRational coeff = monomial.coefficient();
			ExpVector exp = monomial.exponent();
			for (int i = 0; i < exp.length(); i++) {
				result[(int) exp.getVal(i)] = coeff;
			}
		}
		return true;
	}
	return false;
}
 

import edu.jas.poly.Monomial; //导入依赖的package包/类
/**
 * Check if the polynomial has maximum degree 2 in 1 variable and return the
 * coefficients.
 * 
 * @param poly
 * @return <code>null</code> if the polynomials degree > 2 and number of
 *         variables <> 1
 */
public static boolean isQuadratic(GenPolynomial<BigRational> poly, BigRational[] result) {
	if (poly.degree() <= 2 && poly.numberOfVariables() == 1) {
		result[0] = BigRational.ZERO;
		result[1] = BigRational.ZERO;
		result[2] = BigRational.ZERO;
		for (Monomial<BigRational> monomial : poly) {
			BigRational coeff = monomial.coefficient();
			ExpVector exp = monomial.exponent();
			for (int i = 0; i < exp.length(); i++) {
				result[(int) exp.getVal(i)] = coeff;
			}
		}
		return true;
	}
	return false;
}
 

import edu.jas.poly.Monomial; //导入依赖的package包/类
/**
 * Convert a JAS integer polynomial to <code>IExpr</code>.
 * 
 * @param poly
 * @return
 * @throws ArithmeticException
 * @throws ClassCastException
 */
public IExpr integerPoly2Expr(final GenPolynomial<edu.jas.arith.BigInteger> poly)
		throws ArithmeticException, ClassCastException {
	if (poly.length() == 0) {
		return F.C0;
	}
	IASTAppendable result = F.PlusAlloc(poly.length());
	for (Monomial<edu.jas.arith.BigInteger> monomial : poly) {
		edu.jas.arith.BigInteger coeff = monomial.coefficient();
		ExpVector exp = monomial.exponent();
		IASTAppendable monomTimes = F.TimesAlloc(exp.length()+1);
		monomialToExpr(coeff, exp, monomTimes);
		result.append(monomTimes.getOneIdentity(F.C1));
	}
	return result.getOneIdentity(F.C0);
}
 

import edu.jas.poly.Monomial; //导入依赖的package包/类
/**
 * Convert a JAS complex polynomial to <code>IExpr</code>.
 * 
 * @param poly
 * @return
 * @throws ArithmeticException
 * @throws ClassCastException
 */
public IExpr complexPoly2Expr(final GenPolynomial<Complex<BigRational>> poly)
		throws ArithmeticException, ClassCastException {
	if (poly.length() == 0) {
		return F.C0;
	}
	IASTAppendable result = F.PlusAlloc(poly.length());
	for (Monomial<Complex<BigRational>> monomial : poly) {
		Complex<BigRational> coeff = monomial.coefficient();
		ExpVector exp = monomial.exponent();
		IASTAppendable monomTimes = F.TimesAlloc(exp.length()+1);
		monomialToExpr(coeff, exp, monomTimes);
		result.append(monomTimes.getOneIdentity(F.C1));
	}
	return result.getOneIdentity(F.C0);
}
 

import edu.jas.poly.Monomial; //导入依赖的package包/类
/**
 * Converts a <a href="http://krum.rz.uni-mannheim.de/jas/">JAS</a>
 * polynomial to a MathEclipse AST with head <code>Plus</code>
 * 
 * @param poly
 *            a JAS polynomial
 * @param variable
 * @return
 * @throws ArithmeticException
 * @throws ClassCastException
 */
public IAST rationalPoly2Expr(final GenPolynomial<BigRational> poly)
		throws ArithmeticException, ClassCastException {
	if (poly.length() == 0) {
		return F.Plus(F.C0);
	}

	IASTAppendable result = F.PlusAlloc(poly.length());
	for (Monomial<BigRational> monomial : poly) {
		BigRational coeff = monomial.coefficient();
		ExpVector exp = monomial.exponent();
		IASTAppendable monomTimes = F.TimesAlloc(exp.length()+1);
		monomialToExpr(coeff, exp, monomTimes);
		result.append(monomTimes.getOneIdentity(F.C1));
	}
	return result;
}
 

import edu.jas.poly.Monomial; //导入依赖的package包/类
/**
 * Converts a <a href="http://krum.rz.uni-mannheim.de/jas/">JAS</a> polynomial to a MathEclipse AST with head
 * <code>Plus</code>
 * 
 * @param poly
 *            a JAS polynomial
 * @param variable
 * @return
 * @throws ArithmeticException
 * @throws ClassCastException
 */
public IExpr exprPoly2Expr(final GenPolynomial<IExpr> poly, IExpr variable) {
	if (poly.length() == 0) {
		return F.C0;
	}

	IASTAppendable result = F.PlusAlloc(poly.length());
	for (Monomial<IExpr> monomial : poly) {
		IExpr coeff = monomial.coefficient();
		ExpVector exp = monomial.exponent();
		IASTAppendable monomTimes = F.TimesAlloc(exp.length() + 1);
		monomialToExpr(coeff, exp, monomTimes);
		result.append(monomTimes.getOneIdentity(F.C1));
	}
	return result.getOneIdentity(F.C0);
}
 

import edu.jas.poly.Monomial; //导入依赖的package包/类
/**
 * Get exponent vectors and coefficients of monomials of a polynomial expression.
 * 
 * @param polynomial
 * @param variable
 * @param termOrder
 *            the JAS term ordering
 * @return the list of monomials of the univariate polynomial.
 */
public static IAST coefficientRules(IExpr polynomial, final List<IExpr> variablesList,
		final TermOrder termOrder) throws JASConversionException {
	JASIExpr jas = new JASIExpr(variablesList, ExprRingFactory.CONST, termOrder, false);
	GenPolynomial<IExpr> polyExpr = jas.expr2IExprJAS(polynomial);
	IASTAppendable resultList = F.ListAlloc(polyExpr.length());
	for (Monomial<IExpr> monomial : polyExpr) {

		IExpr coeff = monomial.coefficient();
		ExpVector exp = monomial.exponent();
		int len = exp.length();
		IASTAppendable ruleList = F.ListAlloc(len);
		for (int i = 0; i < len; i++) {
			ruleList.append(F.integer(exp.getVal(len - i - 1)));
		}
		resultList.append(F.Rule(ruleList, coeff));
	}
	return resultList;
}
 

import edu.jas.poly.Monomial; //导入依赖的package包/类
/**
 * Convert a JAS complex polynomial to <code>IExpr</code>.
 * 
 * @param poly
 * @return
 * @throws ArithmeticException
 * @throws ClassCastException
 */
public IExpr complexPoly2Expr(final GenPolynomial<Complex<BigRational>> poly)
		throws ArithmeticException, ClassCastException {
	if (poly.length() == 0) {
		return F.C0;
	}
	IASTAppendable result = F.PlusAlloc(poly.length());
	for (Monomial<Complex<BigRational>> monomial : poly) {
		Complex<BigRational> coeff = monomial.coefficient();
		ExpVector exp = monomial.exponent();
		BigRational re = coeff.getRe();
		BigRational im = coeff.getIm();
		IASTAppendable monomTimes = F.Times(F.complex(F.fraction(re.numerator(), re.denominator()),
				F.fraction(im.numerator(), im.denominator())));
		long lExp;
		for (int i = 0; i < exp.length(); i++) {
			lExp = exp.getVal(i);
			if (lExp != 0) {
				monomTimes.append(F.Power(fVariables.get(i), F.integer(lExp)));
			}
		}
		if (monomTimes.isAST1()) {
			result.append(monomTimes.arg1());
		} else {
			result.append(monomTimes);
		}
	}
	if (result.isAST1()) {
		return result.arg1();
	} else {
		return result;
	}
}
 

import edu.jas.poly.Monomial; //导入依赖的package包/类
/**
 * Convert a JAS integer polynomial to <code>IExpr</code>.
 * 
 * @param poly
 * @return
 * @throws ArithmeticException
 * @throws ClassCastException
 */
public IExpr integerPoly2Expr(final GenPolynomial<edu.jas.arith.BigInteger> poly)
		throws ArithmeticException, ClassCastException {
	if (poly.length() == 0) {
		return F.C0;
	}
	IASTAppendable result = F.PlusAlloc(poly.length());
	for (Monomial<edu.jas.arith.BigInteger> monomial : poly) {
		edu.jas.arith.BigInteger coeff = monomial.coefficient();
		ExpVector exp = monomial.exponent();
		IInteger coeffValue = F.integer(coeff.getVal());
		IASTAppendable monomTimes = F.TimesAlloc(exp.length() + 1);
		monomTimes.append(coeffValue);
		long lExp;
		for (int i = 0; i < exp.length(); i++) {
			lExp = exp.getVal(i);
			if (lExp != 0) {
				monomTimes.append(F.Power(fVariables.get(i), F.integer(lExp)));
			}
		}
		if (monomTimes.isAST1()) {
			result.append(monomTimes.arg1());
		} else {
			result.append(monomTimes);
		}
	}
	if (result.isAST1()) {
		return result.arg1();
	} else {
		return result;
	}
}
 

import edu.jas.poly.Monomial; //导入依赖的package包/类
public IExpr modLongPoly2Expr(final GenPolynomial<ModLong> poly) throws ArithmeticException, ClassCastException {
	if (poly.length() == 0) {
		return F.Plus(F.C0);
	}
	IASTAppendable result = F.PlusAlloc(poly.length());
	for (Monomial<ModLong> monomial : poly) {
		ModLong coeff = monomial.coefficient();
		ExpVector exp = monomial.exponent();
		IInteger coeffValue = F.integer(coeff.getVal());
		IASTAppendable monomTimes = F.TimesAlloc(exp.length() + 1);
		monomialToExpr(coeffValue, exp, monomTimes);
		result.append(monomTimes.getOneIdentity(F.C1));
	}
	return result.getOneIdentity(F.C0);
}
 

import edu.jas.poly.Monomial; //导入依赖的package包/类
/**
 * Get exponent vectors and coefficients of monomials of a polynomial expression.
 * 
 * @param polynomial
 * @param variable
 * @param termOrder
 *            the JAS term ordering
 * @param option
 *            the "Modulus" option
 * @return the list of monomials of the univariate polynomial.
 */
private static IAST coefficientRulesModulus(IExpr polynomial, List<IExpr> variablesList,
		final TermOrder termOrder, IExpr option) throws JASConversionException {
	try {
		// found "Modulus" option => use ModIntegerRing
		ModLongRing modIntegerRing = JASModInteger.option2ModLongRing((ISignedNumber) option);
		JASModInteger jas = new JASModInteger(variablesList, modIntegerRing);
		GenPolynomial<ModLong> polyExpr = jas.expr2JAS(polynomial);
		IASTAppendable resultList = F.ListAlloc(polyExpr.length());
		for (Monomial<ModLong> monomial : polyExpr) {
			ModLong coeff = monomial.coefficient();
			ExpVector exp = monomial.exponent();
			int len = exp.length();
			IASTAppendable ruleList = F.ListAlloc(len);
			for (int i = 0; i < len; i++) {
				ruleList.append(F.integer(exp.getVal(len - i - 1)));
			}
			resultList.append(F.Rule(ruleList, F.integer(coeff.getVal())));
		}
		return resultList;
	} catch (ArithmeticException ae) {
		// toInt() conversion failed
		if (Config.DEBUG) {
			ae.printStackTrace();
		}
	}
	return null;
}