An algorithm for computing exactly a general solution to a system of linear equations with coefficients that are polynomials over the integers is presented. The algorithm applies mod-p mappings and then evaluation mappings, eventually solving linear systems of equations with coefficients in GF(p) by a special Gaussian elimination algorithm. Then by applying interpolation and the Chinese Remainder Theorem a general solution is obtained.
For a consistent system, the evaluation-interpolation part of the algorithm computes the determinantal RRE form of the mod-p reduced augmented system matrices. The Chinese Remainder Theorem then uses these to construct an RRE matrix with polynomial entries over the integers, from which a general solution is constructed. For an inconsistent system, only one mod-p mapping is needed.
The average computing time for the algorithm is obtained and compared to that for the exact division method. The new method is found to be far superior. Also, a mod-p/evaluation mapping algorithm for computing matrix products is discussed briefly.
对于一致的系统,算法的评估-内插部分计算mod-p约简增强系统矩阵的行列式RRE形式。然后,中国余数定理使用这些定理来构造一个RRE矩阵,在整数上具有多项式条目,从中构造一个通用解。对于不一致的系统,只需要一个mod-p映射。 P>
获得该算法的平均计算时间,并将其与精确除法的平均计算时间进行比较。发现新方法优越得多。此外,还简要讨论了用于计算矩阵乘积的mod-p /评估映射算法。 P>
机译:多项式系数在常点附近的n阶线性齐次微分方程精确幂级数解的符号算法
机译:具有多项式系数的二阶线性齐次微分方程精确幂级数解的算法
机译:具有多项式系数的二阶线性齐次微分方程精确幂级数解的算法
机译:具有多项式系数的线性差分和q差分方程的有理解
机译:具有有理函数系数的线性微分方程的超几何解。
机译:非线性发展方程组的精确行波解
机译:多项式系数线性方程系统的精确解
机译:多项式系数线性方程组的精确解。