论文标题
MathPartner 2021的新功能
New features in MathPartner 2021
论文作者
论文摘要
我们在MathPartner服务中介绍了新功能，这些功能最近已向用户使用。我们强调了计算算术几何平均值和几何谐波平均值的功能。它们允许计算第一类的完整椭圆积分。它们对于解决许多物理问题很有用，例如，可以计算简单的摆时。接下来，可以计算Semjon Adlaj提出的修改算术几何平均值。因此，可以计算第二种的完整椭圆积分以及椭圆的圆周。此外，还可以计算第一类和第二种的Sylvester矩阵。因此，通过一些字符串，一个人可以计算两个多项式的结果以及二进制形式的判别。还添加了一些新的矩阵函数。 So, today the list of matrix functions includes the transpose, adjugate, conjugate, inverse, generalized inverse, and pseudo inverse of a matrix, the matrix determinant, the kernel, the echelon form, the characteristic polynomial, the Bruhat decomposition, the triangular LSU decomposition, which is an exact block recursive LU decomposition, the QR block recursive分解和奇异值分解。此外，已经实现了两个块回收功能来计算对称正定矩阵的cholesky分解：具有标准乘法算法的稀疏矩阵的一个函数，以及根据Winograd-Strastrassen Algorithm乘以乘法的密集矩阵的另一个功能。线性编程问题也可以解决。因此，MathPartner服务变得更好和方便。它可以在http://mathpar.ukma.edu.ua/以及http://mathpar.com上免费获得。
We introduce new features in the MathPartner service that have recently become available to users. We highlight the functions for calculating both arithmetic-geometric mean and geometric-harmonic mean. They allow calculating complete elliptic integrals of the first kind. They are useful for solving many physics problems, for example, one can calculate the period of a simple pendulum. Next, one can calculate the modified arithmetic-geometric mean proposed by Semjon Adlaj. Consequently, one can calculate the complete elliptic integrals of the second kind as well as the circumference of an ellipse. Furthermore, one can also calculate the Sylvester matrices of the first and the second kind. Thus, by means of a few strings, one can calculate the resultant of two polynomials as well as the discriminant of a binary form. Some new matrix functions are also added. So, today the list of matrix functions includes the transpose, adjugate, conjugate, inverse, generalized inverse, and pseudo inverse of a matrix, the matrix determinant, the kernel, the echelon form, the characteristic polynomial, the Bruhat decomposition, the triangular LSU decomposition, which is an exact block recursive LU decomposition, the QR block recursive decomposition, and the singular value decomposition. In addition, two block-recursive functions have been implemented for calculating the Cholesky decomposition of symmetric positive-definite matrices: one function for sparse matrices with the standard multiplication algorithm and another function for dense matrices with multiplication according to the Winograd--Strassen algorithm. The linear programming problems can be solved too. So, the MathPartner service has become better and handy. It is freely available at http://mathpar.ukma.edu.ua/ as well as at http://mathpar.com.
