X = solve(A,B)
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Over RR_{53} or CC_{53}, if the matrix A is non-singular and square, then highly optimized lapack routines will be called.
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If you know that your matrix is square, and invertible, then providing the hint: MaximalRank=>true allows Macaulay2 to choose the fastest routines. For small matrix sizes, it should not be too noticeable, but for large matrices, the difference in time taken can be dramatic.
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Over higher precision RR or CC, these routines will be much slower than the lower precision lapack routines.
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Giving the option ClosestFit=>true, in the case when the field is RR or CC, uses a least squares algorithm to find a best fit solution.
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Giving both options ClosestFit and MaximalRank allows Macaulay2 to call a faster algorithm.
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(1) This function is limited in scope, but has been designed to be much faster than generic algorithms. (2) If the matrix is a square invertible matrix, giving the option MaximalRank=>true can strongly speed up the computation. (3) For mutable matrices, this function is only currently implemented for densely encoded matrices.
The object solve is a method function with options.