Maxima/Data types

Data Types Maxima data types generally can be categorized as follows: Atomic Non-atomic Atomic Data Types Numerical Strings Constants Non-atomic Data Types Lists Arrays Structures Matrices Sets Matrices "In Maxima, a matrix is implemented as a nested list (namely a list of rows of the matrix)". E.g. :the Maxima mailing list : [Maxima] array and matrix? - answer by Robert Dodier (($MATRIX) ((MLIST) 1 2 3) ((MLIST) 4 5 6)) Construction of matrices from nested lists : (%i3) M:matrix([1,2,3],[4,5,6],[0,-1,-2]); [ 1 2 3 ] [ ] (%o3) [ 4 5 6 ] [ ] [ 0 - 1 - 2 ] Interesting examples by Burkhard Bunk : Maxima Overview by Burkhard Bunk A: matrix([a, b, c], [d, e, f], [g, h, i]); /* (3x3) matrix */ u: matrix([x, y, z]); /* row vector */ v: transpose(matrix([r, s, t])); /* column vector */ Reference to elements etc: u[1,2]; /* second element of u */ v[2,1]; /* second element of v */ A[2,3]; or A[2][3]; /* (2,3) element */ A[2]; /* second row of A */ transpose(transpose(A)[2]); /* second column of A */ Element by element operations: A + B; A - B; A * B; A / B; A ^ s; s ^ A; Matrix operations : A . B; /* matrix multiplication */ A ^^ s; /* matrix exponentiation (including inverse) */ transpose(A); determinant(A); invert(A); Category: Matrices :maxima manual : Category Matrices addcol addrow adjoint augcoefmatrix cauchy_matrix charpoly coefmatrix col columnvector covect copymatrix determinant detout diag diagmatrix doallmxops domxexpt domxmxops domxnctimes doscmxops doscmxplus echelon eigen ematrix entermatrix genmatrix ident invert list_matrix_entries lmxchar matrix matrix_element_add matrix_element_mult matrix_element_transpose matrixmap matrixp mattrace minor ncharpoly newdet nonscalar nonscalarp permanent rank ratmx row scalarmatrixp scalarp setelmx sparse submatrix tracematrix transpose triangularize zeromatrix Function: matrix Function: matrix (row_1, …, row_n) Returns a rectangular matrix which has the rows row_1, …, row_n. Each row is a list of expressions. All rows must be the same length. . operator "The dot operator, for matrix (non-commutative) multiplication. When "." is used in this way, spaces should be left on both sides of it, e.g. A . B This distinguishes it plainly from a decimal point in a floating point number. The operator . represents noncommutative multiplication and scalar product. When the operands are 1-column or 1-row matrices a and b, the expression a.b is equivalent to sum (a[i]*b[i], i, 1, length(a)). If a and b are not complex, this is the scalar product, also called the inner product or dot product, of a and b. The scalar product is defined as conjugate(a).b when a and b are complex; innerproduct in the eigen package provides the complex scalar product. When the operands are more general matrices, the product is the matrix product a and b. The number of rows of b must equal the number of columns of a, and the result has number of rows equal to the number of rows of a and number of columns equal to the number of columns of b. To distinguish . as an arithmetic operator from the decimal point in a floating point number, it may be necessary to leave spaces on either side. For example, 5.e3 is 5000.0 but 5 . e3 is 5 times e3. There are several flags which govern the simplification of expressions involving ., namely dot0nscsimp, dot0simp, dot1simp, dotassoc, dotconstrules, dotdistrib, dotexptsimp, dotident, and dotscrules." ( from Maxima CAS doc) Vectors Category: Vectors : Vectors eigen express nonscalar nonscalarp scalarp Category: Package vectmaxima manual : Package vect vect scalefactors vect_cross vectorpotential vectorsimp