Free mathematical script

Major Features:

1. Provides a portable standard for typesetting mathematical figures, just as TeX/LaTeX has become the standard for typesetting equations.
2. Inspired by MetaPost, with a much cleaner, powerful C -like programming syntax and floating-point numerics;
3. Runs on all major platforms (UNIX, MacOS, Microsoft Windows);
4. Mathematically oriented (e.g. rotation of vectors by complex multiplication);
5. LaTeX typesetting of labels (for document consistency);
6. Uses simplex method and deferred drawing to solve overall size constraint issues between fixed-sized objects (labels and arrowheads) and objects that should scale with figure size;
7. Fully generalizes MetaPost path construction algorithms to three dimensions;
8. Compiles commands into virtual machine code for speed without sacrificing portability;
9. High-level graphics commands are implemented in the Asymptote language itself, allowing them to be easily tailored to specific applications.

PERMPOS is a convenient mathematical tool which contains all possible permutations of M values in N positions. B = PERMPOS(M,N) where M and N are non-negative integers produces a logical (N!/M!(N-M)!)-by-N matrix in which each row contains a unique permation of M trues and (N-M) falses. Note that each column will hence contain (N-1) trues.

B = PERMPOS(V,N) where V is a vector of length M produces a matrix where each row a contains the values of V in preserved order, but uniquely permuted at the N columns. The remaining positions are zero.

Examples:
permpos(2,4) % ->
% 1 1 0 0
% 1 0 1 0
% 1 0 0 1
% 0 1 1 0
% 0 1 0 1
% 0 0 1 1
permpos([-4 9 3],4) % >
% -4 9 3 0
% -4 9 0 3
% -4 0 9 3
% 0 -4 9 3
See also NCHOOSEK, PERMS, RANDPERM, TRUE, FALSE and COMBN, ALLCOMB, BALLATSQ, NONES (Matlab File Exchange)

Requirements:

• MATLAB Release: R13

Why go out on a limb to use povrays SDL language when you can raytrace from the comfort of your favorite python chair? This framework uses all of pythons cool OO setattr, getattr, *args, and **kwargs groovyness to create an extra lightweight fitting over povrays SDL files. It means you can go absolutely bananas turning whatever complex mathematical/algorithmic structures you can comprehend (or not) into squeeky clean visuals and animations. This is also an interesting exercise in structured text file generation; the author was influenced by Guidos bgen modules.

C = INSERTROWS(A,B,IND) inserts the rows of matrix B into the matrix A at the positions IND. Row k of matrix B will be inserted after position IND(k)in the matrix A. If A is a N-by-X matrix and B is a M-by-X matrix, C will be a (N M)-by-X matrix. IND can contain non-integers.

If B is a 1-by-N matrix, B will be inserted for each insertion position specified by IND. If IND is a single value, the whole matrix B will be inserted at that position. If B is a single value, B is expanded to a row vector. In all other cases, the number of elements in IND should be equal to the number of rows in B, and the number of columns, planes etc should be the same for both matrices A and B. If any of the inputs are empty, C will return A.

Examples:
% the size of A,B, and IND all match
C = insertrows(rand(5,2),zeros(2,2),[1.5 3])
% the row vector B is inserted twice
C = insertrows(ones(4,3),1:3,[1 Inf])
% matrix B is expanded to a row vector and inserted twice (as in 2)
C = insertrows(ones(5,3),999,[2 4])
% the whole matrix B is inserted once
C = insertrows(ones(5,3),zeros(2,3),2)
[C, RA, RB] = INSERTROWS(...) will return the row indices RA and RB for which C
corresponds to the rows of either A and B.
[c,ra,rb] = insertrows([1:4].,99,[0 3]) ;
c. % -> [99 1 2 3 99 4] ;
c(ra). % -> [1 2 3 4] ;
c(rb). % -> [99 99] ;
To insert columns, planes, etc., you can permute the inputs and ipermute the result.
A = ones(4,3) ; B = zeros(4,1) ;
C = insertrows(permute(A,[2 1]), permute(B,[2 1]),1) ;
C = ipermute(C,[2 1]) ;
See also PERMUTE, IPERMUTE, RESHAPE, CAT

Requirements:

• MATLAB Release: R13