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Macaulay2Doc :: on

on -- trace a function each time it's run

Synopsis

Description

Ideally, this function would replace f, i.e., we would write f = on f. Unfortunately, all the pre-installed system functions are write-protected; fortunately, their methods are not, and can be replaced.

i1 : ker Matrix := on(lookup(ker,Matrix),GenerateAssertions=>true,Name=>"ker");
i2 : f = x -> kernel (x|x);
i3 : R = QQ[a..c];
i4 : f vars R
-- ker (1) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (1) returned CacheFunction: -*a cache function*-
-- ker (1) called with Matrix: | a b c a b c |
-- ker (1) returned Module: image {1} | -1 0  0  -b 0  -c |
--                                {1} | 0  -1 0  a  -c 0  |
--                                {1} | 0  0  -1 0  b  a  |
--                                {1} | 1  0  0  0  0  0  |
--                                {1} | 0  1  0  0  0  0  |
--                                {1} | 0  0  1  0  0  0  |
assert( ker(map(R^1,R^{{-1}, {-1}, {-1}, {-1}, {-1}, {-1}},{{a,b,c,a,b,c}})) === (image(map(R^{{-1}, {-1}, {-1}, {-1}, {-1}, {-1}},R^{{-1}, {-1}, {-1}, {-2}, {-2}, {-2}},{{-1,0,0,-b,0,-c}, {0,-1,0,a,-c,0}, {0,0,-1,0,b,a}, {1,0,0,0,0,0}, {0,1,0,0,0,0}, {0,0,1,0,0,0}}))))

o4 = image {1} | -1 0  0  -b 0  -c |
           {1} | 0  -1 0  a  -c 0  |
           {1} | 0  0  -1 0  b  a  |
           {1} | 1  0  0  0  0  0  |
           {1} | 0  1  0  0  0  0  |
           {1} | 0  0  1  0  0  0  |

                             6
o4 : R-module, submodule of R

See also

For the programmer

The object on is a function closure.