using functions

using functions

There are many functions in Macaulay 2 that do various things. You can get a brief indication of what a function does by typing its name.

i1 : sin



o1 = sin



o1 : Function



Synopsis:

    Usage: 'y = sin x'

    Input:

    'x'



    Output:

    'y': the sine of 'x'

In this case, we see that the function sin takes a single argument x. We apply a function to its argument by typing them in adjacent positions. It is possible but not necessary to place parentheses around the argument.

i2 : sin 1.2



o2 = 0.932039



o2 : RR

i3 : sin(1.2)



o3 = 0.932039



o3 : RR

i4 : sin(1.0+0.2)



o4 = 0.932039



o4 : RR

In parsing the operator ^ takes precedence over adjacency, so the function is applied after the power is computed in the following code. This may not be what you expect.

i5 : print(10 + 1)^2

121

Some functions take more than one argument, and the arguments are separated by a comma, and then parentheses are needed.

i6 : append



o6 = append



o6 : Function



  --  add to the end of a list



Ways to use 'append' :



    "append"("BasicList","Thing")

i7 : append({a,b,c},d)



o7 = {a, b, c, d}



o7 : List

Some functions take a variable number of arguments.

i8 : join



o8 = join



o8 : Function



  --  join lists



Ways to use 'join' :



    "join"("BasicList","BasicList")

i9 : join({a,b},{c,d},{e,f},{g,h,i})



o9 = {a, b, c, d, e, f, g, h, i}



o9 : List

Functions, like anything else, can be assigned to variables. You may do this to provide handy private abbreviations.

i10 : ap = append;

i11 : ap({a,b,c},d)



o11 = {a, b, c, d}



o11 : List