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For loop with Maxima

for i:1 thru 3 step 1 do;
posix:arithsum(li*cos(ri(t))),1,i-1)+(li*cos(ri(t))/2);
posiy:arithsum(li*sin(ri(t))),1,i-1)+(li*sin(ri(t))/2);


What I wanna do is to get 6 position functions(3 x and 3 y). It should give me values like following:

pos1x:l1*cos(r1(t))/2;
pos2x:l1*cos(r1(t))+l2*cos(r2(t))/2;
pos3x:l1*cos(r1(t))+l2*cos(r2(t))+l3*cos(r3(t))/2;


So, why my code is not working?

1 Answer
1

Couple of things here. (1) for loop takes just one expression as its loop body; typically multiple expressions are combined into one as (e1, e2, e3) or block(e1, e2, e3). Note that for ... do; isn't correct syntax, since it doesn't have a loop body -- the semicolon terminates the for expression. Note also that expressions in the body are separated by commas, not semicolons. (2) You can use subscript notation to index items; Maxima won't automatically construct symbol names such as pos1x. Instead, use subscript notation: posx[1], posy[i], etc.

for

(e1, e2, e3)

block(e1, e2, e3)

for ... do;

for

pos1x

posx[1]

posy[i]

Given that, here's a solution.

(%i1) load (functs);
(%o1) /Applications/Maxima.app/Contents/Resources/opt/share/maxima/5.41.0/shar
e/simplification/functs.mac
(%i2) for i:1 thru 3 step 1 do
(posx[i]:arithsum(l[i]*cos(r[i](t)),1,i-1)+(l[i]*cos(r[i](t))/2),
posy[i]:arithsum(l[i]*sin(r[i](t)),1,i-1)+(l[i]*sin(r[i](t))/2));
(%o2) done
(%i3) [posx[1], posx[2], posx[3]];
l cos(r (t)) 3 l cos(r (t)) l cos(r (t))
1 1 2 2 1 3 3
(%o3) [-------------, ---------------, 2 (l cos(r (t)) + -) + -------------]
2 2 3 3 2 2
(%i4) [posy[1], posy[2], posy[3]];
l sin(r (t)) 3 l sin(r (t)) l sin(r (t))
1 1 2 2 1 3 3
(%o4) [-------------, ---------------, 2 (l sin(r (t)) + -) + -------------]
2 2 3 3 2 2


I am guessing that l[i] and r[i] should be subscripted too. I changed the parentheses in order to fix a syntax problem; if you intended something else, of course you can go ahead and change it again.

l[i]

r[i]

Note that in this formulation posx and posy are so-called undeclared arrays. Undeclared arrays are suitable for representing subscripted symbolic variables. You can get the list of elements via listarray.

posx

posy

listarray

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