Cramer's rule: Difference between revisions
Content added Content deleted
m (→version 2: shrunk a function.) |
m (→version 2: added a better way to express the equations.) |
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values= '-3 -32 -47 49' /*values of each matrix row of numbers.*/ |
values= '-3 -32 -47 49' /*values of each matrix row of numbers.*/ |
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variables= substr('abcdefghijklmnopqrstuvwxyz', 27 - words(values) ) /*variable names.*/ |
variables= substr('abcdefghijklmnopqrstuvwxyz', 27 - words(values) ) /*variable names.*/ |
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call makeM '2 -1 5 |
call makeM ' 2 -1 5 1 3 2 2 -6 1 3 3 -1 5 -2 -3 3' |
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do y=1 for sz; $= /*display the matrix (linear equations)*/ |
do y=1 for sz; $= /*display the matrix (linear equations)*/ |
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do x=1 for sz; $= $ |
do x=1 for sz; $= $ right(psign(@.x.y), w)'*'substr(variables, x, 1) |
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end /*y*/ /* [↑] right─justify matrix elements.*/ |
end /*y*/ /* [↑] right─justify matrix elements.*/ |
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pad= left('', length($) - 2); say $ ' = ' right( word(values, y), wv) |
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end /*x*/ /* [↑] obtain value of the equation. */ |
end /*x*/ /* [↑] obtain value of the equation. */ |
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say; say |
say; say |
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end /*i*/ |
end /*i*/ |
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end /*j*/ |
end /*j*/ |
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say |
say pad substr(variables,k,1) ' = ' right(det(makeL())/det(mat), digits()+2) |
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end /*k*/ |
end /*k*/ |
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exit 0 /*stick a fork in it, we're all done. */ |
exit 0 /*stick a fork in it, we're all done. */ |
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makeL: $=; do x=1 for sz; do y=1 for sz; $= $ !.x.y; end; end; return $ /*matrix─►list*/ |
makeL: $=; do x=1 for sz; do y=1 for sz; $= $ !.x.y; end; end; return $ /*matrix─►list*/ |
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mSize: arg _; do sz=0 for 1e3; if sz*sz==_ then return; end; say 'error,bad matrix';exit 9 |
mSize: arg _; do sz=0 for 1e3; if sz*sz==_ then return; end; say 'error,bad matrix';exit 9 |
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psign: parse arg num; if left(num, 1)\=='-' & x>1 then return "+"num; return num |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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det: procedure; parse arg a b c d 1 nums; call mSize words(nums); |
det: procedure; parse arg a b c d 1 nums; call mSize words(nums); _= 0 |
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if sz==2 then return a*d - b*c |
if sz==2 then return a*d - b*c |
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do j=1 for sz |
do j=1 for sz |
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end /*j*/ |
end /*j*/ |
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aa= aa - (-1 ** odd) * @.i.1 * det($) |
aa= aa - (-1 ** odd) * @.i.1 * det($) |
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end; /*i*/; return aa |
end; /*i*/; return aa |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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makeM: procedure expose @. values mat sz w |
makeM: procedure expose @. values mat sz w wv; parse arg mat; call mSize words(mat) |
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#= 0; |
#= 0; wv= 0; w= 0 |
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do j=1 for sz |
do j=1 for sz; wv= max(wv, length( word( values, j) ) ) |
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do k=1 for sz; #= #+1; @.k.j= word(mat, #); w= max(w, length(@.k.j) |
do k=1 for sz; #= #+1; @.k.j= word(mat, #); w= max(w, length(@.k.j)) |
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end /*k*/ |
end /*k*/ |
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end; /*j*/; return</lang> |
end; /*j*/; w= w + 1; return</lang> |
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{{out|output|text= when using the internal default inputs:}} |
{{out|output|text= when using the internal default inputs:}} |
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<pre> |
<pre> |
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2 -1 5 1 = |
2*w -1*x +5*y +1*z = -3 |
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3 2 2 -6 = |
3*w +2*x +2*y -6*z = -32 |
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1 3 3 -1 = |
1*w +3*x +3*y -1*z = -47 |
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5 -2 -3 3 = |
5*w -2*x -3*y +3*z = 49 |
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w = 2 |
w = 2 |
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x = -12 |
x = -12 |
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y = -4 |
y = -4 |
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z = 1 |
z = 1 |
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</pre> |
</pre> |
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