Euler's identity: Difference between revisions
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m (→{{header|REXX}}: simplified cos, sin, sqrt functions, added whitespace.) |
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<br>program. |
<br>program. |
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<lang rexx>/*REXX program proves Euler's identity by showing that: e^(i pi) + 1 ≡ 0 */ |
<lang rexx>/*REXX program proves Euler's identity by showing that: e^(i pi) + 1 ≡ 0 */ |
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numeric digits length( pi() ) - |
numeric digits length( pi() ) - length(.) /*define pi; set # dec. digs precision*/ |
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cosPI= fmt( cos(pi) ) /*calculate the value of cos(pi). */ |
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sinPI= fmt( sin(pi) ) /* " " " " sin(pi). */ |
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say ' cos(pi) = ' |
say ' cos(pi) = ' cosPI /*display " " " cos(Pi). */ |
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say ' sin(pi) = ' |
say ' sin(pi) = ' sinPI /* " " " " sin(Pi). */ |
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say /*separate the wheat from the chaff. */ |
say /*separate the wheat from the chaff. */ |
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$= cosPI + mult( sqrt(-1), sinPI ) + 1 /*calc. product of sin(x) and sqrt(-1).*/ |
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say 'e^(i pi) + 1 = ' fmt($) |
say ' e^(i pi) + 1 = ' fmt($) ' ' word("unproven proven", ($=0) + 1) |
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exit /*stick a fork in it, we're all done. */ |
exit /*stick a fork in it, we're all done. */ |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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fmt: procedure; parse arg x; x=format(x,,digits()%2,0); return left('', x>=0)x / |
fmt: procedure; parse arg x; x= format(x, , digits() %2, 0); return left('', x>=0)x /1 |
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mult: procedure; parse arg a,b; if a=0 | b=0 then return 0; return a*b |
mult: procedure; parse arg a,b; if a=0 | b=0 then return 0; return a*b |
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pi: pi= 3.1415926535897932384626433832795028841971693993751058209749445923; return pi |
pi: pi= 3.1415926535897932384626433832795028841971693993751058209749445923; return pi |
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cos: procedure; parse arg x; z= 1; _= 1; q= x*x; i= -1; return .sinCos() |
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sin: procedure; parse arg x 1 z 1 _; q= x*x; i= 1; return .sinCos() |
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.sinCos: do k=2 by 2 until p=z; p=z; _= -_ * q/(k*(k+i)); z= z+_; end; return z |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); i=; h= d+6 |
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numeric digits; numeric form; if x<0 then do; x= -x; i= 'i'; end; m.= 9 |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); i=; m.=9; h=d+6 |
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numeric digits; numeric form; if x<0 then do; x= -x; i= 'i'; end |
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parse value format(x, 2, 1, , 0) 'E0' with g 'E' _ .; g= g * .5'e'_ % 2 |
parse value format(x, 2, 1, , 0) 'E0' with g 'E' _ .; g= g * .5'e'_ % 2 |
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do j=0 while h>9; m.j= h; h= h % 2 + 1; end |
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do k=j+5 to 0 by -1; numeric digits m.k; g= (g+x/g) *.5; end; return g || i</lang> |
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{{out|output|text= when using the internal default input:}} |
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numeric digits d; return (g/1)i /*make complex if X < 0.*/</lang> |
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{{out|output}} |
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<pre> |
<pre> |
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cos(pi) = -1 |
cos(pi) = -1 |
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sin(pi) = 0 |
sin(pi) = 0 |
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e^(i pi) + 1 = 0 proven |
e^(i pi) + 1 = 0 proven |
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</pre> |
</pre> |
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