Expression 19: "D" equals "R" left parenthesis, "L" , left bracket, negative 1 , negative 1 , 0 , right bracket , right parenthesisD=RL,−1,−1,0
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Expression 20: "N" equals length left parenthesis, "D" , right parenthesisN=lengthD
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A: added increments in angle. X,Y: constructed locations.
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Expression 22: "A" left parenthesis, "p" , right parenthesis equals Start sum from "k" equals 1 to "p" minus 1, end sum, "M" left parenthesis, "k" , "p" , right parenthesis left brace, "D" left bracket, "k" , right bracket equals positive 1 : positive 45 , "D" left bracket, "k" , right bracket equals negative 1 : negative 45 , 0 , right braceAp=p−1∑k=1Mk,pDk=+1:+45,Dk=−1:−45,0
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Expression 23: "X" left parenthesis, "p" , right parenthesis equals negative Start sum from "m" equals 1 to "p" , end sum, "S" left parenthesis, "m" , right parenthesis "M" left parenthesis, "m" , "p" , right parenthesis sine left parenthesis, StartFraction, pi Over 180 , EndFraction "A" left parenthesis, "m" , right parenthesis , right parenthesisXp=−p∑m=1SmMm,psinπ180Am
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Expression 24: "Y" left parenthesis, "p" , right parenthesis equals Start sum from "m" equals 1 to "p" , end sum, "S" left parenthesis, "m" , right parenthesis "M" left parenthesis, "m" , "p" , right parenthesis cosine left parenthesis, StartFraction, pi Over 180 , EndFraction "A" left parenthesis, "m" , right parenthesis , right parenthesisYp=p∑m=1SmMm,pcosπ180Am
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Z: stack depth. M: mask all ops between deeper pushs/pops S:select step operations
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Expression 26: "Z" equals Start sum from "n" equals 1 to left bracket, 1... "N" , right bracket , end sum, left brace, "D" left bracket, "n" , right bracket equals positive 1 : 1 , "D" left bracket, "n" , right bracket equals negative 1 : negative 1 , 0 , right braceZ=1...N∑n=1Dn=+1:1,Dn=−1:−1,0
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Expression 27: "M" left parenthesis, "m" , "p" , right parenthesis equals left brace, "Z" left bracket, "m" , right bracket equals min left parenthesis, "Z" left bracket, "m" ... "p" , right bracket , right parenthesis : 1 , 0 , right braceMm,p=Zm=minZm...p:1,0
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Expression 28: "S" left parenthesis, "m" , right parenthesis equals left brace, "D" left bracket, "m" , right bracket equals "s" : 1 , "D" left bracket, "m" , right bracket equals "b" : .5 , 0 , right braceSm=Dm=s:1,Dm=b:.5,0
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Expression 29: left bracket, left brace, "D" left bracket, "j" plus 1 , right bracket equals 0 : left parenthesis, 0 , StartFraction, 0 Over 0 , EndFraction , right parenthesis , left parenthesis, "X" left parenthesis, "j" , right parenthesis , "Y" left parenthesis, "j" , right parenthesis , right parenthesis , right brace for "j" equals left bracket, 0... "N" , right bracket , right bracketDj+1=0:0,00,Xj,Yjforj=0...N
