DIRECTORYAlgebra3d,Complex,Matrix3d,RealFns,SV2d,SVVector3d;Algebra3dImpl: PROGRAMIMPORTS Complex, RealFnsEXPORTS Algebra3d =BEGINPoint2d: TYPE = Matrix3d.Point2d;Polygon: TYPE = REF PolygonObj;PolygonObj: TYPE = SV2d.PolygonObj;Vec: TYPE = Complex.Vec;Vector: TYPE = SVVector3d.Vector;root3Over2: REAL;	-- a loadtime constantLinearFormula: PRIVATE PROC [a, b: REAL] RETURNS [root: REAL, rootCount: NAT] = {IF a = 0 THEN {IF b = 0 THEN {root _ 0.0; rootCount _ 0; RETURN}ELSE {root _ 0.0; rootCount _ 0; RETURN}	-- inconsistent case}ELSE {IF b = 0  THEN {root _ 0.0; rootCount _ 1; RETURN}ELSE {root _ -b/a; rootCount _ 1; RETURN};};};QuadraticFormula: PUBLIC PROC [a, b, c: REAL] RETURNS [roots: ARRAY [1..2] OF REAL, rootCount: NAT] = {discriminant, temp: REAL;IF a = 0 THEN {[roots[1], rootCount] _ LinearFormula [b, c];RETURN;};IF c = 0 THEN {roots[1] _ 0.0;[roots[2], rootCount] _ LinearFormula[a, b];rootCount _ rootCount + 1;IF roots[1] > roots[2] THEN { -- swap themtemp _ roots[1];roots[1] _ roots[2];roots[2] _ temp;};RETURN};discriminant _ b*b - 4*a*c; -- 3 mult, 1 addSELECT discriminant FROM=0 => {rootCount _ 1;roots[1] _ -b/(2*a);RETURN};	-- 1 mult, 1 div (4 mult, 1 div, 1 add total)<0 => {rootCount _ 0;RETURN}; -- (3 mult, 1 add total)>0 => {sqrtRadical: REAL _ RealFns.SqRt[discriminant];term: REAL;rootCount _ 2;term _ IF b < 0 THEN sqrtRadical - b ELSE -sqrtRadical - b;roots[1] _ term/(2.0*a);roots[2] _ (2.0*c)/term;IF roots[1] > roots[2] THEN { -- swap themtemp _ roots[1];roots[1] _ roots[2];roots[2] _ temp;};RETURN}; -- 1 SqRt, 2 mult, 2 div, 2 add (1 SqRt, 5 mult, 2 div, 3 add total)ENDCASE => ERROR;}; -- end of QuadraticFormulaToPolar: PRIVATE PROC [vec: Vec] RETURNS [r: REAL, radians: REAL] = {r _ Complex.Abs[vec];radians _ Complex.Arg[vec];};ComplexRoot: PRIVATE PROC [index: REAL, vec: Vec] RETURNS [rootVec: Vec] = {r, radians, resultR, resultRadians: REAL;[r, radians] _ ToPolar[vec];resultR _ RealFns.Root[index, r];resultRadians _ radians/index;rootVec _ Complex.FromPolar[resultR, resultRadians];};Init: PROC = {root3Over2 _ RealFns.SqRt[3]/2.0;};Init[];END.  @  File: Algebra3dImpl.mesaLast edited by Bier on December 18, 1982 1:37 amAuthor: Eric Bier on August 4, 1983 3:36 pmContents: The quadratic formula, cubic formula and quartic formulaGLOBALSThe solution to the equation "ax + b = 0".The solution to the equation "ax2+bx+c=0".  If a=0 this is just a linear equation.  Ifc = 0, one root is zero and we solve a linear equation.  Otherwise, we use thequadratic formula in either the form [-b+-(b2-4ac)1/2]/2a or (2c)/[-b-+(b2-4ac)1/2]depending on the sign of b.  We will arrange the roots so that roots[1] < roots[2].ÊŽ  –"Cedar" style˜ Ihead1šœ™Iprocšœ0™0Lšœ+™+LšœB™BšœÏk	˜
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