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@@ -41,176 +41,176 @@ Unit UComplex;
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after this operator any real can be passed to a function
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as a complex arg !! }
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- operator := (r : real) z : complex;
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+ operator := (const r : real) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- { operator := (i : longint) z : complex;
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+ { operator := (const i : longint) z : complex;
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not needed because longint can be converted to real }
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{ four operator : +, -, * , / and comparison = }
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- operator + (z1, z2 : complex) z : complex;
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+ operator + (const z1, z2 : complex) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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{ these ones are created because the code
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is simpler and thus faster }
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- operator + (z1 : complex; r : real) z : complex;
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+ operator + (const z1 : complex;const r : real) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- operator + (r : real; z1 : complex) z : complex;
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+ operator + (const r : real;const z1 : complex) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- operator - (z1, z2 : complex) z : complex;
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+ operator - (const z1, z2 : complex) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- operator - (z1 : complex;r : real) z : complex;
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+ operator - (const z1 : complex;const r : real) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- operator - (r : real; z1 : complex) z : complex;
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+ operator - (const r : real;const z1 : complex) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- operator * (z1, z2 : complex) z : complex;
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+ operator * (const z1, z2 : complex) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- operator * (z1 : complex; r : real) z : complex;
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+ operator * (const z1 : complex;const r : real) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- operator * (r : real; z1 : complex) z : complex;
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+ operator * (const r : real;const z1 : complex) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- operator / (znum, zden : complex) z : complex;
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+ operator / (const znum, zden : complex) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- operator / (znum : complex; r : real) z : complex;
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+ operator / (const znum : complex;const r : real) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- operator / (r : real; zden : complex) z : complex;
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+ operator / (const r : real;const zden : complex) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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{ ** is the exponentiation operator }
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- operator ** (z1, z2 : complex) z : complex;
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+ operator ** (const z1, z2 : complex) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- operator ** (z1 : complex; r : real) z : complex;
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+ operator ** (const z1 : complex;const r : real) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- operator ** (r : real; z1 : complex) z : complex;
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+ operator ** (const r : real;const z1 : complex) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- operator = (z1, z2 : complex) b : boolean;
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+ operator = (const z1, z2 : complex) b : boolean;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- operator = (z1 : complex;r : real) b : boolean;
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+ operator = (const z1 : complex;const r : real) b : boolean;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- operator = (r : real; z1 : complex) b : boolean;
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+ operator = (const r : real;const z1 : complex) b : boolean;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- operator - (z1 : complex) z : complex;
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+ operator - (const z1 : complex) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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- function cinit(_re,_im : real) : complex;inline;
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- function csamevalue(z1, z2 : complex) : boolean;
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+ function cinit(const _re,_im : real) : complex;inline;
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+ function csamevalue(const z1, z2 : complex) : boolean;
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{ complex functions }
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- function cong (z : complex) : complex; { conjuge }
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+ function cong (const z : complex) : complex; { conjuge }
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{ inverse function 1/z }
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- function cinv (z : complex) : complex;
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+ function cinv (const z : complex) : complex;
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{ complex functions with real return values }
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- function cmod (z : complex) : real; { module }
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- function carg (z : complex) : real; { argument : a / z = p.e^ia }
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+ function cmod (const z : complex) : real; { module }
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+ function carg (const z : complex) : real; { argument : a / z = p.e^ia }
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{ fonctions elementaires }
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- function cexp (z : complex) : complex; { exponential }
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- function cln (z : complex) : complex; { natural logarithm }
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- function csqr (z: complex) : complex; { square }
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- function csqrt (z : complex) : complex; { square root }
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+ function cexp (const z : complex) : complex; { exponential }
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+ function cln (const z : complex) : complex; { natural logarithm }
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+ function csqr (const z: complex) : complex; { square }
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+ function csqrt (const z : complex) : complex; { square root }
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{ complex trigonometric functions }
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- function ccos (z : complex) : complex; { cosinus }
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- function csin (z : complex) : complex; { sinus }
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- function ctg (z : complex) : complex; { tangent }
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+ function ccos (const z : complex) : complex; { cosinus }
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+ function csin (const z : complex) : complex; { sinus }
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+ function ctg (const z : complex) : complex; { tangent }
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{ inverse complex trigonometric functions }
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- function carc_cos (z : complex) : complex; { arc cosinus }
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- function carc_sin (z : complex) : complex; { arc sinus }
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- function carc_tg (z : complex) : complex; { arc tangent }
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+ function carc_cos (const z : complex) : complex; { arc cosinus }
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+ function carc_sin (const z : complex) : complex; { arc sinus }
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+ function carc_tg (const z : complex) : complex; { arc tangent }
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{ hyperbolic complex functions }
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- function cch (z : complex) : complex; { hyperbolic cosinus }
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- function csh (z : complex) : complex; { hyperbolic sinus }
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- function cth (z : complex) : complex; { hyperbolic tangent }
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+ function cch (const z : complex) : complex; { hyperbolic cosinus }
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+ function csh (const z : complex) : complex; { hyperbolic sinus }
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+ function cth (const z : complex) : complex; { hyperbolic tangent }
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{ inverse hyperbolic complex functions }
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- function carg_ch (z : complex) : complex; { hyperbolic arc cosinus }
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- function carg_sh (z : complex) : complex; { hyperbolic arc sinus }
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- function carg_th (z : complex) : complex; { hyperbolic arc tangente }
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+ function carg_ch (const z : complex) : complex; { hyperbolic arc cosinus }
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+ function carg_sh (const z : complex) : complex; { hyperbolic arc sinus }
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+ function carg_th (const z : complex) : complex; { hyperbolic arc tangente }
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{ functions to write out a complex value }
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- function cstr(z : complex) : string;
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- function cstr(z:complex;len : integer) : string;
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- function cstr(z:complex;len,dec : integer) : string;
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+ function cstr(const z : complex) : string;
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+ function cstr(const z:complex;const len : integer) : string;
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+ function cstr(const z:complex;const len,dec : integer) : string;
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implementation
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- function cinit(_re,_im : real) : complex;inline;
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+ function cinit(const _re,_im : real) : complex;inline;
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begin
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cinit.re:=_re;
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cinit.im:=_im;
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end;
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- function csamevalue(z1, z2: complex): boolean;
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+ function csamevalue(const z1, z2: complex): boolean;
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begin
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csamevalue:=SameValue(z1.re, z2.re) and SameValue(z1.im, z2.im);
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end;
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- operator := (r : real) z : complex;
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+ operator := (const r : real) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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@@ -222,7 +222,7 @@ Unit UComplex;
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{ four base operations +, -, * , / }
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- operator + (z1, z2 : complex) z : complex;
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+ operator + (const z1, z2 : complex) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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@@ -232,7 +232,7 @@ Unit UComplex;
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z.im := z1.im + z2.im;
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end;
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- operator + (z1 : complex; r : real) z : complex;
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+ operator + (const z1 : complex;const r : real) z : complex;
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{ addition : z := z1 + r }
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{$ifdef TEST_INLINE}
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inline;
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@@ -242,7 +242,7 @@ Unit UComplex;
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z.im := z1.im;
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end;
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- operator + (r : real; z1 : complex) z : complex;
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+ operator + (const r : real;const z1 : complex) z : complex;
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{ addition : z := r + z1 }
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{$ifdef TEST_INLINE}
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inline;
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@@ -253,7 +253,7 @@ Unit UComplex;
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z.im := z1.im;
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end;
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- operator - (z1, z2 : complex) z : complex;
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+ operator - (const z1, z2 : complex) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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@@ -263,7 +263,7 @@ Unit UComplex;
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z.im := z1.im - z2.im;
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end;
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- operator - (z1 : complex; r : real) z : complex;
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+ operator - (const z1 : complex;const r : real) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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@@ -273,7 +273,7 @@ Unit UComplex;
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z.im := z1.im;
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end;
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- operator - (z1 : complex) z : complex;
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+ operator - (const z1 : complex) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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@@ -283,7 +283,7 @@ Unit UComplex;
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z.im := -z1.im;
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end;
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- operator - (r : real; z1 : complex) z : complex;
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+ operator - (const r : real;const z1 : complex) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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@@ -293,7 +293,7 @@ Unit UComplex;
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z.im := - z1.im;
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end;
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- operator * (z1, z2 : complex) z : complex;
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+ operator * (const z1, z2 : complex) z : complex;
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{ multiplication : z := z1 * z2 }
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{$ifdef TEST_INLINE}
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inline;
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@@ -303,7 +303,7 @@ Unit UComplex;
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z.im := (z1.re * z2.im) + (z1.im * z2.re);
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end;
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- operator * (z1 : complex; r : real) z : complex;
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+ operator * (const z1 : complex;const r : real) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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@@ -313,7 +313,7 @@ Unit UComplex;
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z.im := z1.im * r;
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end;
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- operator * (r : real; z1 : complex) z : complex;
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+ operator * (const r : real;const z1 : complex) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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@@ -323,7 +323,7 @@ Unit UComplex;
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z.im := z1.im * r;
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end;
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- operator / (znum, zden : complex) z : complex;
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+ operator / (const znum, zden : complex) z : complex;
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{$ifdef TEST_INLINE}
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inline;
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{$endif TEST_INLINE}
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@@ -358,14 +358,14 @@ Unit UComplex;
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end;
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end;
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- operator / (znum : complex; r : real) z : complex;
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+ operator / (const znum : complex;const r : real) z : complex;
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{ division : z := znum / r }
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begin
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z.re := znum.re / r;
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z.im := znum.im / r;
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end;
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- operator / (r : real; zden : complex) z : complex;
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+ operator / (const r : real;const zden : complex) z : complex;
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{ division : z := r / zden }
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var denom : real;
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begin
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@@ -375,20 +375,20 @@ Unit UComplex;
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z.im := - (r * zden.im) / denom;
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end;
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- function cmod (z : complex): real;
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+ function cmod (const z : complex): real;
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{ module : r = |z| }
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begin
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with z do
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cmod := sqrt((re * re) + (im * im));
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end;
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- function carg (z : complex): real;
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+ function carg (const z : complex): real;
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{ argument : 0 / z = p ei0 }
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begin
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carg := arctan2(z.im, z.re);
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end;
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- function cong (z : complex) : complex;
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+ function cong (const z : complex) : complex;
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{ complex conjugee :
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if z := x + i.y
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then cong is x - i.y }
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@@ -397,7 +397,7 @@ Unit UComplex;
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cong.im := - z.im;
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end;
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- function cinv (z : complex) : complex;
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+ function cinv (const z : complex) : complex;
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{ inverse : r := 1 / z }
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var
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denom : real;
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@@ -408,19 +408,19 @@ Unit UComplex;
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cinv.im:=-z.im/denom;
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end;
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- operator = (z1, z2 : complex) b : boolean;
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+ operator = (const z1, z2 : complex) b : boolean;
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{ returns TRUE if z1 = z2 }
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begin
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b := (z1.re = z2.re) and (z1.im = z2.im);
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end;
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- operator = (z1 : complex; r :real) b : boolean;
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+ operator = (const z1 : complex;const r :real) b : boolean;
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{ returns TRUE if z1 = r }
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begin
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b := (z1.re = r) and (z1.im = 0.0)
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end;
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- operator = (r : real; z1 : complex) b : boolean;
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+ operator = (const r : real;const z1 : complex) b : boolean;
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{ returns TRUE if z1 = r }
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begin
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b := (z1.re = r) and (z1.im = 0.0)
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@@ -429,7 +429,7 @@ Unit UComplex;
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{ fonctions elementaires }
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- function cexp (z : complex) : complex;
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+ function cexp (const z : complex) : complex;
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{ exponantial : r := exp(z) }
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{ exp(x + iy) = exp(x).exp(iy) = exp(x).[cos(y) + i sin(y)] }
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var expz : real;
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@@ -439,7 +439,7 @@ Unit UComplex;
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cexp.im := expz * sin(z.im);
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end;
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- function cln (z : complex) : complex;
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+ function cln (const z : complex) : complex;
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{ natural logarithm : r := ln(z) }
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{ ln( p exp(i0)) = ln(p) + i0 + 2kpi }
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begin
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@@ -447,14 +447,14 @@ Unit UComplex;
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cln.im := arctan2(z.im, z.re);
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end;
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- function csqr(z: complex): complex;
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+ function csqr(const z: complex): complex;
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{ square : r := z*z }
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begin
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csqr.re := z.re * z.re - z.im * z.im;
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csqr.im := 2 * z.re * z.im;
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end;
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- function csqrt (z : complex) : complex;
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+ function csqrt (const z : complex) : complex;
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{ square root : r := sqrt(z) }
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var
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root, q : real;
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@@ -483,19 +483,19 @@ Unit UComplex;
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end;
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- operator ** (z1, z2 : complex) z : complex;
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+ operator ** (const z1, z2 : complex) z : complex;
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{ exp : z := z1 ** z2 }
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begin
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z := cexp(z2*cln(z1));
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end;
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- operator ** (z1 : complex; r : real) z : complex;
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+ operator ** (const z1 : complex;const r : real) z : complex;
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{ multiplication : z := z1 * r }
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begin
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z := cexp( r *cln(z1));
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end;
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- operator ** (r : real; z1 : complex) z : complex;
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+ operator ** (const r : real;const z1 : complex) z : complex;
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{ multiplication : z := r + z1 }
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begin
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z := cexp(z1*ln(r));
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@@ -503,7 +503,7 @@ Unit UComplex;
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{ direct trigonometric functions }
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- function ccos (z : complex) : complex;
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+ function ccos (const z : complex) : complex;
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{ complex cosinus }
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{ cos(x+iy) = cos(x).cos(iy) - sin(x).sin(iy) }
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{ cos(ix) = cosh(x) et sin(ix) = i.sinh(x) }
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@@ -512,7 +512,7 @@ Unit UComplex;
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ccos.im := - sin(z.re) * sinh(z.im);
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end;
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- function csin (z : complex) : complex;
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+ function csin (const z : complex) : complex;
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{ sinus complex }
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{ sin(x+iy) = sin(x).cos(iy) + cos(x).sin(iy) }
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{ cos(ix) = cosh(x) et sin(ix) = i.sinh(x) }
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@@ -521,7 +521,7 @@ Unit UComplex;
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csin.im := cos(z.re) * sinh(z.im);
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end;
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- function ctg (z : complex) : complex;
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+ function ctg (const z : complex) : complex;
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{ tangente }
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var ccosz, temp : complex;
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begin
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@@ -532,21 +532,21 @@ Unit UComplex;
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{ fonctions trigonometriques inverses }
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- function carc_cos (z : complex) : complex;
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+ function carc_cos (const z : complex) : complex;
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{ arc cosinus complex }
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{ arccos(z) = -i.argch(z) }
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begin
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carc_cos := -i*carg_ch(z);
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end;
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- function carc_sin (z : complex) : complex;
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+ function carc_sin (const z : complex) : complex;
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{ arc sinus complex }
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{ arcsin(z) = -i.argsh(i.z) }
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begin
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carc_sin := -i*carg_sh(i*z);
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end;
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- function carc_tg (z : complex) : complex;
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+ function carc_tg (const z : complex) : complex;
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{ arc tangente complex }
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{ arctg(z) = -i.argth(i.z) }
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begin
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@@ -555,7 +555,7 @@ Unit UComplex;
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{ hyberbolic complex functions }
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- function cch (z : complex) : complex;
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+ function cch (const z : complex) : complex;
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{ hyberbolic cosinus }
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{ cosh(x+iy) = cosh(x).cosh(iy) + sinh(x).sinh(iy) }
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{ cosh(iy) = cos(y) et sinh(iy) = i.sin(y) }
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@@ -564,7 +564,7 @@ Unit UComplex;
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cch.im := sinh(z.re) * sin(z.im);
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end;
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- function csh (z : complex) : complex;
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+ function csh (const z : complex) : complex;
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|
{ hyberbolic sinus }
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{ sinh(x+iy) = sinh(x).cosh(iy) + cosh(x).sinh(iy) }
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{ cosh(iy) = cos(y) et sinh(iy) = i.sin(y) }
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@@ -573,20 +573,19 @@ Unit UComplex;
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csh.im := cosh(z.re) * sin(z.im);
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|
end;
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- function cth (z : complex) : complex;
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+ function cth (const z : complex) : complex;
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|
{ hyberbolic complex tangent }
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{ th(x) = sinh(x) / cosh(x) }
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{ cosh(x) > 1 qq x }
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|
var temp : complex;
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|
begin
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|
temp := cch(z);
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|
- z := csh(z);
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|
- cth := z / temp;
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|
+ cth := csh(z) / temp;
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|
end;
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|
{ inverse complex hyperbolic functions }
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|
- function carg_ch (z : complex) : complex;
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|
+ function carg_ch (const z : complex) : complex;
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|
{ hyberbolic arg cosinus }
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|
{ _________ }
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|
{ argch(z) = -/+ ln(z + i.V 1 - z.z) }
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|
@@ -594,7 +593,7 @@ Unit UComplex;
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|
carg_ch:=-cln(z+i*csqrt(1.0-z*z));
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|
|
end;
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|
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|
- function carg_sh (z : complex) : complex;
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|
+ function carg_sh (const z : complex) : complex;
|
|
|
{ hyperbolic arc sinus }
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|
|
{ ________ }
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|
|
{ argsh(z) = ln(z + V 1 + z.z) }
|
|
@@ -602,7 +601,7 @@ Unit UComplex;
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|
|
carg_sh:=cln(z+csqrt(z*z+1.0));
|
|
|
end;
|
|
|
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|
|
- function carg_th (z : complex) : complex;
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|
|
+ function carg_th (const z : complex) : complex;
|
|
|
{ hyperbolic arc tangent }
|
|
|
{ argth(z) = 1/2 ln((z + 1) / (1 - z)) }
|
|
|
begin
|
|
@@ -610,7 +609,7 @@ Unit UComplex;
|
|
|
end;
|
|
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|
|
{ functions to write out a complex value }
|
|
|
- function cstr(z : complex) : string;
|
|
|
+ function cstr(const z : complex) : string;
|
|
|
var
|
|
|
istr : string;
|
|
|
begin
|
|
@@ -624,7 +623,7 @@ Unit UComplex;
|
|
|
cstr:=cstr+'+'+istr+'i';
|
|
|
end;
|
|
|
|
|
|
- function cstr(z:complex;len : integer) : string;
|
|
|
+ function cstr(const z:complex;const len : integer) : string;
|
|
|
var
|
|
|
istr : string;
|
|
|
begin
|
|
@@ -638,7 +637,7 @@ Unit UComplex;
|
|
|
cstr:=cstr+'+'+istr+'i';
|
|
|
end;
|
|
|
|
|
|
- function cstr(z:complex;len,dec : integer) : string;
|
|
|
+ function cstr(const z:complex;const len,dec : integer) : string;
|
|
|
var
|
|
|
istr : string;
|
|
|
begin
|