immutable class CPX{T < $REAL_NUMBER{T}} < $CPX_NUMBER{T,CPX{T}} |
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**** | Complex numbers.
_ Some of the algorithms are taken from: Press, Flannery, Teukolsky, and Vettering, "Numerical Recipes in C", second edition, Cambridge University Press, 1993. _ Some of the choices of branch cut were chosen to be consistent with: Guy L. Steele, "Common Lisp, The Language", second edition, 1990, Digital Press. |
$CPX_NUMBER{_,_} | $NFE{_} | $IS_EQ | $STR | $NIL | $IS_NIL |
CPX | CPXD |
attr re,im:T; |
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**** | Real and imaginary parts. |
attr re,im:T; |
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**** | Real and imaginary parts. |
attr re,im:T; |
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**** | Real and imaginary parts. |
attr re,im:T; |
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**** | Real and imaginary parts. |
abs: SAME |
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**** | For conformance with $NFE |
abs_squared:T |
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**** | The square of the absolute magnitude of self. |
absolute:T |
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**** | The absolute magnitude of self. Cannot overload abs From Numerical Recipes in C, 2nd ed. p. 949. |
acos:SAME |
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**** | -i log(z + sqrt(1-z^2)) better to use: (pi/2)-asin(z) Steele p. 305.*** |
acosh:SAME |
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**** | log(z+(z+1)sqrt((z-1)/(z+1))) Steele p. 308*** |
asin:SAME |
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**** | -i log(iz + sqrt(1-z^2)) Steele p. 305.*** |
asinh:SAME |
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**** | log(z+sqrt(1+z^2)) Steele p. 308*** |
atan:SAME |
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**** | (log(1+i*y)-log(1-i*y))/(2*i) Steele p. 307.*** |
atanh:SAME |
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**** | log((1+z)sqrt(1/(1-z^2))) Steele p. 308*** |
cis(f:T):SAME |
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**** | Ignores self, e^i*f=cos f + i sin f . Steele p. 304. |
conjugate:SAME |
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**** | The complex conjugate of self. |
cos:SAME |
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cosh:SAME |
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**** | (e^z+e^(-z))/2 Steele p. 308*** |
create(f: FLT): SAME |
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create(f: FLTD): SAME |
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create(re,im:T):SAME |
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**** | A complex number with real part `re' and imaginary part `im'. |
create(i: INT): SAME |
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create_from_polar(mag,phase:T):SAME |
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**** | A complex number with magnitude `mag' and phase `phase'. |
create_real(x:T):SAME |
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cube:SAME |
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**** | Self cubed |
cube_root:SAME |
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**** | The cube root of self. preliminary, but working. |
div(c:SAME):SAME |
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**** | The ratio of self and `c'. From Numerical Recipes in C, 2nd ed. p. 949. |
div(f:T):SAME |
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**** | Self div the floating point f. |
exp:SAME |
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**** | The complex exponential `e^self'. |
is_eq(c: SAME): BOOL |
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**** | Return true if the two numbers are equal |
is_eq(arg: $OB): BOOL .. Included as is_eq |
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is_nil:BOOL |
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**** | Return true if self is nil |
is_within(r:T,c:SAME):BOOL |
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**** | self is within a circle around c with radius r |
log:SAME |
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**** | The complex logarithm. The chosen branch is `log |z| + i phase(z)'. Same convention as Steele, p. 302. |
magnitude:T |
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**** | The absolute magnitude of self. |
magnitude_squared:T |
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**** | The square of the absolute magnitude of self. |
maxval: SAME |
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**** | Maximum values of real and imaginary part |
minus(c:SAME):SAME |
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**** | The difference of self and `c'. |
negate:SAME |
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**** | The additive inverse of self. |
nil:SAME |
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**** | Return a nil valued complex number with real and imaginary parts both nil |
one: SAME |
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**** | A unit value (real part=1, imaginary part=0) |
phase:T |
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**** | The angle part of the polar represenation of self. `-pi < res <= pi'. Also get "-pi" from a negative real part and a "-0.0" imaginary part. They say 0+0i should be +0, 0-0i should be -0, -0+0i should be +pi, and -0-0i should be -pi. Same convention as Steele, p. 303. |
plus(c:SAME):SAME |
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**** | The sum of self and `c'. |
pow(c:SAME):SAME |
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**** | self^c = exp(c*log(self)) |
reciprocal:SAME |
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**** | The multiplicative inverse of self. |
sign:SAME |
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**** | If not zero, a number with same phase as self but unit magnitude. If it is, then returns self. Steele, p. 304*** |
sin:SAME |
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sinh:SAME |
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**** | (e^z-e^(-z))/2 Steele p. 308*** |
sqrt:SAME |
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**** | The square root of self. From Numerical Recipes in C, 2nd ed. p. 949. Steele, p. 302 chooses the branch cut by `e^((log z)/2)' |
square:SAME |
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**** | Self squared |
str:STR |
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**** | A string representation of self of the form "1.02+3.23i". |
tan:SAME |
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tanh:SAME |
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**** | (e^z-e^(-z))/(e^z+e^(-z)) Steele p. 308*** |
times(c:SAME):SAME |
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**** | The product of self and `c'. |
times(f:T):SAME |
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**** | Self times the floating point c. |
zero: SAME |
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**** | A zero valued complex number |