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Calling Sequence
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ComplexBox( re, im )
ComplexBox( re )
ComplexBox( z )
ComplexBox( z, rr, ri )
ComplexBox( b )
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Parameters
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re
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-
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RealBox object; the real part of the complex box
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im
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-
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RealBox object; the imaginary part of the complex box
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z
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-
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complex constant (of type complexcons)
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rr, ri
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nonnegative real constants
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b
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-
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ComplexBox object
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precopt
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-
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(optional) equation of the form precision = n, where n is a positive integer
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Description
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A ComplexBox object represents a pair of RealBox objects comprising its real and complex parts.
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Creating Complex Boxes
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In this section we describe the construction of complex box objects.
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The simplest way to create a ComplexBox object is to pass a complex number to the ComplexBox object constructor.
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b := ComplexBox( 2.3 + 4.1*I );
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| (1) |
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type( b, ':-ComplexBox' );
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The real and imaginary parts of the resulting ComplexBox object are of type RealBox. You can access them by calling the Re and Im methods.
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type( Re( b ), ':-RealBox' );
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type( Im( b ), ':-RealBox' );
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You can optionally pass separate real and imaginary radii to add to the real and complex parts of the box. You can pass both rr and ri, or neither, but to avoid confusion you cannot pass just one.
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b := ComplexBox( 2.3 + 4.1*I, 0.1 );
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b := ComplexBox( 2.3 + 4.1*I, 0.1, 0.3 );
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| (5) |
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The second way to create a ComplexBox object is to pass the RealBox objects for its real and imaginary parts.
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b := ComplexBox( RealBox( 2.3, 0.1 ), RealBox( 7.77, 0.05 ) );
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type( b, ':-ComplexBox' );
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The imaginary part is optional:
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b := ComplexBox( RealBox( 2.3, 0.01 ) );
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type( b, ':-ComplexBox' );
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The resulting Complexbox object has a zero imaginary part.
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As for objects of type RealBox, a ComplexBox object is also of type BoxObject.
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type( b, ':-BoxObject' );
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Use the 'precision' = n option to control the precision used in these methods. For more details on precision, see BoxPrecision.
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Special Values and Constants
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The ComplexBox constructor recognizes several special values for which particular methods are invoked. These include the values , , , , and .
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In addition, the symbolic constant can be used and computed to high precision by using the precision= option.
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| (12) |
| (13) |
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ComplexBox( Pi, 'precision' = 1000 );
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| (14) |
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Elementary Functions
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The elementary functions that are available as methods for ComplexBox objects are listed as follows.
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Elementary
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abs
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compute the absolute value of a ComplexBox
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argument
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compute the argument of a ComplexBox
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csgn
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compute the sign of a ComplexBox
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exp
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compute the exponential of a ComplexBox
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expm1
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compute the exponential minus one of a ComplexBox
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expPiI
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compute the exponential of PiI times a ComplexBox
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Im
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compute the imaginary part of a ComplexBox
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log
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compute the logarithm of a ComplexBox
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log1p
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compute the logarithm of a ComplexBox minus one
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Re
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compute the real part of a ComplexBox
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rsqrt
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compute the reciprocal square root of a ComplexBox
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signum
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compute the signum of a ComplexBox
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sqrt
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compute the square root of a ComplexBox
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Circular and Hyperbolic Functions
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Most of the standard circular and hyperbolic functions have been provided as ComplexBox object methods. Those defined are listed below.
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Circular
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arccos
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compute the inverse cosine of a ComplexBox
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arccot
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compute the inverse cotangent of a ComplexBox
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arccsc
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compute the inverse cosecant of a ComplexBox
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arcsec
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compute the inverse secant of a ComplexBox
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arcsin
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compute the inverse sine of a ComplexBox
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arctan
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compute the inverse tangent of a ComplexBox
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cos
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compute the cosine of a ComplexBox
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cospi
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compute the cosine of a ComplexBox times Pi
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cot
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compute the cotangent of a ComplexBox
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cotpi
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compute the cotangent of a ComplexBox times Pi
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csc
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compute the cosecant of a ComplexBox
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sec
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compute the secant of a ComplexBox
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sin
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compute the sine of a ComplexBox
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sinc
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compute the sinc of a ComplexBox
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sincpi
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compute the sinc of a ComplexBox times Pi
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sinpi
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compute the sine of a ComplexBox times Pi
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tan
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compute the tangent of a ComplexBox
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tanpi
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compute the tangent of a ComplexBox times Pi
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Hyperbolic
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arccosh
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compute the inverse hyperbolic cosine of a ComplexBox
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arcsinh
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compute the inverse hyperbolic sine of a ComplexBox
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arctanh
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compute the inverse hyperbolic tangent of a ComplexBox
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cosh
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compute the hyperbolic cosine of a ComplexBox
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coth
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compute the hyperbolic cotangent of a ComplexBox
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csch
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compute the hyperbolic cosecant of a ComplexBox
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sech
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compute the hyperbolic secant of a ComplexBox
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sinh
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compute the hyperbolic sine of a ComplexBox
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sinhcosh
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compute the hyperbolic sine and hyperbolic cosine of a ComplexBox
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tanh
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compute the hyperbolic tangent of a ComplexBox
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Special Functions
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Many special and hypergeometric functions are available as ComplexBox object methods, as listed here:
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Special
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BesselI
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compute the Bessel I function of a ComplexBox
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BesselJ
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compute the Bessel J function of a ComplexBox
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BesselK
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compute the Bessel K function of a ComplexBox
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BesselY
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compute the Bessel Y function of a ComplexBox
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ChebyshevT
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compute the Chebyshev T function of a ComplexBox
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ChebyshevU
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compute the Chebyshev U function of a ComplexBox
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Chi
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compute the hyperbolic cosine integral of a ComplexBox
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Ci
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compute the cosine integral of a ComplexBox
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dilog
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compute the dilogarithm of a ComplexBox
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Ei
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compute the exponential integral of a ComplexBox
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GAMMA
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compute the GAMMA function of a ComplexBox
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HermiteH
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compute the Hermite H function of a ComplexBox
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hypergeom
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general hypergeometric function of a ComplexBox
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KummerU
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Kummer U function of a ComplexBox
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LegendreP
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Legendre P function of a ComplexBox
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LegendreQ
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Legendre Q function of a ComplexBox
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Li
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compute the logarithmic integral of a ComplexBox
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lnGAMMA
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compute the log-GAMMA function of a ComplexBox
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Psi
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compute the digamma function of a ComplexBox
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rGAMMA
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compute the reciprocal GAMMA function of a ComplexBox
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Shi
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compute the hyperbolic sine integral of a ComplexBox
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Si
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compute the sine integral of a ComplexBox
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Zeta
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compute the Riemann zeta function of a ComplexBox
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Compatibility
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The ComplexBox command was introduced in Maple 2022.
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