70 lines
3.6 KiB
Plaintext
70 lines
3.6 KiB
Plaintext
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USING: help math math-internals ;
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HELP: complex f
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{ $description "The class of complex numbers with non-zero imaginary part." } ;
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HELP: real "( z -- x )"
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{ $values { "z" "a complex number" } { "x" "a real number" } }
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{ $description "Outputs the real part of a complex number. This acts as the identity on real numbers." }
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{ $notes "This word also acts as the class word for the class of real numbers, which is a disjoint union of rationals and floats." } ;
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HELP: imaginary "( z -- y )"
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{ $values { "z" "a complex number" } { "y" "a real number" } }
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{ $description "Outputs the imaginary part of a complex number. This outputs zero for real numbers." } ;
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HELP: (rect>) "( x y -- z )"
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{ $values { "x" "a real number" } { "y" "a real number" } { "z" "a complex number" } }
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{ $description "Creates a complex number from real and imaginary components." }
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{ $warning "This word does not check that the arguments are real numbers, which can have undefined consequences. Use the " { $link rect> } " word instead." } ;
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HELP: number f
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{ $description "The class of numbers." } ;
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HELP: rect> "( x y -- z )"
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{ $values { "x" "a real number" } { "y" "a real number" } { "z" "a complex number" } }
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{ $description "Creates a complex number from real and imaginary components." } ;
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HELP: >rect "( z -- x y )"
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{ $values { "z" "a complex number" } { "x" "a real number" } { "y" "a real number" } }
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{ $description "Extracts the real and imaginary components of a complex number." } ;
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HELP: conjugate "( z -- z* )"
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{ $values { "z" "a complex number" } { "z*" "a complex number" } }
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{ $description "Computes the complex conjugate by flipping the sign of the imaginary part of " { $snippet "z" } "." } ;
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HELP: arg "( z -- arg )"
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{ $values { "z" "a complex number" } { "arg" "a number in the interval " { $snippet "(-pi,pi]" } } }
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{ $description "Computes the complex argument." } ;
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HELP: >polar "( z -- abs arg )"
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{ $values { "z" "a complex number" } { "abs" "a non-negative real number" } { "arg" "a number in the interval " { $snippet "(-pi,pi]" } } }
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{ $description "Creates a complex number from an absolute value and argument (polar form)." } ;
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HELP: cis "( arg --- z )"
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{ $values { "arg" "a real number" } { "z" "a complex number on the unit circle" } }
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{ $description "Computes a point on the unit circle using Euler's formula for " { $snippet "exp(arg*i)" } "." }
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{ $see-also exp } ;
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HELP: polar> "( abs arg -- z )"
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{ $values { "z" "a complex number" } { "abs" "a non-negative real number" } { "arg" "a real number" } }
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{ $description "Converts an absolute value and argument (polar form) to a complex number." } ;
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HELP: quadrant "( z -- n )"
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{ $values { "z" "a complex number" } { "n" "0, 1, 2, or 3" } }
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{ $description "If the imaginary axis runs from bottom to top and the real axis runs from left to right, the quadrants of the complex plane run anti-clockwise starting from the positive real axis:" { $code "1|0" "---" "2|3" } } ;
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HELP: 2>rect "( x y -- xr xi yr yi )"
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{ $values { "x" "a complex number" } { "y" "a complex number" } { "xr" "real part of " { $snippet "x" } } { "xi" "imaginary part of " { $snippet "x" } } { "yr" "real part of " { $snippet "y" } } { "yi" "imaginary part of " { $snippet "y" } } }
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{ $description "Extracts real and imaginary components of two numbers at once." } ;
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HELP: complex/ "( x y -- r i m )"
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{ $values { "x" "a complex number" } { "y" "a complex number" } { "r" "a real number" } { "i" "a real number" } { "m" "a real number" } }
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{ $description
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"Complex division kernel. If we use the notation from " { $link 2>rect } ", this word computes:"
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{ $code
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"r = xr*yr+xi*yi"
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"i = xi*yr-xr*yi"
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"m = yr*yr+yi*yi"
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}
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} ;
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