1math::rationalfunctions(n)           Math           math::rationalfunctions(n)
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5______________________________________________________________________________
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NAME

8       math::rationalfunctions - Polynomial functions
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SYNOPSIS

11       package require Tcl  ?8.4?
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13       package require math::rationalfunctions  ?1.0.1?
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15       ::math::rationalfunctions::rationalFunction num den
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17       ::math::rationalfunctions::ratioCmd num den
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19       ::math::rationalfunctions::evalRatio rational x
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21       ::math::rationalfunctions::addRatio ratio1 ratio2
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23       ::math::rationalfunctions::subRatio ratio1 ratio2
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25       ::math::rationalfunctions::multRatio ratio1 ratio2
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27       ::math::rationalfunctions::divRatio ratio1 ratio2
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29       ::math::rationalfunctions::derivPolyn ratio
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31       ::math::rationalfunctions::coeffsNumerator ratio
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33       ::math::rationalfunctions::coeffsDenominator ratio
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35______________________________________________________________________________
36

DESCRIPTION

38       This package deals with rational functions of one variable:
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40       ·      the  basic  arithmetic operations are extended to rational func‐
41              tions
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43       ·      computing the derivatives of these functions
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45       ·      evaluation through a general procedure or  via  specific  proce‐
46              dures)
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PROCEDURES

49       The package defines the following public procedures:
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51       ::math::rationalfunctions::rationalFunction num den
52              Return  an  (encoded) list that defines the rational function. A
53              rational function
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55
56                           1 + x^3
57                 f(x) = ------------
58                        1 + 2x + x^2
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60
61              can be defined via:
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64                 set f [::math::rationalfunctions::rationalFunction [list 1 0 0 1]  [list 1 2 1]]
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66
67              list num
68                     Coefficients of the numerator of  the  rational  function
69                     (in ascending order)
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71
72              list den
73                     Coefficients  of the denominator of the rational function
74                     (in ascending order)
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76
77       ::math::rationalfunctions::ratioCmd num den
78              Create a new procedure that evaluates the rational function. The
79              name  of  the function is automatically generated. Useful if you
80              need to evaluate the function many times, as the procedure  con‐
81              sists of a single [expr] command.
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83              list num
84                     Coefficients  of  the  numerator of the rational function
85                     (in ascending order)
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87
88              list den
89                     Coefficients of the denominator of the rational  function
90                     (in ascending order)
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92
93       ::math::rationalfunctions::evalRatio rational x
94              Evaluate the rational function at x.
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96              list rational
97                     The  rational  function's  definition (as returned by the
98                     rationalFunction command).  order)
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100              float x
101                     The coordinate at which to evaluate the function
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103
104       ::math::rationalfunctions::addRatio ratio1 ratio2
105              Return a new rational function which is the sum of the two  oth‐
106              ers.
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108              list ratio1
109                     The first rational function operand
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111              list ratio2
112                     The second rational function operand
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114
115       ::math::rationalfunctions::subRatio ratio1 ratio2
116              Return  a  new  rational function which is the difference of the
117              two others.
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119              list ratio1
120                     The first rational function operand
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122              list ratio2
123                     The second rational function operand
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126       ::math::rationalfunctions::multRatio ratio1 ratio2
127              Return a new rational function which is the product of  the  two
128              others.   If  one  of the arguments is a scalar value, the other
129              rational function is simply scaled.
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131              list ratio1
132                     The first rational function operand or a scalar
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134              list ratio2
135                     The second rational function operand or a scalar
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137
138       ::math::rationalfunctions::divRatio ratio1 ratio2
139              Divide the first rational function by the second rational  func‐
140              tion and return the result. The remainder is dropped
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142              list ratio1
143                     The first rational function operand
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145              list ratio2
146                     The second rational function operand
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148
149       ::math::rationalfunctions::derivPolyn ratio
150              Differentiate the rational function and return the result.
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152              list ratio
153                     The rational function to be differentiated
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155
156       ::math::rationalfunctions::coeffsNumerator ratio
157              Return  the  coefficients of the numerator of the rational func‐
158              tion.
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160              list ratio
161                     The rational function to be examined
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164       ::math::rationalfunctions::coeffsDenominator ratio
165              Return the coefficients of the denominator of the rational func‐
166              tion.
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168              list ratio
169                     The rational function to be examined
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171

REMARKS ON THE IMPLEMENTATION

173       The  implementation of the rational functions relies on the math::poly‐
174       nomials package. For further remarks  see  the  documentation  on  that
175       package.
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BUGS, IDEAS, FEEDBACK

178       This  document,  and the package it describes, will undoubtedly contain
179       bugs and other problems.  Please report such in the  category  math  ::
180       rationalfunctions         of         the         Tcllib        Trackers
181       [http://core.tcl.tk/tcllib/reportlist].  Please also report  any  ideas
182       for enhancements you may have for either package and/or documentation.
183
184       When proposing code changes, please provide unified diffs, i.e the out‐
185       put of diff -u.
186
187       Note further that  attachments  are  strongly  preferred  over  inlined
188       patches.  Attachments  can  be  made  by  going to the Edit form of the
189       ticket immediately after its creation, and  then  using  the  left-most
190       button in the secondary navigation bar.
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KEYWORDS

193       math, rational functions
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CATEGORY

196       Mathematics
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199       Copyright (c) 2005 Arjen Markus <arjenmarkus@users.sourceforge.net>
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204tcllib                               1.0.1          math::rationalfunctions(n)
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