iconEuler Reference

Output Formats

Output formats, and conversions to radians etc.

In general, Euler either sets an output format for all numbers of a specific type, or uses functions to print a value in some format. E.g., one can select fracformat or use printfrac.

Note that the default format for Euler is longformat with 12 digits of precision. Zero rounding is on so that very small numbers print as 0. Dense output is on. This prints row vectors in a very dense form with brackets.

function rad ()

  rad(d[,min,sec]) converts to radians
  
  rad(x) transfers degree x to radians. If min and sec are present,
  these will be used to set minutes and seconds of the angle.
  
  x° works too instead of rad(x).
  
  See: 
degprint (Output Formats)
function deg (x:real)

  deg(x) transfers radians x to degrees
  
  See: 
rad (Output Formats),
degprint (Output Formats)
function degprint (x : real scalar, dms:integer=1)

  Print radians x in degrees.
  
  This function returns a string with a representation of the radial
  angle x in degrees. By default, the function will print minutes and
  seconds. Turn this off with <dms.
  
  See: 
degformat (Output Formats)
function degformat (on:integer=1)

  Use degree format from now on.
  
  This calls _useformat with the degprint function.
  
  See: 
userformat (Euler Core),
degprint (Output Formats)
function polarprint (x:complex scalar, format="%g")

  Print x in polar form, if it is complex.
  
  Prints the complex number in the form (r,phi°). The format for r
  can be set with format="...".
  
  >load format; polarprint(1+I,format="%0.12g")
  (1.41421356237,45°)
  
  See: 
polarformat (Output Formats),
polar (Mathematical Functions),
polar (Maxima Documentation)
function polarformat (on:integer=1)

  Sets the format to polar form.
  
  See: 
userformat (Euler Core),
polarprint (Output Formats)

Intervals

function ipmprint (x:interval scalar)

  Print an interval using plus-minus notation.
  
  >ipmprint(~1,2~)
  1.5±0.5
  
  See: 
ipmformat (Output Formats)
function ipmformat (on:integer=1)

  Set the format to plus-minus notation
  
  See: 
ipmprint (Output Formats)
function print (x:real scalar, digits:integer=2, length:integer=10, ..
    unit:string="")

  Print the real number x formatted.
  
  The default format is two digits after the comma, and a total
  length of 10 digits. An optional unit can be added.
  
  Note that "x="+x is also a very nice way to print the variable x.
  Morever, "type x" will print the variable x. For units, there is
  the conversion operator ->.
  
  >print(101/891,unit="%")
  0.11%
  >2.5miles->" km"
  4.02336 km
  
  See: 
printf (Euler Core),
printf (Maxima Documentation)
function format 

  format(n,m) sets the output format to m digits and width n.
  
  Turns zero rounding and dense output off. Then calls the builtin
  function _format, which sets the output width to n places, and the
  precision digits to m.
  
  >format(6,2); (1:10)/3, longformat; // reset to default
  0.33  0.67  1.00  1.33  1.67  2.00  2.33  2.67  3.00  3.33
  >format(20,5); (1:4)'/3, longformat; // reset to default
  0.33333
  0.66667
  1.00000
  1.33333
  
  See: 
zerorounding (Euler Core),
denseoutput (Euler Core)
function goodformat 

  goodformat(n,m) sets the output format to m digits and width n.
  
  This turn zero rounding on and dense output on. Then it calls the
  builtin function _goodformat, which sets the width to m digits and
  the precession to n digits. The width will only be used for matrix
  output with more than one row due to the dense output format.
  
  The difference to format is that the output uses no decimal dot, if
  possible. Moreover, the dense output prints row vectors with
  brackets.
  
  >goodformat(6,2); (1:10)/3, longformat; // reset to default
  [ 0.33  0.67  1  1.3  1.7  2  2.3  2.7  3  3.3 ]
  >goodformat(6,2); (1:4)'/3, longformat; // reset to default
  0.33
  0.67
  1
  1.3
  
  See: 
zerorounding (Euler Core),
denseoutput (Euler Core)
function expformat 

  expformat(n,m) sets the output format to m digits and width n.
  
  Turns zero rounding off and dense output on. This works like
  format, but uses exponential output always. It calls the builtin
  function _expformat.
  
  >expformat(6,2); (1:10)/3, longformat; // reset to default
  [ 3.33e-001  6.67e-001  1.00e+000  1.33e+000  1.67e+000  2.00e+000
  2.33e+000  2.67e+000  3.00e+000  3.33e+000 ]
  
  See: 
zerorounding (Euler Core),
denseoutput (Euler Core)
function fixedformat 

  fixedformat(n,m) sets the output format to m digits and width n.
  
  This works like expformat, but always uses fixed point format. It
  calls the builtin function _fixedformat.
  
  Turns zero rounding on. Zero rounding is used to round very small
  numbers to 0.
  
  See: 
zerorounding (Euler Core),
denseoutput (Euler Core)
function longestformat 

  Sets a very long format for numbers.
  
  Turns zero rounding and dense output off. Uses a format, that
  allows to see the internal accuracy of IEEE double precision.
  
  See: 
zerorounding (Euler Core),
denseoutput (Euler Core)
function longformat 

  Sets a long format for numbers
  
  This is the default format for Euler with 12 digits precision.
  Turns zero rounding and dense output on, and uses a good format,
  which does not show a decimal dot if possible.
  
  See: 
goodformat (Output Formats)
function shortformat 

  Sets a short format for numbers.
  
  See: 
longformat (Output Formats)
function shortestformat 

  Sets a very short format for numbers.
  
  See: 
longformat (Output Formats)

Fractional

function fracformat (n:integer=0, eps=1e-10)

  Sets the fractional format.
  
  Turns zero rounding on. If n>0 it turns dense output off. A
  continued fraction is used to approximate the numbers with
  fractions. The accuracy can be set with eps.
  
  >fracformat; (1:10)/3, longformat;
  [ 1/3  2/3  1  4/3  5/3  2  7/3  8/3  3  10/3 ]
  >fracformat(10); (1:4)'/3, longformat;
  1/3
  2/3
  1
  4/3
  
function fracprint (x:numerical, n:integer=10, eps=1e-10)

  Prints x in fractional format with n places.
  
  Uses a temporary format to print a value in fractional format. The
  format is then reset to the default longformat.
  
  >fracprint(pi,eps=0.01)
  22/7
  
function frac (x:numerical, mixed:integer=0)

  Returns a string containing the fractional representation of x.
  
  This can be used to convert a number to a fraction contained in a
  string. If mixed, then the integer part is separated from the
  fractional part. The function uses the builtin function _frac to
  find a continued fraction, which approximates the number.
  
  The function can also be used for vectors and matrices to convert
  decimals into good fractions, e.g. for Maxima.
  
  >frac(2/3+5/4,>mixed)
  1+11/12
  
  >(1:4)/3; &%
  [0.33333333333333, 0.66666666666667, 1, 1.333333333333333]
  >frac((1:4)/3); &%
  1  2     4
  [-, -, 1, -]
  3  3     3
  
  See: 
fracformat (Output Formats)

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