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13.4 Interface to GP/Pari

Module: sage.interfaces.gp

Interface to GP/Pari

Type gp.[tab] for a list of all the functions available from your Gp install. Type gp.[tab]? for Gp's help about a given function. Type gp(...) to create a new Gp object, and gp.eval(...) to run a string using Gp (and get the result back as a string).

We illustrate objects that wrap GP objects (gp is the PARI interpreter): 

sage: M = gp('[1,2;3,4]')
sage: M
[1, 2; 3, 4]
sage: M * M
[7, 10; 15, 22]
sage: M + M
[2, 4; 6, 8]
sage: M.matdet()
-2


sage: E = gp.ellinit([1,2,3,4,5])
sage: E.ellglobalred()
[10351, [1, -1, 0, -1], 1]
sage: E.ellan(20)
[1, 1, 0, -1, -3, 0, -1, -3, -3, -3, -1, 0, 1, -1, 0, -1, 5, -3, 4, 3]


sage: primitive_root(7)
3
sage: x = gp("znlog( Mod(2,7), Mod(3,7))")
sage: 3^x % 7
2


sage: print gp("taylor(sin(x),x)")
x - 1/6*x^3 + 1/120*x^5 - 1/5040*x^7 + 1/362880*x^9 - 1/39916800*x^11 +
1/6227020800*x^13 - 1/1307674368000*x^15 + O(x^16)

GP has a powerful very efficient algorithm for numerical computation of integrals. 

sage: gp("a = intnum(x=0,6,sin(x))")
0.03982971334963397945434770208               # 32-bit
0.039829713349633979454347702077075594548     # 64-bit
sage: gp("a")
0.03982971334963397945434770208               # 32-bit
0.039829713349633979454347702077075594548     # 64-bit
sage: gp.kill("a")
sage: gp("a")
a

Note that gp ASCII plots do work in SAGE, as follows: 

sage: print gp.eval("plot(x=0,6,sin(x))")

0.9988963 |''''''''''''_x"...x_''''''''''''''''''''''''''''''''''''''''''|
          |          x"        "x                                        |
          |        _"            "_                                      |
          |       x                x                                     |
          |      "                  "                                    |
          |     "                    "                                   |
          |   _"                      "_                                 |
          |  _                          _                                |
          | _                            _                               |
          |_                              _                              |
          _,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
          |                                "                             |
          |                                 "                            |
          |                                  "                           |
          |                                   "                          "
          |                                    "_                      _"|
          |                                      _                    _  |
          |                                       _                  _   |
          |                                        x                x    |
          |                                         "_            _"     |
          |                                           x_        _x       |
-0.998955 |............................................."x____x".........|
          0                                                              6

The GP interface reads in even very long input (using files) in a robust manner, as long as you are creating a new object. 

sage: t = '"%s"'%10^10000   # ten thousand character string.
sage: a = gp.eval(t)            
sage: a = gp(t)

In SAGE, the PARI large galois groups datafiles should be installed by default: 

sage: f = gp('x^9 - x - 2')
sage: f.polgalois()
[362880, -1, 34, "S9"]

Author Log:

Module-level Functions

gp_console( )

gp_version( )

sage: gp.version()      # random output
((2, 3, 1), 'GP/PARI CALCULATOR Version 2.3.1 (0)')

is_GpElement( x)

reduce_load_GP( )

Class: Gp

class Gp
Interface to the PARI gp interpreter.

Type gp.[tab] for a list of all the functions available from your Gp install. Type gp.[tab]? for Gp's help about a given function. Type gp(...) to create a new Gp object, and gp.eval(...) to run a string using Gp (and get the result back as a string).

Gp( self, [stacksize=10000000], [maxread=100000], [script_subdirectory=None], [logfile=None], [server=None], [server_tmpdir=None], [init_list_length=1024])

Functions: console,$ $ get,$ $ get_precision,$ $ get_real_precision,$ $ help,$ $ kill,$ $ new_with_bits_prec,$ $ quit,$ $ read,$ $ set,$ $ set_precision,$ $ set_real_precision,$ $ trait_names,$ $ version

get( self, var)
Get the value of the variable var.

get_precision( self)
Return the current PARI precision for real number computations.

get_real_precision( self)
Return the current PARI precision for real number computations.

quit( self, [verbose=False], [timeout=0.25])

sage: a = gp('10'); a
10
sage: gp.quit()
sage: a
(invalid object -- defined in terms of closed session)
sage: gp(pi)
3.1415926535897932384626433832795028842    # 64-bit
3.141592653589793238462643383              # 32-bit

set( self, var, value)
Set the variable var to the given value.

set_precision( self, [prec=None])
Sets the current PARI precision (in decimal digits) for real number computations, and returns the old one.

set_real_precision( self, [prec=None])
Sets the current PARI precision (in decimal digits) for real number computations, and returns the old one.

Special Functions: __reduce__,$ $ _equality_symbol,$ $ _eval_line,$ $ _false_symbol,$ $ _next_var_name,$ $ _object_class,$ $ _quit_string,$ $ _read_in_file_command,$ $ _repr_,$ $ _true_symbol

Class: GpElement

class GpElement

This example illustrates dumping and loading GP elements to compressed strings. 

sage: a = gp(39393)
sage: loads(a.dumps()) == a
True

Since dumping and loading uses the string representation of the object, it need not result in an identical object from the point of view of PARI: 

sage: E = gp('ellinit([1,2,3,4,5])')
sage: loads(E.dumps()) == E
False
sage: loads(E.dumps())
[1, 2, 3, 4, 5, 9, 11, 29, 35, -183, -3429, -10351, 6128487/10351,
[-1.618909932267371342378000940, -0.3155450338663143288109995302 -
2.092547096911958607981689447*I, -0.3155450338663143288109995302 +
2.092547096911958607981689447*I]~, 2.780740013766729771063197627,
-1.390370006883364885531598814 + 1.068749776356193066159263547*I,
-1.554824121162190164275074561 + 3.415713103000000000000000000 E-29*I,
0.7774120605810950821375372806 - 1.727349756386839866714149879*I,
2.971915267817909670771647951] # 32-bit
[1, 2, 3, 4, 5, 9, 11, 29, 35, -183, -3429, -10351, 6128487/10351,
[-1.6189099322673713423780009396072169750,
-0.31554503386631432881099953019639151248 -
2.0925470969119586079816894466366945829*I,
-0.31554503386631432881099953019639151248 +
2.0925470969119586079816894466366945829*I]~,
2.7807400137667297710631976271813584994,
-1.3903700068833648855315988135906792497 +
1.0687497763561930661592635474375038788*I,
-1.5548241211621901642750745610982915039 +
7.9528267991764473360000000000000000000 E-39*I,
0.77741206058109508213753728054914575197 -
1.7273497563868398667141498789110695181*I,
2.9719152678179096707716479509361896060]  # 64-bit
sage: E
[1, 2, 3, 4, 5, 9, 11, 29, 35, -183, -3429, -10351, 6128487/10351,
[-1.618909932267371342378000940, -0.3155450338663143288109995302 -
2.092547096911958607981689447*I, -0.3155450338663143288109995302 +
2.092547096911958607981689447*I]~, 2.780740013766729771063197627,
-1.390370006883364885531598814 + 1.068749776356193066159263547*I,
-1.554824121162190164275074561 + 3.415713103 E-29*I,
0.7774120605810950821375372806 - 1.727349756386839866714149879*I,
2.971915267817909670771647951]   # 32-bit
[1, 2, 3, 4, 5, 9, 11, 29, 35, -183, -3429, -10351, 6128487/10351,
[-1.6189099322673713423780009396072169750,
-0.31554503386631432881099953019639151248 -
2.0925470969119586079816894466366945829*I,
-0.31554503386631432881099953019639151248 +
2.0925470969119586079816894466366945829*I]~,
2.7807400137667297710631976271813584994,
-1.3903700068833648855315988135906792497 +
1.0687497763561930661592635474375038788*I,
-1.5548241211621901642750745610982915039 + 7.952826799176447336 E-39*I,
0.77741206058109508213753728054914575197 -
1.7273497563868398667141498789110695181*I,
2.9719152678179096707716479509361896060]  # 64-bit

The two elliptic curves look the same, but internally the floating point numbers are slightly different.

Functions: trait_names

Special Functions: __bool__,$ $ __float__,$ $ __len__,$ $ __long__,$ $ _complex_mpfr_field_

__float__( self)
Return Python float.

__long__( self)
Return Python long.

_complex_mpfr_field_( self, CC)

sage: CC(gp(1+15*I))
 1.00000000000000 + 15.0000000000000*I
sage: CC(gp(11243.9812+15*I))
 11243.9812000000 + 15.0000000000000*I
sage: ComplexField(10)(gp(11243.9812+15*I))
 1.1e4 + 15.*I

Class: GpFunction

class GpFunction

Special Functions: _sage_doc_

Class: GpFunctionElement

class GpFunctionElement

Special Functions: _sage_doc_

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Release 2007.10.28, documentation updated on October 28, 2007.
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