Abstract interface to Maxima¶

Maxima is a free GPL’d general purpose computer algebra system whose development started in 1968 at MIT. It contains symbolic manipulation algorithms, as well as implementations of special functions, including elliptic functions and generalized hypergeometric functions. Moreover, Maxima has implementations of many functions relating to the invariant theory of the symmetric group \(S_n\). (However, the commands for group invariants, and the corresponding Maxima documentation, are in French.) For many links to Maxima documentation see http://maxima.sourceforge.net/docs.shtml/.

AUTHORS:

William Stein (2005-12): Initial version
David Joyner: Improved documentation
William Stein (2006-01-08): Fixed bug in parsing
William Stein (2006-02-22): comparisons (following suggestion of David Joyner)
William Stein (2006-02-24): greatly improved robustness by adding sequence numbers to IO bracketing in _eval_line
Robert Bradshaw, Nils Bruin, Jean-Pierre Flori (2010,2011): Binary library interface

This is an abstract class implementing the functions shared between the Pexpect and library interfaces to Maxima.

class sage.interfaces.maxima_abstract.MaximaAbstract(name='maxima_abstract')[source]¶

Bases: ExtraTabCompletion, Interface

Abstract interface to Maxima.

INPUT:

name – string

OUTPUT: the interface

EXAMPLES:

This class should not be instantiated directly, but should be used through its subclass MaximaLib (which is a singleton), or through the Pexpect interface Maxima.

sage: from sage.interfaces.maxima_abstract import MaximaAbstract sage: from sage.interfaces.maxima_lib import maxima sage: isinstance(maxima, MaximaAbstract) True

completions(s, verbose=True)[source]¶

Return all commands that complete the command starting with the string s. This is like typing s[tab] in the Maxima interpreter.

INPUT:

s – string
verbose – boolean (default: True)

OUTPUT: array of strings

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: sorted(maxima.completions('gc', verbose=False))
['gc', 'gcd', 'gcdex', 'gcfactor', 'gctime']

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> sorted(maxima.completions('gc', verbose=False))
['gc', 'gcd', 'gcdex', 'gcfactor', 'gctime']

Sage Live

from sage.interfaces.maxima_lib import maxima
sorted(maxima.completions('gc', verbose=False))

console()[source]¶

Start the interactive Maxima console. This is a completely separate maxima session from this interface. To interact with this session, you should instead use maxima.interact().

OUTPUT: none

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima.console()             # not tested (since we can't)
Maxima 5.46.0 https://maxima.sourceforge.io
using Lisp ECL 21.2.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
This is a development version of Maxima. The function bug_report()
provides bug reporting information.
(%i1)

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima.console()             # not tested (since we can't)
Maxima 5.46.0 https://maxima.sourceforge.io
using Lisp ECL 21.2.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
This is a development version of Maxima. The function bug_report()
provides bug reporting information.
(%i1)

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima.console()             # not tested (since we can't)

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima.interact()     # not tested
  --> Switching to Maxima <--
maxima: 2+2
4
maxima:
  --> Exiting back to Sage <--

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima.interact()     # not tested
  --> Switching to Maxima <--
maxima: 2+2
4
maxima:
  --> Exiting back to Sage <--

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima.interact()     # not tested

cputime(t=None)[source]¶

Return the amount of CPU time that this Maxima session has used.

INPUT:

t – float (default: None); if var{t} is not None, then it returns the difference between the current CPU time and var{t}

OUTPUT: float

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: t = maxima.cputime()
sage: _ = maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'], [1,1,1])
sage: maxima.cputime(t) # output random
0.568913

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> t = maxima.cputime()
>>> _ = maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'], [Integer(1),Integer(1),Integer(1)])
>>> maxima.cputime(t) # output random
0.568913

Sage Live

from sage.interfaces.maxima_lib import maxima
t = maxima.cputime()
_ = maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'], [1,1,1])
maxima.cputime(t) # output random

de_solve(de, vars, ics=None)[source]¶

Solve a 1st or 2nd order ordinary differential equation (ODE) in two variables, possibly with initial conditions.

INPUT:

de – string representing the ODE
vars – list of strings representing the two variables
ics – a triple of numbers [a,b1,b2] representing y(a)=b1, y’(a)=b2

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'], [1,1,1])
y = 3*x-2*%e^(x-1)
sage: maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'])
y = %k1*%e^x+%k2*%e^-x+3*x
sage: maxima.de_solve('diff(y,x) + 3*x = y', ['x','y'])
y = (%c-3*(...-x...-1)*%e^-x)*%e^x
sage: maxima.de_solve('diff(y,x) + 3*x = y', ['x','y'],[1,1])
y = -...%e^-1*(5*%e^x-3*%e*x-3*%e)...

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'], [Integer(1),Integer(1),Integer(1)])
y = 3*x-2*%e^(x-1)
>>> maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'])
y = %k1*%e^x+%k2*%e^-x+3*x
>>> maxima.de_solve('diff(y,x) + 3*x = y', ['x','y'])
y = (%c-3*(...-x...-1)*%e^-x)*%e^x
>>> maxima.de_solve('diff(y,x) + 3*x = y', ['x','y'],[Integer(1),Integer(1)])
y = -...%e^-1*(5*%e^x-3*%e*x-3*%e)...

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'], [1,1,1])
maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'])
maxima.de_solve('diff(y,x) + 3*x = y', ['x','y'])
maxima.de_solve('diff(y,x) + 3*x = y', ['x','y'],[1,1])

de_solve_laplace(de, vars, ics=None)[source]¶

Solve an ordinary differential equation (ODE) using Laplace transforms.

INPUT:

de – string representing the ODE (e.g., de = “diff(f(x),x,2)=diff(f(x),x)+sin(x)”)
vars – list of strings representing the variables (e.g., vars = ["x","f"])
ics – list of numbers representing initial conditions, with symbols allowed which are represented by strings (eg, f(0)=1, f’(0)=2 is ics = [0,1,2])

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima.clear('x'); maxima.clear('f')
sage: maxima.de_solve_laplace("diff(f(x),x,2) = 2*diff(f(x),x)-f(x)", ["x","f"], [0,1,2])
f(x) = x*%e^x+%e^x

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima.clear('x'); maxima.clear('f')
>>> maxima.de_solve_laplace("diff(f(x),x,2) = 2*diff(f(x),x)-f(x)", ["x","f"], [Integer(0),Integer(1),Integer(2)])
f(x) = x*%e^x+%e^x

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima.clear('x'); maxima.clear('f')
maxima.de_solve_laplace("diff(f(x),x,2) = 2*diff(f(x),x)-f(x)", ["x","f"], [0,1,2])

Sage

sage: maxima.clear('x'); maxima.clear('f')
sage: f = maxima.de_solve_laplace("diff(f(x),x,2) = 2*diff(f(x),x)-f(x)", ["x","f"])
sage: f
f(x) = x*%e^x*('at('diff(f(x),x,1),x = 0))-f(0)*x*%e^x+f(0)*%e^x
sage: print(f)
                                   !
                       x  d        !                  x          x
            f(x) = x %e  (-- (f(x))!     ) - f(0) x %e  + f(0) %e
                          dx       !
                                   !x = 0

Python

>>> from sage.all import *
>>> maxima.clear('x'); maxima.clear('f')
>>> f = maxima.de_solve_laplace("diff(f(x),x,2) = 2*diff(f(x),x)-f(x)", ["x","f"])
>>> f
f(x) = x*%e^x*('at('diff(f(x),x,1),x = 0))-f(0)*x*%e^x+f(0)*%e^x
>>> print(f)
                                   !
                       x  d        !                  x          x
            f(x) = x %e  (-- (f(x))!     ) - f(0) x %e  + f(0) %e
                          dx       !
                                   !x = 0

Sage Live

maxima.clear('x'); maxima.clear('f')
f = maxima.de_solve_laplace("diff(f(x),x,2) = 2*diff(f(x),x)-f(x)", ["x","f"])
f
print(f)

Note

The second equation sets the values of \(f(0)\) and \(f'(0)\) in Maxima, so subsequent ODEs involving these variables will have these initial conditions automatically imposed.

demo(s)[source]¶

Run Maxima’s demo for s.

INPUT:

s – string

OUTPUT: none

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima.demo('cf') # not tested
read and interpret file: .../share/maxima/5.34.1/demo/cf.dem

At the '_' prompt, type ';' and <enter> to get next demonstration.
frac1:cf([1,2,3,4])
...

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima.demo('cf') # not tested
read and interpret file: .../share/maxima/5.34.1/demo/cf.dem

At the '_' prompt, type ';' and <enter> to get next demonstration.
frac1:cf([1,2,3,4])
...

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima.demo('cf') # not tested

describe(s)[source]¶: alias of help().

example(s)[source]¶

Return Maxima’s examples for s.

INPUT:

s – string

OUTPUT: Maxima’s examples for s

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima.example('arrays')
a[n]:=n*a[n-1]
                                a  := n a
                                 n       n - 1
a[0]:1
a[5]
                                      120
a[n]:=n
a[6]
                                       6
a[4]
                                      24
                                     done

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima.example('arrays')
a[n]:=n*a[n-1]
                                a  := n a
                                 n       n - 1
a[0]:1
a[5]
                                      120
a[n]:=n
a[6]
                                       6
a[4]
                                      24
                                     done

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima.example('arrays')

function(args, defn, rep=None, latex=None)[source]¶

Return the Maxima function with given arguments and definition.

INPUT:

args – string with variable names separated by commas
defn – string (or Maxima expression) that defines a function of the arguments in Maxima
rep – an optional string; if given, this is how the function will print

OUTPUT: Maxima function

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: f = maxima.function('x', 'sin(x)')
sage: f(3.2)  # abs tol 2e-16
-0.058374143427579909
sage: f = maxima.function('x,y', 'sin(x)+cos(y)')
sage: f(2, 3.5)  # abs tol 2e-16
sin(2)-0.9364566872907963
sage: f
sin(x)+cos(y)

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> f = maxima.function('x', 'sin(x)')
>>> f(RealNumber('3.2'))  # abs tol 2e-16
-0.058374143427579909
>>> f = maxima.function('x,y', 'sin(x)+cos(y)')
>>> f(Integer(2), RealNumber('3.5'))  # abs tol 2e-16
sin(2)-0.9364566872907963
>>> f
sin(x)+cos(y)

Sage Live

from sage.interfaces.maxima_lib import maxima
f = maxima.function('x', 'sin(x)')
f(3.2)  # abs tol 2e-16
f = maxima.function('x,y', 'sin(x)+cos(y)')
f(2, 3.5)  # abs tol 2e-16
f

Sage

sage: g = f.integrate('z')
sage: g
(cos(y)+sin(x))*z
sage: g(1,2,3)
3*(cos(2)+sin(1))

Python

>>> from sage.all import *
>>> g = f.integrate('z')
>>> g
(cos(y)+sin(x))*z
>>> g(Integer(1),Integer(2),Integer(3))
3*(cos(2)+sin(1))

Sage Live

g = f.integrate('z')
g
g(1,2,3)

The function definition can be a Maxima object:

Sage

sage: an_expr = maxima('sin(x)*gamma(x)')
sage: t = maxima.function('x', an_expr)
sage: t
gamma(x)*sin(x)
sage: t(2)
 sin(2)
sage: float(t(2))
0.9092974268256817
sage: loads(t.dumps())
gamma(x)*sin(x)

Python

>>> from sage.all import *
>>> an_expr = maxima('sin(x)*gamma(x)')
>>> t = maxima.function('x', an_expr)
>>> t
gamma(x)*sin(x)
>>> t(Integer(2))
 sin(2)
>>> float(t(Integer(2)))
0.9092974268256817
>>> loads(t.dumps())
gamma(x)*sin(x)

Sage Live

an_expr = maxima('sin(x)*gamma(x)')
t = maxima.function('x', an_expr)
t
t(2)
float(t(2))
loads(t.dumps())

help(s)[source]¶

Return Maxima’s help for s.

INPUT:

s – string

OUTPUT: Maxima’s help for s

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima.help('gcd')
-- Function: gcd (<p_1>, <p_2>, <x_1>, ...)
...

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima.help('gcd')
-- Function: gcd (<p_1>, <p_2>, <x_1>, ...)
...

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima.help('gcd')

plot2d(*args)[source]¶

Plot a 2d graph using Maxima / gnuplot.

maxima.plot2d(f, ‘[var, min, max]’, options)

INPUT:

f – string representing a function (such as f=”sin(x)”) [var, xmin, xmax]
options – an optional string representing plot2d options in gnuplot format

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima.plot2d('sin(x)','[x,-5,5]')   # not tested
sage: opts = '[gnuplot_term, ps], [gnuplot_out_file, "sin-plot.eps"]'
sage: maxima.plot2d('sin(x)','[x,-5,5]',opts)    # not tested

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima.plot2d('sin(x)','[x,-5,5]')   # not tested
>>> opts = '[gnuplot_term, ps], [gnuplot_out_file, "sin-plot.eps"]'
>>> maxima.plot2d('sin(x)','[x,-5,5]',opts)    # not tested

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima.plot2d('sin(x)','[x,-5,5]')   # not tested
opts = '[gnuplot_term, ps], [gnuplot_out_file, "sin-plot.eps"]'
maxima.plot2d('sin(x)','[x,-5,5]',opts)    # not tested

The eps file is saved in the current directory.

plot2d_parametric(r, var, trange, nticks=50, options=None)[source]¶

Plot r = [x(t), y(t)] for t = tmin…tmax using gnuplot with options.

INPUT:

r – string representing a function (such as r=”[x(t),y(t)]”)
var – string representing the variable (such as var = “t”)
trange – [tmin, tmax] are numbers with tmintmax
nticks – integer (default: 50)
options – an optional string representing plot2d options in gnuplot format

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima.plot2d_parametric(["sin(t)","cos(t)"], "t",[-3.1,3.1])   # not tested

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima.plot2d_parametric(["sin(t)","cos(t)"], "t",[-RealNumber('3.1'),RealNumber('3.1')])   # not tested

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima.plot2d_parametric(["sin(t)","cos(t)"], "t",[-3.1,3.1])   # not tested

Sage

sage: opts = '[gnuplot_preamble, "set nokey"], [gnuplot_term, ps], [gnuplot_out_file, "circle-plot.eps"]'
sage: maxima.plot2d_parametric(["sin(t)","cos(t)"], "t", [-3.1,3.1], options=opts)   # not tested

Python

>>> from sage.all import *
>>> opts = '[gnuplot_preamble, "set nokey"], [gnuplot_term, ps], [gnuplot_out_file, "circle-plot.eps"]'
>>> maxima.plot2d_parametric(["sin(t)","cos(t)"], "t", [-RealNumber('3.1'),RealNumber('3.1')], options=opts)   # not tested

Sage Live

opts = '[gnuplot_preamble, "set nokey"], [gnuplot_term, ps], [gnuplot_out_file, "circle-plot.eps"]'
maxima.plot2d_parametric(["sin(t)","cos(t)"], "t", [-3.1,3.1], options=opts)   # not tested

The eps file is saved to the current working directory.

Here is another fun plot:

Sage

sage: maxima.plot2d_parametric(["sin(5*t)","cos(11*t)"], "t", [0,2*pi()], nticks=400)    # not tested

Python

>>> from sage.all import *
>>> maxima.plot2d_parametric(["sin(5*t)","cos(11*t)"], "t", [Integer(0),Integer(2)*pi()], nticks=Integer(400))    # not tested

Sage Live

maxima.plot2d_parametric(["sin(5*t)","cos(11*t)"], "t", [0,2*pi()], nticks=400)    # not tested

plot3d(*args)[source]¶

Plot a 3d graph using Maxima / gnuplot.

maxima.plot3d(f, ‘[x, xmin, xmax]’, ‘[y, ymin, ymax]’, ‘[grid, nx, ny]’, options)

INPUT:

f – string representing a function (such as f=”sin(x)”) [var, min, max]
args should be of the form ‘[x, xmin, xmax]’, ‘[y, ymin, ymax]’, ‘[grid, nx, ny]’, options

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima.plot3d('1 + x^3 - y^2', '[x,-2,2]', '[y,-2,2]', '[grid,12,12]')    # not tested
sage: maxima.plot3d('sin(x)*cos(y)', '[x,-2,2]', '[y,-2,2]', '[grid,30,30]')   # not tested
sage: opts = '[gnuplot_term, ps], [gnuplot_out_file, "sin-plot.eps"]'
sage: maxima.plot3d('sin(x+y)', '[x,-5,5]', '[y,-1,1]', opts)    # not tested

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima.plot3d('1 + x^3 - y^2', '[x,-2,2]', '[y,-2,2]', '[grid,12,12]')    # not tested
>>> maxima.plot3d('sin(x)*cos(y)', '[x,-2,2]', '[y,-2,2]', '[grid,30,30]')   # not tested
>>> opts = '[gnuplot_term, ps], [gnuplot_out_file, "sin-plot.eps"]'
>>> maxima.plot3d('sin(x+y)', '[x,-5,5]', '[y,-1,1]', opts)    # not tested

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima.plot3d('1 + x^3 - y^2', '[x,-2,2]', '[y,-2,2]', '[grid,12,12]')    # not tested
maxima.plot3d('sin(x)*cos(y)', '[x,-2,2]', '[y,-2,2]', '[grid,30,30]')   # not tested
opts = '[gnuplot_term, ps], [gnuplot_out_file, "sin-plot.eps"]'
maxima.plot3d('sin(x+y)', '[x,-5,5]', '[y,-1,1]', opts)    # not tested

The eps file is saved in the current working directory.

plot3d_parametric(r, vars, urange, vrange, options=None)[source]¶

Plot a 3d parametric graph with r=(x,y,z), x = x(u,v), y = y(u,v), z = z(u,v), for u = umin…umax, v = vmin…vmax using gnuplot with options.

INPUT:

x, y, z – string representing a function (such as x="u2+v2", …) vars is a list or two strings representing variables (such as vars = [“u”,”v”])
urange – [umin, umax]
vrange – [vmin, vmax] are lists of numbers with umin umax, vmin vmax
options – (optional) string representing plot2d options in gnuplot format

OUTPUT: displays a plot on screen or saves to a file

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima.plot3d_parametric(["v*sin(u)","v*cos(u)","v"], ["u","v"],[-3.2,3.2],[0,3])     # not tested
sage: opts = '[gnuplot_term, ps], [gnuplot_out_file, "sin-cos-plot.eps"]'
sage: maxima.plot3d_parametric(["v*sin(u)","v*cos(u)","v"], ["u","v"],[-3.2,3.2],[0,3],opts)      # not tested

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima.plot3d_parametric(["v*sin(u)","v*cos(u)","v"], ["u","v"],[-RealNumber('3.2'),RealNumber('3.2')],[Integer(0),Integer(3)])     # not tested
>>> opts = '[gnuplot_term, ps], [gnuplot_out_file, "sin-cos-plot.eps"]'
>>> maxima.plot3d_parametric(["v*sin(u)","v*cos(u)","v"], ["u","v"],[-RealNumber('3.2'),RealNumber('3.2')],[Integer(0),Integer(3)],opts)      # not tested

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima.plot3d_parametric(["v*sin(u)","v*cos(u)","v"], ["u","v"],[-3.2,3.2],[0,3])     # not tested
opts = '[gnuplot_term, ps], [gnuplot_out_file, "sin-cos-plot.eps"]'
maxima.plot3d_parametric(["v*sin(u)","v*cos(u)","v"], ["u","v"],[-3.2,3.2],[0,3],opts)      # not tested

The eps file is saved in the current working directory.

Here is a torus:

Sage

sage: _ = maxima.eval("expr_1: cos(y)*(10.0+6*cos(x)); expr_2: sin(y)*(10.0+6*cos(x)); expr_3: -6*sin(x);")
sage: maxima.plot3d_parametric(["expr_1","expr_2","expr_3"], ["x","y"],[0,6],[0,6])  # not tested

Python

>>> from sage.all import *
>>> _ = maxima.eval("expr_1: cos(y)*(10.0+6*cos(x)); expr_2: sin(y)*(10.0+6*cos(x)); expr_3: -6*sin(x);")
>>> maxima.plot3d_parametric(["expr_1","expr_2","expr_3"], ["x","y"],[Integer(0),Integer(6)],[Integer(0),Integer(6)])  # not tested

Sage Live

_ = maxima.eval("expr_1: cos(y)*(10.0+6*cos(x)); expr_2: sin(y)*(10.0+6*cos(x)); expr_3: -6*sin(x);")
maxima.plot3d_parametric(["expr_1","expr_2","expr_3"], ["x","y"],[0,6],[0,6])  # not tested

Here is a Möbius strip:

Sage

sage: x = "cos(u)*(3 + v*cos(u/2))"
sage: y = "sin(u)*(3 + v*cos(u/2))"
sage: z = "v*sin(u/2)"
sage: maxima.plot3d_parametric([x,y,z],["u","v"],[-3.1,3.2],[-1/10,1/10])   # not tested

Python

>>> from sage.all import *
>>> x = "cos(u)*(3 + v*cos(u/2))"
>>> y = "sin(u)*(3 + v*cos(u/2))"
>>> z = "v*sin(u/2)"
>>> maxima.plot3d_parametric([x,y,z],["u","v"],[-RealNumber('3.1'),RealNumber('3.2')],[-Integer(1)/Integer(10),Integer(1)/Integer(10)])   # not tested

Sage Live

x = "cos(u)*(3 + v*cos(u/2))"
y = "sin(u)*(3 + v*cos(u/2))"
z = "v*sin(u/2)"
maxima.plot3d_parametric([x,y,z],["u","v"],[-3.1,3.2],[-1/10,1/10])   # not tested

plot_list(ptsx, ptsy, options=None)[source]¶

Plots a curve determined by a sequence of points.

INPUT:

ptsx – [x1,…,xn], where the xi and yi are real,
ptsy – [y1,…,yn]
options – string representing maxima plot2d options

The points are (x1,y1), (x2,y2), etc.

This function requires maxima 5.9.2 or newer.

Note

More that 150 points can sometimes lead to the program hanging. Why?

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: zeta_ptsx = [(pari(1/2 + i*I/10).zeta().real()).precision(1)          # needs sage.libs.pari
....:              for i in range(70,150)]
sage: zeta_ptsy = [(pari(1/2 + i*I/10).zeta().imag()).precision(1)          # needs sage.libs.pari
....:              for i in range(70,150)]
sage: maxima.plot_list(zeta_ptsx, zeta_ptsy)        # not tested            # needs sage.libs.pari
sage: opts='[gnuplot_preamble, "set nokey"], [gnuplot_term, ps], [gnuplot_out_file, "zeta.eps"]'
sage: maxima.plot_list(zeta_ptsx, zeta_ptsy, opts)  # not tested            # needs sage.libs.pari

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> zeta_ptsx = [(pari(Integer(1)/Integer(2) + i*I/Integer(10)).zeta().real()).precision(Integer(1))          # needs sage.libs.pari
...              for i in range(Integer(70),Integer(150))]
>>> zeta_ptsy = [(pari(Integer(1)/Integer(2) + i*I/Integer(10)).zeta().imag()).precision(Integer(1))          # needs sage.libs.pari
...              for i in range(Integer(70),Integer(150))]
>>> maxima.plot_list(zeta_ptsx, zeta_ptsy)        # not tested            # needs sage.libs.pari
>>> opts='[gnuplot_preamble, "set nokey"], [gnuplot_term, ps], [gnuplot_out_file, "zeta.eps"]'
>>> maxima.plot_list(zeta_ptsx, zeta_ptsy, opts)  # not tested            # needs sage.libs.pari

Sage Live

from sage.interfaces.maxima_lib import maxima
zeta_ptsx = [(pari(1/2 + i*I/10).zeta().real()).precision(1)          # needs sage.libs.pari
             for i in range(70,150)]
zeta_ptsy = [(pari(1/2 + i*I/10).zeta().imag()).precision(1)          # needs sage.libs.pari
             for i in range(70,150)]
maxima.plot_list(zeta_ptsx, zeta_ptsy)        # not tested            # needs sage.libs.pari
opts='[gnuplot_preamble, "set nokey"], [gnuplot_term, ps], [gnuplot_out_file, "zeta.eps"]'
maxima.plot_list(zeta_ptsx, zeta_ptsy, opts)  # not tested            # needs sage.libs.pari

plot_multilist(pts_list, options=None)[source]¶

Plots a list of list of points pts_list=[pts1,pts2,…,ptsn], where each ptsi is of the form [[x1,y1],…,[xn,yn]] x’s must be integers and y’s reals options is a string representing maxima plot2d options.

INPUT:

pts_lst – list of points; each point must be of the form [x,y] where x is an integer and y is a real
var – string; representing Maxima’s plot2d options

Requires maxima 5.9.2 at least.

Note

More that 150 points can sometimes lead to the program hanging.

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: xx = [i/10.0 for i in range(-10,10)]
sage: yy = [i/10.0 for i in range(-10,10)]
sage: x0 = [0 for i in range(-10,10)]
sage: y0 = [0 for i in range(-10,10)]
sage: zeta_ptsx1 = [(pari(1/2+i*I/10).zeta().real()).precision(1)           # needs sage.libs.pari
....:               for i in range(10)]
sage: zeta_ptsy1 = [(pari(1/2+i*I/10).zeta().imag()).precision(1)           # needs sage.libs.pari
....:               for i in range(10)]
sage: maxima.plot_multilist([[zeta_ptsx1,zeta_ptsy1], [xx,y0], [x0,yy]])    # not tested
sage: zeta_ptsx1 = [(pari(1/2+i*I/10).zeta().real()).precision(1)           # needs sage.libs.pari
....:               for i in range(10,150)]
sage: zeta_ptsy1 = [(pari(1/2+i*I/10).zeta().imag()).precision(1)           # needs sage.libs.pari
....:               for i in range(10,150)]
sage: maxima.plot_multilist([[zeta_ptsx1,zeta_ptsy1], [xx,y0], [x0,yy]])    # not tested
sage: opts='[gnuplot_preamble, "set nokey"]'
sage: maxima.plot_multilist([[zeta_ptsx1,zeta_ptsy1], [xx,y0], [x0,yy]],    # not tested
....:                       opts)

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> xx = [i/RealNumber('10.0') for i in range(-Integer(10),Integer(10))]
>>> yy = [i/RealNumber('10.0') for i in range(-Integer(10),Integer(10))]
>>> x0 = [Integer(0) for i in range(-Integer(10),Integer(10))]
>>> y0 = [Integer(0) for i in range(-Integer(10),Integer(10))]
>>> zeta_ptsx1 = [(pari(Integer(1)/Integer(2)+i*I/Integer(10)).zeta().real()).precision(Integer(1))           # needs sage.libs.pari
...               for i in range(Integer(10))]
>>> zeta_ptsy1 = [(pari(Integer(1)/Integer(2)+i*I/Integer(10)).zeta().imag()).precision(Integer(1))           # needs sage.libs.pari
...               for i in range(Integer(10))]
>>> maxima.plot_multilist([[zeta_ptsx1,zeta_ptsy1], [xx,y0], [x0,yy]])    # not tested
>>> zeta_ptsx1 = [(pari(Integer(1)/Integer(2)+i*I/Integer(10)).zeta().real()).precision(Integer(1))           # needs sage.libs.pari
...               for i in range(Integer(10),Integer(150))]
>>> zeta_ptsy1 = [(pari(Integer(1)/Integer(2)+i*I/Integer(10)).zeta().imag()).precision(Integer(1))           # needs sage.libs.pari
...               for i in range(Integer(10),Integer(150))]
>>> maxima.plot_multilist([[zeta_ptsx1,zeta_ptsy1], [xx,y0], [x0,yy]])    # not tested
>>> opts='[gnuplot_preamble, "set nokey"]'
>>> maxima.plot_multilist([[zeta_ptsx1,zeta_ptsy1], [xx,y0], [x0,yy]],    # not tested
...                       opts)

Sage Live

from sage.interfaces.maxima_lib import maxima
xx = [i/10.0 for i in range(-10,10)]
yy = [i/10.0 for i in range(-10,10)]
x0 = [0 for i in range(-10,10)]
y0 = [0 for i in range(-10,10)]
zeta_ptsx1 = [(pari(1/2+i*I/10).zeta().real()).precision(1)           # needs sage.libs.pari
              for i in range(10)]
zeta_ptsy1 = [(pari(1/2+i*I/10).zeta().imag()).precision(1)           # needs sage.libs.pari
              for i in range(10)]
maxima.plot_multilist([[zeta_ptsx1,zeta_ptsy1], [xx,y0], [x0,yy]])    # not tested
zeta_ptsx1 = [(pari(1/2+i*I/10).zeta().real()).precision(1)           # needs sage.libs.pari
              for i in range(10,150)]
zeta_ptsy1 = [(pari(1/2+i*I/10).zeta().imag()).precision(1)           # needs sage.libs.pari
              for i in range(10,150)]
maxima.plot_multilist([[zeta_ptsx1,zeta_ptsy1], [xx,y0], [x0,yy]])    # not tested
opts='[gnuplot_preamble, "set nokey"]'
maxima.plot_multilist([[zeta_ptsx1,zeta_ptsy1], [xx,y0], [x0,yy]],    # not tested
                      opts)

solve_linear(eqns, vars)[source]¶

Wraps maxima’s linsolve.

INPUT:

eqns – list of m strings; each representing a linear question in m = n variables
vars – list of n strings; each representing a variable

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: eqns = ["x + z = y","2*a*x - y = 2*a^2","y - 2*z = 2"]
sage: vars = ["x","y","z"]
sage: maxima.solve_linear(eqns, vars)
[x = a+1,y = 2*a,z = a-1]

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> eqns = ["x + z = y","2*a*x - y = 2*a^2","y - 2*z = 2"]
>>> vars = ["x","y","z"]
>>> maxima.solve_linear(eqns, vars)
[x = a+1,y = 2*a,z = a-1]

Sage Live

from sage.interfaces.maxima_lib import maxima
eqns = ["x + z = y","2*a*x - y = 2*a^2","y - 2*z = 2"]
vars = ["x","y","z"]
maxima.solve_linear(eqns, vars)

unit_quadratic_integer(n)[source]¶

Finds a unit of the ring of integers of the quadratic number field \(\QQ(\sqrt{n})\), \(n>1\), using the qunit maxima command.

INPUT:

n – integer

EXAMPLES:

Sage

sage: # needs sage.rings.number_field
sage: from sage.interfaces.maxima_lib import maxima
sage: u = maxima.unit_quadratic_integer(101); u
a + 10
sage: u.parent()
Number Field in a with defining polynomial x^2 - 101 with a = 10.04987562112089?
sage: u = maxima.unit_quadratic_integer(13)
sage: u
5*a + 18
sage: u.parent()
Number Field in a with defining polynomial x^2 - 13 with a = 3.605551275463990?

Python

>>> from sage.all import *
>>> # needs sage.rings.number_field
>>> from sage.interfaces.maxima_lib import maxima
>>> u = maxima.unit_quadratic_integer(Integer(101)); u
a + 10
>>> u.parent()
Number Field in a with defining polynomial x^2 - 101 with a = 10.04987562112089?
>>> u = maxima.unit_quadratic_integer(Integer(13))
>>> u
5*a + 18
>>> u.parent()
Number Field in a with defining polynomial x^2 - 13 with a = 3.605551275463990?

Sage Live

# needs sage.rings.number_field
from sage.interfaces.maxima_lib import maxima
u = maxima.unit_quadratic_integer(101); u
u.parent()
u = maxima.unit_quadratic_integer(13)
u
u.parent()

version()[source]¶

Return the version of Maxima that Sage includes.

OUTPUT: none

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima.version()  # random
'5.41.0'

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima.version()  # random
'5.41.0'

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima.version()  # random

class sage.interfaces.maxima_abstract.MaximaAbstractElement(parent, value, is_name=False, name=None)[source]¶

Bases: ExtraTabCompletion, InterfaceElement

Element of Maxima through an abstract interface.

EXAMPLES:

Elements of this class should not be created directly. The targeted parent of a concrete inherited class should be used instead:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: xp = maxima(x)
sage: type(xp)
<class 'sage.interfaces.maxima_lib.MaximaLibElement'>

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> xp = maxima(x)
>>> type(xp)
<class 'sage.interfaces.maxima_lib.MaximaLibElement'>

Sage Live

from sage.interfaces.maxima_lib import maxima
xp = maxima(x)
type(xp)

comma(args)[source]¶

Form the expression that would be written ‘self, args’ in Maxima.

INPUT:

args – string

OUTPUT: Maxima object

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima('sqrt(2) + I').comma('numer')
I+1.41421356237309...
sage: maxima('sqrt(2) + I*a').comma('a=5')
5*I+sqrt(2)

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima('sqrt(2) + I').comma('numer')
I+1.41421356237309...
>>> maxima('sqrt(2) + I*a').comma('a=5')
5*I+sqrt(2)

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima('sqrt(2) + I').comma('numer')
maxima('sqrt(2) + I*a').comma('a=5')

derivative(var='x', n=1)[source]¶: alias of diff().

diff(var='x', n=1)[source]¶

Return the \(n\)-th derivative of self.

INPUT:

var – variable (default: 'x')
n – integer (default: 1)

OUTPUT: \(n\)-th derivative of self with respect to the variable var

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: f = maxima('x^2')
sage: f.diff()
2*x
sage: f.diff('x')
2*x
sage: f.diff('x', 2)
2
sage: maxima('sin(x^2)').diff('x',4)
16*x^4*sin(x^2)-12*sin(x^2)-48*x^2*cos(x^2)

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> f = maxima('x^2')
>>> f.diff()
2*x
>>> f.diff('x')
2*x
>>> f.diff('x', Integer(2))
2
>>> maxima('sin(x^2)').diff('x',Integer(4))
16*x^4*sin(x^2)-12*sin(x^2)-48*x^2*cos(x^2)

Sage Live

from sage.interfaces.maxima_lib import maxima
f = maxima('x^2')
f.diff()
f.diff('x')
f.diff('x', 2)
maxima('sin(x^2)').diff('x',4)

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: f = maxima('x^3 + 17*y^2')
sage: f.diff('x')
3*x^2
sage: f.diff('y')
34*y

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> f = maxima('x^3 + 17*y^2')
>>> f.diff('x')
3*x^2
>>> f.diff('y')
34*y

Sage Live

from sage.interfaces.maxima_lib import maxima
f = maxima('x^3 + 17*y^2')
f.diff('x')
f.diff('y')

dot(other)[source]¶

Implement the notation self . other.

INPUT:

other – matrix; argument to dot

OUTPUT: Maxima matrix

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: A = maxima('matrix ([a1],[a2])')
sage: B = maxima('matrix ([b1, b2])')
sage: A.dot(B)
matrix([a1*b1,a1*b2],[a2*b1,a2*b2])

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> A = maxima('matrix ([a1],[a2])')
>>> B = maxima('matrix ([b1, b2])')
>>> A.dot(B)
matrix([a1*b1,a1*b2],[a2*b1,a2*b2])

Sage Live

from sage.interfaces.maxima_lib import maxima
A = maxima('matrix ([a1],[a2])')
B = maxima('matrix ([b1, b2])')
A.dot(B)

imag()[source]¶

Return the imaginary part of this Maxima element.

OUTPUT: Maxima real

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima('2 + (2/3)*%i').imag()
2/3

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima('2 + (2/3)*%i').imag()
2/3

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima('2 + (2/3)*%i').imag()

integral(var='x', min=None, max=None)[source]¶

Return the integral of self with respect to the variable \(x\).

INPUT:

var – variable
min – (default: None)
max – (default: None)

OUTPUT: the definite integral if xmin is not None

an indefinite integral otherwise

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima('x^2+1').integral()
x^3/3+x
sage: maxima('x^2+ 1 + y^2').integral('y')
y^3/3+x^2*y+y
sage: maxima('x / (x^2+1)').integral()
log(x^2+1)/2
sage: maxima('1/(x^2+1)').integral()
atan(x)
sage: maxima('1/(x^2+1)').integral('x', 0, infinity)
%pi/2
sage: maxima('x/(x^2+1)').integral('x', -1, 1)
0

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima('x^2+1').integral()
x^3/3+x
>>> maxima('x^2+ 1 + y^2').integral('y')
y^3/3+x^2*y+y
>>> maxima('x / (x^2+1)').integral()
log(x^2+1)/2
>>> maxima('1/(x^2+1)').integral()
atan(x)
>>> maxima('1/(x^2+1)').integral('x', Integer(0), infinity)
%pi/2
>>> maxima('x/(x^2+1)').integral('x', -Integer(1), Integer(1))
0

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima('x^2+1').integral()
maxima('x^2+ 1 + y^2').integral('y')
maxima('x / (x^2+1)').integral()
maxima('1/(x^2+1)').integral()
maxima('1/(x^2+1)').integral('x', 0, infinity)
maxima('x/(x^2+1)').integral('x', -1, 1)

Sage

sage: f = maxima('exp(x^2)').integral('x',0,1)
sage: f.sage()
-1/2*I*sqrt(pi)*erf(I)
sage: f.numer()
1.46265174590718...

Python

>>> from sage.all import *
>>> f = maxima('exp(x^2)').integral('x',Integer(0),Integer(1))
>>> f.sage()
-1/2*I*sqrt(pi)*erf(I)
>>> f.numer()
1.46265174590718...

Sage Live

f = maxima('exp(x^2)').integral('x',0,1)
f.sage()
f.numer()

integrate(var='x', min=None, max=None)[source]¶: alias of integral().

nintegral(var='x', a=0, b=1, desired_relative_error='1e-8', maximum_num_subintervals=200)[source]¶

Return a numerical approximation to the integral of self from \(a\) to \(b\).

INPUT:

var – variable to integrate with respect to
a – lower endpoint of integration
b – upper endpoint of integration
desired_relative_error – (default: '1e-8') the desired relative error
maximum_num_subintervals – (default: 200) maxima number of subintervals

OUTPUT: approximation to the integral

estimated absolute error of the approximation
the number of integrand evaluations
an error code:
- 0 – no problems were encountered
- 1 – too many subintervals were done
- 2 – excessive roundoff error
- 3 – extremely bad integrand behavior
- 4 – failed to converge
- 5 – integral is probably divergent or slowly convergent
- 6 – the input is invalid

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima('exp(-sqrt(x))').nintegral('x',0,1)
(0.5284822353142306, 4.163...e-11, 231, 0)

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima('exp(-sqrt(x))').nintegral('x',Integer(0),Integer(1))
(0.5284822353142306, 4.163...e-11, 231, 0)

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima('exp(-sqrt(x))').nintegral('x',0,1)

Note that GP also does numerical integration, and can do so to very high precision very quickly:

Sage

sage: # needs sage.libs.pari
sage: gp('intnum(x=0,1,exp(-sqrt(x)))')
0.52848223531423071361790491935415653022
sage: _ = gp.set_precision(80)
sage: gp('intnum(x=0,1,exp(-sqrt(x)))')
0.52848223531423071361790491935415653021675547587292866196865279321015401702040079

Python

>>> from sage.all import *
>>> # needs sage.libs.pari
>>> gp('intnum(x=0,1,exp(-sqrt(x)))')
0.52848223531423071361790491935415653022
>>> _ = gp.set_precision(Integer(80))
>>> gp('intnum(x=0,1,exp(-sqrt(x)))')
0.52848223531423071361790491935415653021675547587292866196865279321015401702040079

Sage Live

# needs sage.libs.pari
gp('intnum(x=0,1,exp(-sqrt(x)))')
_ = gp.set_precision(80)
gp('intnum(x=0,1,exp(-sqrt(x)))')

numer()[source]¶

Return numerical approximation to self as a Maxima object.

OUTPUT: Maxima object

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: a = maxima('sqrt(2)').numer(); a
1.41421356237309...
sage: type(a)
<class 'sage.interfaces.maxima_lib.MaximaLibElement'>

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> a = maxima('sqrt(2)').numer(); a
1.41421356237309...
>>> type(a)
<class 'sage.interfaces.maxima_lib.MaximaLibElement'>

Sage Live

from sage.interfaces.maxima_lib import maxima
a = maxima('sqrt(2)').numer(); a
type(a)

partial_fraction_decomposition(var='x')[source]¶

Return the partial fraction decomposition of self with respect to the variable var.

INPUT:

var – string

OUTPUT: Maxima object

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: f = maxima('1/((1+x)*(x-1))')
sage: f.partial_fraction_decomposition('x')
1/(2*(x-1))-1/(2*(x+1))
sage: print(f.partial_fraction_decomposition('x'))
                     1           1
                 --------- - ---------
                 2 (x - 1)   2 (x + 1)

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> f = maxima('1/((1+x)*(x-1))')
>>> f.partial_fraction_decomposition('x')
1/(2*(x-1))-1/(2*(x+1))
>>> print(f.partial_fraction_decomposition('x'))
                     1           1
                 --------- - ---------
                 2 (x - 1)   2 (x + 1)

Sage Live

from sage.interfaces.maxima_lib import maxima
f = maxima('1/((1+x)*(x-1))')
f.partial_fraction_decomposition('x')
print(f.partial_fraction_decomposition('x'))

real()[source]¶

Return the real part of this Maxima element.

OUTPUT: Maxima real

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima('2 + (2/3)*%i').real()
2

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima('2 + (2/3)*%i').real()
2

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima('2 + (2/3)*%i').real()

str()[source]¶

Return string representation of this Maxima object.

OUTPUT: string

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima('sqrt(2) + 1/3').str()
'sqrt(2)+1/3'

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima('sqrt(2) + 1/3').str()
'sqrt(2)+1/3'

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima('sqrt(2) + 1/3').str()

subst(val)[source]¶

Substitute a value or several values into this Maxima object.

INPUT:

val – string representing substitution(s) to perform

OUTPUT: Maxima object

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima('a^2 + 3*a + b').subst('b=2')
a^2+3*a+2
sage: maxima('a^2 + 3*a + b').subst('a=17')
b+340
sage: maxima('a^2 + 3*a + b').subst('a=17, b=2')
342

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima('a^2 + 3*a + b').subst('b=2')
a^2+3*a+2
>>> maxima('a^2 + 3*a + b').subst('a=17')
b+340
>>> maxima('a^2 + 3*a + b').subst('a=17, b=2')
342

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima('a^2 + 3*a + b').subst('b=2')
maxima('a^2 + 3*a + b').subst('a=17')
maxima('a^2 + 3*a + b').subst('a=17, b=2')

class sage.interfaces.maxima_abstract.MaximaAbstractElementFunction(parent, name, defn, args, latex)[source]¶

Bases: MaximaAbstractElement

Create a Maxima function with the parent parent, name name, definition defn, arguments args and latex representation latex.

INPUT:

parent – an instance of a concrete Maxima interface
name – string
defn – string
args – string; comma separated names of arguments
latex – string

OUTPUT: Maxima function

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: maxima.function('x,y','e^cos(x)')
e^cos(x)

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> maxima.function('x,y','e^cos(x)')
e^cos(x)

Sage Live

from sage.interfaces.maxima_lib import maxima
maxima.function('x,y','e^cos(x)')

arguments(split=True)[source]¶

Return the arguments of this Maxima function.

INPUT:

split – boolean; if True return a tuple of strings, otherwise return a string of comma-separated arguments

OUTPUT: string if split is False

a list of strings if split is True

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: f = maxima.function('x,y','sin(x+y)')
sage: f.arguments()
['x', 'y']
sage: f.arguments(split=False)
'x,y'
sage: f = maxima.function('', 'sin(x)')
sage: f.arguments()
[]

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> f = maxima.function('x,y','sin(x+y)')
>>> f.arguments()
['x', 'y']
>>> f.arguments(split=False)
'x,y'
>>> f = maxima.function('', 'sin(x)')
>>> f.arguments()
[]

Sage Live

from sage.interfaces.maxima_lib import maxima
f = maxima.function('x,y','sin(x+y)')
f.arguments()
f.arguments(split=False)
f = maxima.function('', 'sin(x)')
f.arguments()

definition()[source]¶

Return the definition of this Maxima function as a string.

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: f = maxima.function('x,y','sin(x+y)')
sage: f.definition()
'sin(x+y)'

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> f = maxima.function('x,y','sin(x+y)')
>>> f.definition()
'sin(x+y)'

Sage Live

from sage.interfaces.maxima_lib import maxima
f = maxima.function('x,y','sin(x+y)')
f.definition()

integral(var)[source]¶

Return the integral of self with respect to the variable var.

INPUT:

var – a variable

OUTPUT: Maxima function

Note that integrate is an alias of integral.

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: x,y = var('x,y')
sage: f = maxima.function('x','sin(x)')
sage: f.integral(x)
-cos(x)
sage: f.integral(y)
sin(x)*y

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> x,y = var('x,y')
>>> f = maxima.function('x','sin(x)')
>>> f.integral(x)
-cos(x)
>>> f.integral(y)
sin(x)*y

Sage Live

from sage.interfaces.maxima_lib import maxima
x,y = var('x,y')
f = maxima.function('x','sin(x)')
f.integral(x)
f.integral(y)

integrate(var)[source]¶: alias of integral().

sage.interfaces.maxima_abstract.maxima_console()[source]¶

Spawn a new Maxima command-line session.

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_abstract import maxima_console
sage: maxima_console()                    # not tested
Maxima 5.46.0 https://maxima.sourceforge.io
...

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_abstract import maxima_console
>>> maxima_console()                    # not tested
Maxima 5.46.0 https://maxima.sourceforge.io
...

Sage Live

from sage.interfaces.maxima_abstract import maxima_console
maxima_console()                    # not tested

sage.interfaces.maxima_abstract.maxima_version()[source]¶

Return Maxima version.

Currently this calls a new copy of Maxima.

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_abstract import maxima_version
sage: maxima_version()  # random
'5.41.0'

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_abstract import maxima_version
>>> maxima_version()  # random
'5.41.0'

Sage Live

from sage.interfaces.maxima_abstract import maxima_version
maxima_version()  # random

sage.interfaces.maxima_abstract.reduce_load_MaximaAbstract_function(parent, defn, args, latex)[source]¶

Unpickle a Maxima function.

EXAMPLES:

Sage

sage: from sage.interfaces.maxima_lib import maxima
sage: from sage.interfaces.maxima_abstract import reduce_load_MaximaAbstract_function
sage: f = maxima.function('x,y','sin(x+y)')
sage: _,args = f.__reduce__()
sage: g = reduce_load_MaximaAbstract_function(*args)
sage: g == f
True

Python

>>> from sage.all import *
>>> from sage.interfaces.maxima_lib import maxima
>>> from sage.interfaces.maxima_abstract import reduce_load_MaximaAbstract_function
>>> f = maxima.function('x,y','sin(x+y)')
>>> _,args = f.__reduce__()
>>> g = reduce_load_MaximaAbstract_function(*args)
>>> g == f
True

Sage Live

from sage.interfaces.maxima_lib import maxima
from sage.interfaces.maxima_abstract import reduce_load_MaximaAbstract_function
f = maxima.function('x,y','sin(x+y)')
_,args = f.__reduce__()
g = reduce_load_MaximaAbstract_function(*args)
g == f