Interface to FriCAS#
Todo
some conversions in
sage.functionsare still missing and all should be checked and tested
FriCAS is a free GPL-compatible (modified BSD license) general purpose computer algebra system based on Axiom. The FriCAS website can be found at http://fricas.sourceforge.net/.
AUTHORS:
Mike Hansen (2009-02): Split off the FriCAS interface from the Axiom interface.
Martin Rubey, Bill Page (2016-08): Completely separate from Axiom, implement more complete translation from FriCAS to SageMath types.
EXAMPLES:
sage: fricas('3 * 5')
15
sage: a = fricas(3) * fricas(5); a
15
>>> from sage.all import *
>>> fricas('3 * 5')
15
>>> a = fricas(Integer(3)) * fricas(Integer(5)); a
15
The type of a is FriCASElement, i.e., an element of the
FriCAS interpreter:
sage: type(a)
<class 'sage.interfaces.fricas.FriCASElement'>
sage: a.parent()
FriCAS
>>> from sage.all import *
>>> type(a)
<class 'sage.interfaces.fricas.FriCASElement'>
>>> a.parent()
FriCAS
The underlying FriCAS type of a is also available, via the type method:
sage: a.typeOf()
PositiveInteger
>>> from sage.all import *
>>> a.typeOf()
PositiveInteger
FriCAS objects are normally displayed using “ASCII art”:
sage: fricas(2/3)
2
-
3
sage: fricas('x^2 + 3/7')
2 3
x + -
7
>>> from sage.all import *
>>> fricas(Integer(2)/Integer(3))
2
-
3
>>> fricas('x^2 + 3/7')
2 3
x + -
7
Functions defined in FriCAS are available as methods of the fricas object:
sage: F = fricas.factor('x^5 - y^5'); F
4 3 2 2 3 4
- (y - x)(y + x y + x y + x y + x )
sage: type(F)
<class 'sage.interfaces.fricas.FriCASElement'>
sage: F.typeOf()
Factored(Polynomial(Integer))
>>> from sage.all import *
>>> F = fricas.factor('x^5 - y^5'); F
4 3 2 2 3 4
- (y - x)(y + x y + x y + x y + x )
>>> type(F)
<class 'sage.interfaces.fricas.FriCASElement'>
>>> F.typeOf()
Factored(Polynomial(Integer))
We can also create a FriCAS polynomial and apply the function
factor from FriCAS. The notation f.factor() is consistent
with how the rest of SageMath works:
sage: f = fricas('x^5 - y^5')
sage: f^2
10 5 5 10
y - 2 x y + x
sage: f.factor()
4 3 2 2 3 4
- (y - x)(y + x y + x y + x y + x )
>>> from sage.all import *
>>> f = fricas('x^5 - y^5')
>>> f**Integer(2)
10 5 5 10
y - 2 x y + x
>>> f.factor()
4 3 2 2 3 4
- (y - x)(y + x y + x y + x y + x )
For many FriCAS types, translation to an appropriate SageMath type is available:
sage: f.factor().sage()
(y - x) * (y^4 + y^3*x + y^2*x^2 + y*x^3 + x^4)
>>> from sage.all import *
>>> f.factor().sage()
(y - x) * (y^4 + y^3*x + y^2*x^2 + y*x^3 + x^4)
Control-C interruption works well with the FriCAS interface. For example, try the following sum but with a much bigger range, and hit control-C:
sage: f = fricas('(x^5 - y^5)^10000') # not tested
Interrupting FriCAS...
...
KeyboardInterrupt: Ctrl-c pressed while running FriCAS
>>> from sage.all import *
>>> f = fricas('(x^5 - y^5)^10000') # not tested
Interrupting FriCAS...
...
KeyboardInterrupt: Ctrl-c pressed while running FriCAS
Let us demonstrate some features of FriCAS. FriCAS can guess a differential equation for the generating function for integer partitions:
sage: fricas("guessADE([partition n for n in 0..40], homogeneous==4)")
[
[
n
[x ]f(x):
2 3 (iv) 2 2 , 3 ,,,
x f(x) f (x) + (20 x f(x) f (x) + 5 x f(x) )f (x)
+
2 2 ,, 2
- 39 x f(x) f (x)
+
2 , 2 2 , 3 ,, 2 , 4
(12 x f(x)f (x) - 15 x f(x) f (x) + 4 f(x) )f (x) + 6 x f (x)
+
, 3 2 , 2
10 x f(x)f (x) - 16 f(x) f (x)
=
0
,
2 3 4
f(x) = 1 + x + 2 x + 3 x + O(x )]
]
>>> from sage.all import *
>>> fricas("guessADE([partition n for n in 0..40], homogeneous==4)")
[
[
n
[x ]f(x):
2 3 (iv) 2 2 , 3 ,,,
x f(x) f (x) + (20 x f(x) f (x) + 5 x f(x) )f (x)
<BLANKLINE>
+
2 2 ,, 2
- 39 x f(x) f (x)
<BLANKLINE>
+
2 , 2 2 , 3 ,, 2 , 4
(12 x f(x)f (x) - 15 x f(x) f (x) + 4 f(x) )f (x) + 6 x f (x)
<BLANKLINE>
+
, 3 2 , 2
10 x f(x)f (x) - 16 f(x) f (x)
<BLANKLINE>
=
0
,
2 3 4
f(x) = 1 + x + 2 x + 3 x + O(x )]
]
FriCAS can solve linear ordinary differential equations:
sage: fricas.set("y", "operator y")
sage: fricas.set("deq", "x^3*D(y x, x, 3) + x^2*D(y x, x, 2) - 2*x*D(y x, x) + 2*y x - 2*x^4")
sage: fricas.set("sol", "solve(deq, y, x)"); fricas("sol")
5 3 2
x - 10 x + 20 x + 4
[particular = ----------------------,
15 x
3 2 3 3 2
2 x - 3 x + 1 x - 1 x - 3 x - 1
basis = [---------------, ------, -------------]]
x x x
sage: fricas("sol.particular").sage()
1/15*(x^5 - 10*x^3 + 20*x^2 + 4)/x
sage: fricas("sol.basis").sage()
[(2*x^3 - 3*x^2 + 1)/x, (x^3 - 1)/x, (x^3 - 3*x^2 - 1)/x]
sage: fricas.eval(")clear values y deq sol")
''
>>> from sage.all import *
>>> fricas.set("y", "operator y")
>>> fricas.set("deq", "x^3*D(y x, x, 3) + x^2*D(y x, x, 2) - 2*x*D(y x, x) + 2*y x - 2*x^4")
>>> fricas.set("sol", "solve(deq, y, x)"); fricas("sol")
5 3 2
x - 10 x + 20 x + 4
[particular = ----------------------,
15 x
3 2 3 3 2
2 x - 3 x + 1 x - 1 x - 3 x - 1
basis = [---------------, ------, -------------]]
x x x
>>> fricas("sol.particular").sage()
1/15*(x^5 - 10*x^3 + 20*x^2 + 4)/x
>>> fricas("sol.basis").sage()
[(2*x^3 - 3*x^2 + 1)/x, (x^3 - 1)/x, (x^3 - 3*x^2 - 1)/x]
>>> fricas.eval(")clear values y deq sol")
''
FriCAS can expand expressions into series:
sage: x = var('x'); ex = sqrt(cos(x)); a = fricas(ex).series(x=0); a
1 2 1 4 19 6 559 8 29161 10 11
1 - - x - -- x - ---- x - ------ x - --------- x + O(x )
4 96 5760 645120 116121600
sage: a.coefficients()[38].sage()
-29472026335337227150423659490832640468979/274214482066329363682430667508979749984665600000000
sage: ex = sqrt(atan(x)); a = fricas(ex).series(x=0); a
1 5 9
- - -
2 1 2 31 2 6
x - - x + --- x + O(x )
6 360
sage: a.coefficient(9/2).sage()
31/360
sage: x = fricas("x::TaylorSeries Fraction Integer")
sage: y = fricas("y::TaylorSeries Fraction Integer")
sage: 2*(1+2*x+sqrt(1-4*x)-2*x*y).recip()
2 3 2 2 3 4 4 5
1 + (x y + x ) + 2 x + (x y + 2 x y + 6 x ) + (4 x y + 18 x )
+
3 3 4 2 5 6 5 2 6 7
(x y + 3 x y + 13 x y + 57 x ) + (6 x y + 40 x y + 186 x )
+
4 4 5 3 6 2 7 8
(x y + 4 x y + 21 x y + 130 x y + 622 x )
+
6 3 7 2 8 9
(8 x y + 66 x y + 432 x y + 2120 x )
+
5 5 6 4 7 3 8 2 9 10
(x y + 5 x y + 30 x y + 220 x y + 1466 x y + 7338 x ) + O(11)
>>> from sage.all import *
>>> x = var('x'); ex = sqrt(cos(x)); a = fricas(ex).series(x=Integer(0)); a
1 2 1 4 19 6 559 8 29161 10 11
1 - - x - -- x - ---- x - ------ x - --------- x + O(x )
4 96 5760 645120 116121600
>>> a.coefficients()[Integer(38)].sage()
-29472026335337227150423659490832640468979/274214482066329363682430667508979749984665600000000
>>> ex = sqrt(atan(x)); a = fricas(ex).series(x=Integer(0)); a
1 5 9
- - -
2 1 2 31 2 6
x - - x + --- x + O(x )
6 360
>>> a.coefficient(Integer(9)/Integer(2)).sage()
31/360
>>> x = fricas("x::TaylorSeries Fraction Integer")
>>> y = fricas("y::TaylorSeries Fraction Integer")
>>> Integer(2)*(Integer(1)+Integer(2)*x+sqrt(Integer(1)-Integer(4)*x)-Integer(2)*x*y).recip()
2 3 2 2 3 4 4 5
1 + (x y + x ) + 2 x + (x y + 2 x y + 6 x ) + (4 x y + 18 x )
+
3 3 4 2 5 6 5 2 6 7
(x y + 3 x y + 13 x y + 57 x ) + (6 x y + 40 x y + 186 x )
+
4 4 5 3 6 2 7 8
(x y + 4 x y + 21 x y + 130 x y + 622 x )
+
6 3 7 2 8 9
(8 x y + 66 x y + 432 x y + 2120 x )
+
5 5 6 4 7 3 8 2 9 10
(x y + 5 x y + 30 x y + 220 x y + 1466 x y + 7338 x ) + O(11)
FriCAS does some limits right:
sage: x = var('x'); ex = x^2*exp(-x)*Ei(x) - x; fricas(ex).limit(x=oo)
1
>>> from sage.all import *
>>> x = var('x'); ex = x**Integer(2)*exp(-x)*Ei(x) - x; fricas(ex).limit(x=oo)
1
- class sage.interfaces.fricas.FriCAS(name='fricas', command=None, script_subdirectory=None, logfile=None, server=None, server_tmpdir=None)[source]#
Bases:
ExtraTabCompletion,ExpectInterface to a FriCAS interpreter.
- console()[source]#
Spawn a new FriCAS command-line session.
EXAMPLES:
sage: fricas.console() # not tested FriCAS (AXIOM fork) Computer Algebra System Version: FriCAS 1.0.5 Timestamp: Thursday February 19, 2009 at 06:57:33 ----------------------------------------------------------------------------- Issue )copyright to view copyright notices. Issue )summary for a summary of useful system commands. Issue )quit to leave AXIOM and return to shell. -----------------------------------------------------------------------------
>>> from sage.all import * >>> fricas.console() # not tested FriCAS (AXIOM fork) Computer Algebra System Version: FriCAS 1.0.5 Timestamp: Thursday February 19, 2009 at 06:57:33 ----------------------------------------------------------------------------- Issue )copyright to view copyright notices. Issue )summary for a summary of useful system commands. Issue )quit to leave AXIOM and return to shell. -----------------------------------------------------------------------------
- eval(code, strip=True, synchronize=False, locals=None, allow_use_file=True, split_lines='nofile', reformat=True, **kwds)[source]#
Evaluate
codeusing FriCAS.Except
reformat, all arguments are passed tosage.interfaces.expect.Expect.eval().INPUT:
reformat– bool; remove the output markers when True.
This can also be used to pass system commands to FriCAS.
EXAMPLES:
sage: fricas.set("x", "1783"); fricas("x") 1783 sage: fricas.eval(")cl val x"); '' sage: fricas("x") x
>>> from sage.all import * >>> fricas.set("x", "1783"); fricas("x") 1783 >>> fricas.eval(")cl val x"); '' >>> fricas("x") x
- get(var)[source]#
Get the string representation of the value (more precisely, the OutputForm) of a variable or expression in FriCAS.
If FriCAS cannot evaluate \(var\) an error is raised.
EXAMPLES:
sage: fricas.set('xx', '2') sage: fricas.get('xx') '2' sage: a = fricas('(1 + sqrt(2))^5') sage: fricas.get(a.name()) ' +-+\n29 \\|2 + 41' sage: fricas.get('(1 + sqrt(2))^5') ' +-+\n29 \\|2 + 41' sage: fricas.new('(1 + sqrt(2))^5') +-+ 29 \|2 + 41
>>> from sage.all import * >>> fricas.set('xx', '2') >>> fricas.get('xx') '2' >>> a = fricas('(1 + sqrt(2))^5') >>> fricas.get(a.name()) ' +-+\n29 \\|2 + 41' >>> fricas.get('(1 + sqrt(2))^5') ' +-+\n29 \\|2 + 41' >>> fricas.new('(1 + sqrt(2))^5') +-+ 29 \|2 + 41
- get_boolean(var)[source]#
Return the value of a FriCAS boolean as a boolean, without checking that it is a boolean.
- get_integer(var)[source]#
Return the value of a FriCAS integer as an integer, without checking that it is an integer.
- get_string(var)[source]#
Return the value of a FriCAS string as a string, without checking that it is a string.
- get_unparsed_InputForm(var)[source]#
Return the unparsed
InputFormas a string.Todo
catch errors, especially when InputForm is not available:
for example when integration returns
"failed"UnivariatePolynomial
should we provide workarounds, too?
- set(var, value)[source]#
Set a variable to a value in FriCAS.
INPUT:
var,value: strings, the first representing a valid FriCAS variable identifier, the second a FriCAS expression.
OUTPUT: None
EXAMPLES:
sage: fricas.set('xx', '2') sage: fricas.get('xx') '2'
>>> from sage.all import * >>> fricas.set('xx', '2') >>> fricas.get('xx') '2'
- class sage.interfaces.fricas.FriCASElement(parent, value, is_name=False, name=None)[source]#
Bases:
ExpectElement,FriCASElementInstances of this class represent objects in FriCAS.
Using the method
sage()we can translate some of them to SageMath objects:- _sage_()[source]#
Convert
selfto a Sage object.EXAMPLES:
Floats:
sage: fricas(2.1234).sage() 2.12340000000000 sage: _.parent() Real Field with 53 bits of precision sage: a = RealField(100)(pi) sage: fricas(a).sage() 3.1415926535897932384626433833 sage: _.parent() Real Field with 100 bits of precision sage: fricas(a).sage() == a True sage: fricas(2.0).sage() 2.00000000000000 sage: _.parent() Real Field with 53 bits of precision
>>> from sage.all import * >>> fricas(RealNumber('2.1234')).sage() 2.12340000000000 >>> _.parent() Real Field with 53 bits of precision >>> a = RealField(Integer(100))(pi) >>> fricas(a).sage() 3.1415926535897932384626433833 >>> _.parent() Real Field with 100 bits of precision >>> fricas(a).sage() == a True >>> fricas(RealNumber('2.0')).sage() 2.00000000000000 >>> _.parent() Real Field with 53 bits of precision
Algebraic numbers:
sage: a = fricas('(1 + sqrt(2))^5'); a +-+ 29 \|2 + 41 sage: b = a.sage(); b 82.0121933088198? sage: b.radical_expression() 29*sqrt(2) + 41
>>> from sage.all import * >>> a = fricas('(1 + sqrt(2))^5'); a +-+ 29 \|2 + 41 >>> b = a.sage(); b 82.0121933088198? >>> b.radical_expression() 29*sqrt(2) + 41
Integers modulo n:
sage: fricas("((42^17)^1783)::IntegerMod(5^(5^5))").sage() == Integers(5^(5^5))((42^17)^1783) True
>>> from sage.all import * >>> fricas("((42^17)^1783)::IntegerMod(5^(5^5))").sage() == Integers(Integer(5)**(Integer(5)**Integer(5)))((Integer(42)**Integer(17))**Integer(1783)) True
Matrices over a prime field:
sage: fricas("matrix [[1::PF 3, 2],[2, 0]]").sage().parent() Full MatrixSpace of 2 by 2 dense matrices over Finite Field of size 3
>>> from sage.all import * >>> fricas("matrix [[1::PF 3, 2],[2, 0]]").sage().parent() Full MatrixSpace of 2 by 2 dense matrices over Finite Field of size 3
We can also convert FriCAS’s polynomials to Sage polynomials:
sage: a = fricas("x^2 + 1"); a.typeOf() Polynomial(Integer) sage: a.sage() x^2 + 1 sage: _.parent() Univariate Polynomial Ring in x over Integer Ring sage: fricas('x^2 + y^2 + 1/2').sage() y^2 + x^2 + 1/2 sage: _.parent() Multivariate Polynomial Ring in y, x over Rational Field sage: fricas("1$Polynomial Integer").sage() 1 sage: fricas("x^2/2").sage() 1/2*x^2 sage: x = polygen(QQ, 'x') sage: fricas(x+3).sage() x + 3 sage: fricas(x+3).domainOf() Polynomial(Integer...) sage: fricas(matrix([[2,3],[4,x+5]])).diagonal().sage() (2, x + 5) sage: f = fricas("(y^2+3)::UP(y, INT)").sage(); f y^2 + 3 sage: f.parent() Univariate Polynomial Ring in y over Integer Ring sage: fricas("(y^2+sqrt 3)::UP(y, AN)").sage() y^2 + 1.732050807568878?
>>> from sage.all import * >>> a = fricas("x^2 + 1"); a.typeOf() Polynomial(Integer) >>> a.sage() x^2 + 1 >>> _.parent() Univariate Polynomial Ring in x over Integer Ring >>> fricas('x^2 + y^2 + 1/2').sage() y^2 + x^2 + 1/2 >>> _.parent() Multivariate Polynomial Ring in y, x over Rational Field >>> fricas("1$Polynomial Integer").sage() 1 >>> fricas("x^2/2").sage() 1/2*x^2 >>> x = polygen(QQ, 'x') >>> fricas(x+Integer(3)).sage() x + 3 >>> fricas(x+Integer(3)).domainOf() Polynomial(Integer...) >>> fricas(matrix([[Integer(2),Integer(3)],[Integer(4),x+Integer(5)]])).diagonal().sage() (2, x + 5) >>> f = fricas("(y^2+3)::UP(y, INT)").sage(); f y^2 + 3 >>> f.parent() Univariate Polynomial Ring in y over Integer Ring >>> fricas("(y^2+sqrt 3)::UP(y, AN)").sage() y^2 + 1.732050807568878?
Rational functions:
sage: fricas("x^2 + 1/z").sage() x^2 + 1/z
>>> from sage.all import * >>> fricas("x^2 + 1/z").sage() x^2 + 1/z
Expressions:
sage: fricas(pi).sage() pi sage: fricas("sin(x+y)/exp(z)*log(1+%e)").sage() e^(-z)*log(e + 1)*sin(x + y) sage: fricas("factorial(n)").sage() factorial(n) sage: fricas("integrate(sin(x+y), x=0..1)").sage() -cos(y + 1) + cos(y) sage: fricas("integrate(x*sin(1/x), x=0..1)").sage() 'failed' sage: fricas("integrate(sin((x^2+1)/x),x)").sage() integral(sin((x^2 + 1)/x), x)
>>> from sage.all import * >>> fricas(pi).sage() pi >>> fricas("sin(x+y)/exp(z)*log(1+%e)").sage() e^(-z)*log(e + 1)*sin(x + y) >>> fricas("factorial(n)").sage() factorial(n) >>> fricas("integrate(sin(x+y), x=0..1)").sage() -cos(y + 1) + cos(y) >>> fricas("integrate(x*sin(1/x), x=0..1)").sage() 'failed' >>> fricas("integrate(sin((x^2+1)/x),x)").sage() integral(sin((x^2 + 1)/x), x)
Todo
Converting matrices and lists takes much too long.
Matrices:
sage: fricas("matrix [[x^n/2^m for n in 0..5] for m in 0..3]").sage() # long time [ 1 x x^2 x^3 x^4 x^5] [ 1/2 1/2*x 1/2*x^2 1/2*x^3 1/2*x^4 1/2*x^5] [ 1/4 1/4*x 1/4*x^2 1/4*x^3 1/4*x^4 1/4*x^5] [ 1/8 1/8*x 1/8*x^2 1/8*x^3 1/8*x^4 1/8*x^5]
>>> from sage.all import * >>> fricas("matrix [[x^n/2^m for n in 0..5] for m in 0..3]").sage() # long time [ 1 x x^2 x^3 x^4 x^5] [ 1/2 1/2*x 1/2*x^2 1/2*x^3 1/2*x^4 1/2*x^5] [ 1/4 1/4*x 1/4*x^2 1/4*x^3 1/4*x^4 1/4*x^5] [ 1/8 1/8*x 1/8*x^2 1/8*x^3 1/8*x^4 1/8*x^5]
Lists:
sage: fricas("[2^n/x^n for n in 0..5]").sage() # long time [1, 2/x, 4/x^2, 8/x^3, 16/x^4, 32/x^5] sage: fricas("[matrix [[i for i in 1..n]] for n in 0..5]").sage() # long time [[], [1], [1 2], [1 2 3], [1 2 3 4], [1 2 3 4 5]]
>>> from sage.all import * >>> fricas("[2^n/x^n for n in 0..5]").sage() # long time [1, 2/x, 4/x^2, 8/x^3, 16/x^4, 32/x^5] >>> fricas("[matrix [[i for i in 1..n]] for n in 0..5]").sage() # long time [[], [1], [1 2], [1 2 3], [1 2 3 4], [1 2 3 4 5]]
Error handling:
sage: s = fricas.guessPade("[fibonacci i for i in 0..10]"); s n x [[[x ]- ----------]] 2 x + x - 1 sage: s.sage() Traceback (most recent call last): ... NotImplementedError: the translation of the FriCAS Expression 'FEseries' to sage is not yet implemented sage: s = fricas("series(sqrt(1+x), x=0)"); s 1 1 2 1 3 5 4 7 5 21 6 33 7 429 8 1 + - x - - x + -- x - --- x + --- x - ---- x + ---- x - ----- x 2 8 16 128 256 1024 2048 32768 + 715 9 2431 10 11 ----- x - ------ x + O(x ) 65536 262144 sage: s.sage() Traceback (most recent call last): ... NotImplementedError: the translation of the FriCAS object 1 1 2 1 3 5 4 7 5 21 6 33 7 429 8 1 + - x - - x + -- x - --- x + --- x - ---- x + ---- x - ----- x 2 8 16 128 256 1024 2048 32768 + 715 9 2431 10 11 ----- x - ------ x + O(x ) 65536 262144 to sage is not yet implemented: An error occurred when FriCAS evaluated 'unparse(...::InputForm)': Cannot convert the value from type Any to InputForm .
>>> from sage.all import * >>> s = fricas.guessPade("[fibonacci i for i in 0..10]"); s n x [[[x ]- ----------]] 2 x + x - 1 >>> s.sage() Traceback (most recent call last): ... NotImplementedError: the translation of the FriCAS Expression 'FEseries' to sage is not yet implemented >>> s = fricas("series(sqrt(1+x), x=0)"); s 1 1 2 1 3 5 4 7 5 21 6 33 7 429 8 1 + - x - - x + -- x - --- x + --- x - ---- x + ---- x - ----- x 2 8 16 128 256 1024 2048 32768 + 715 9 2431 10 11 ----- x - ------ x + O(x ) 65536 262144 >>> s.sage() Traceback (most recent call last): ... NotImplementedError: the translation of the FriCAS object <BLANKLINE> 1 1 2 1 3 5 4 7 5 21 6 33 7 429 8 1 + - x - - x + -- x - --- x + --- x - ---- x + ---- x - ----- x 2 8 16 128 256 1024 2048 32768 + 715 9 2431 10 11 ----- x - ------ x + O(x ) 65536 262144 <BLANKLINE> to sage is not yet implemented: An error occurred when FriCAS evaluated 'unparse(...::InputForm)': <BLANKLINE> Cannot convert the value from type Any to InputForm .
- class sage.interfaces.fricas.FriCASExpectFunction(parent, name)[source]#
Bases:
ExpectFunctionTranslate the pythonized function identifier back to a FriCAS operation name.
- class sage.interfaces.fricas.FriCASFunctionElement(object, name)[source]#
Bases:
FunctionElementMake FriCAS operation names valid python function identifiers.
- sage.interfaces.fricas.fricas_console()[source]#
Spawn a new FriCAS command-line session.
EXAMPLES:
sage: fricas_console() # not tested FriCAS (AXIOM fork) Computer Algebra System Version: FriCAS 1.0.5 Timestamp: Thursday February 19, 2009 at 06:57:33 ----------------------------------------------------------------------------- Issue )copyright to view copyright notices. Issue )summary for a summary of useful system commands. Issue )quit to leave AXIOM and return to shell. -----------------------------------------------------------------------------
>>> from sage.all import * >>> fricas_console() # not tested FriCAS (AXIOM fork) Computer Algebra System Version: FriCAS 1.0.5 Timestamp: Thursday February 19, 2009 at 06:57:33 ----------------------------------------------------------------------------- Issue )copyright to view copyright notices. Issue )summary for a summary of useful system commands. Issue )quit to leave AXIOM and return to shell. -----------------------------------------------------------------------------
- sage.interfaces.fricas.is_FriCASElement(x)[source]#
Return
Trueifxis of typeFriCASElement.EXAMPLES:
sage: from sage.interfaces.fricas import is_FriCASElement sage: is_FriCASElement(2) doctest:...: DeprecationWarning: the function is_FriCASElement is deprecated; use isinstance(x, sage.interfaces.abc.FriCASElement) instead See https://github.com/sagemath/sage/issues/34804 for details. False sage: is_FriCASElement(fricas(2)) True
>>> from sage.all import * >>> from sage.interfaces.fricas import is_FriCASElement >>> is_FriCASElement(Integer(2)) doctest:...: DeprecationWarning: the function is_FriCASElement is deprecated; use isinstance(x, sage.interfaces.abc.FriCASElement) instead See https://github.com/sagemath/sage/issues/34804 for details. False >>> is_FriCASElement(fricas(Integer(2))) True
- sage.interfaces.fricas.reduce_load_fricas()[source]#
Return the FriCAS interface object defined in
sage.interfaces.fricas.EXAMPLES:
sage: from sage.interfaces.fricas import reduce_load_fricas sage: reduce_load_fricas() FriCAS
>>> from sage.all import * >>> from sage.interfaces.fricas import reduce_load_fricas >>> reduce_load_fricas() FriCAS