Convert PARI objects to Sage types¶
-
sage.libs.pari.convert_sage.
gen_to_sage
(z, locals=None)¶ Convert a PARI gen to a Sage/Python object.
INPUT:
z
– PARIgen
locals
– optional dictionary used in fallback cases that involvesage_eval()
OUTPUT:
One of the following depending on the PARI type of
z
a
Integer
ifz
is an integer (typet_INT
)a
Rational
ifz
is a rational (typet_FRAC
)a
RealNumber
ifz
is a real number (typet_REAL
). The precision will be equivalent.a
NumberFieldElement_quadratic
or aComplexNumber
ifz
is a complex number (typet_COMPLEX
). The former is used when the real and imaginary parts are integers or rationals and the latter when they are floating point numbers. In that case The precision will be the maximal precision of the real and imaginary parts.a Python list if
z
is a vector or a list (typet_VEC
,t_COL
)a Python string if
z
is a string (typet_STR
)a Python list of Python integers if
z
is a small vector (typet_VECSMALL
)a matrix if
z
is a matrix (typet_MAT
)a padic element (type
t_PADIC
)a
Infinity
ifz
is an infinity (typet_INF
)
EXAMPLES:
sage: from sage.libs.pari.convert_sage import gen_to_sage
Converting an integer:
sage: z = pari('12'); z 12 sage: z.type() 't_INT' sage: a = gen_to_sage(z); a 12 sage: a.parent() Integer Ring sage: gen_to_sage(pari('7^42')) 311973482284542371301330321821976049
Converting a rational number:
sage: z = pari('389/17'); z 389/17 sage: z.type() 't_FRAC' sage: a = gen_to_sage(z); a 389/17 sage: a.parent() Rational Field sage: gen_to_sage(pari('5^30 / 3^50')) 931322574615478515625/717897987691852588770249
Converting a real number:
sage: pari.set_real_precision(70) 15 sage: z = pari('1.234'); z 1.234000000000000000000000000000000000000000000000000000000000000000000 sage: a = gen_to_sage(z); a 1.234000000000000000000000000000000000000000000000000000000000000000000000000 sage: a.parent() Real Field with 256 bits of precision sage: pari.set_real_precision(15) 70 sage: a = gen_to_sage(pari('1.234')); a 1.23400000000000000 sage: a.parent() Real Field with 64 bits of precision
For complex numbers, the parent depends on the PARI type:
sage: z = pari('(3+I)'); z 3 + I sage: z.type() 't_COMPLEX' sage: a = gen_to_sage(z); a i + 3 sage: a.parent() Number Field in i with defining polynomial x^2 + 1 with i = 1*I sage: z = pari('(3+I)/2'); z 3/2 + 1/2*I sage: a = gen_to_sage(z); a 1/2*i + 3/2 sage: a.parent() Number Field in i with defining polynomial x^2 + 1 with i = 1*I sage: z = pari('1.0 + 2.0*I'); z 1.00000000000000 + 2.00000000000000*I sage: a = gen_to_sage(z); a 1.00000000000000000 + 2.00000000000000000*I sage: a.parent() Complex Field with 64 bits of precision sage: z = pari('1 + 1.0*I'); z 1 + 1.00000000000000*I sage: a = gen_to_sage(z); a 1.00000000000000000 + 1.00000000000000000*I sage: a.parent() Complex Field with 64 bits of precision sage: z = pari('1.0 + 1*I'); z 1.00000000000000 + I sage: a = gen_to_sage(z); a 1.00000000000000000 + 1.00000000000000000*I sage: a.parent() Complex Field with 64 bits of precision
Converting polynomials:
sage: f = pari('(2/3)*x^3 + x - 5/7 + y') sage: f.type() 't_POL' sage: R.<x,y> = QQ[] sage: gen_to_sage(f, {'x': x, 'y': y}) 2/3*x^3 + x + y - 5/7 sage: parent(gen_to_sage(f, {'x': x, 'y': y})) Multivariate Polynomial Ring in x, y over Rational Field sage: x,y = SR.var('x,y') sage: gen_to_sage(f, {'x': x, 'y': y}) 2/3*x^3 + x + y - 5/7 sage: parent(gen_to_sage(f, {'x': x, 'y': y})) Symbolic Ring sage: gen_to_sage(f) Traceback (most recent call last): ... NameError: name 'x' is not defined
Converting vectors:
sage: z1 = pari('[-3, 2.1, 1+I]'); z1 [-3, 2.10000000000000, 1 + I] sage: z2 = pari('[1.0*I, [1,2]]~'); z2 [1.00000000000000*I, [1, 2]]~ sage: z1.type(), z2.type() ('t_VEC', 't_COL') sage: a1 = gen_to_sage(z1) sage: a2 = gen_to_sage(z2) sage: type(a1), type(a2) (<... 'list'>, <... 'list'>) sage: [parent(b) for b in a1] [Integer Ring, Real Field with 64 bits of precision, Number Field in i with defining polynomial x^2 + 1 with i = 1*I] sage: [parent(b) for b in a2] [Complex Field with 64 bits of precision, <... 'list'>] sage: z = pari('Vecsmall([1,2,3,4])') sage: z.type() 't_VECSMALL' sage: a = gen_to_sage(z); a [1, 2, 3, 4] sage: type(a) <... 'list'> sage: [parent(b) for b in a] [<... 'int'>, <... 'int'>, <... 'int'>, <... 'int'>]
Matrices:
sage: z = pari('[1,2;3,4]') sage: z.type() 't_MAT' sage: a = gen_to_sage(z); a [1 2] [3 4] sage: a.parent() Full MatrixSpace of 2 by 2 dense matrices over Integer Ring
Conversion of p-adics:
sage: z = pari('569 + O(7^8)'); z 2 + 4*7 + 4*7^2 + 7^3 + O(7^8) sage: a = gen_to_sage(z); a 2 + 4*7 + 4*7^2 + 7^3 + O(7^8) sage: a.parent() 7-adic Field with capped relative precision 8
Conversion of infinities:
sage: gen_to_sage(pari('oo')) +Infinity sage: gen_to_sage(pari('-oo')) -Infinity
Conversion of strings:
sage: s = pari('"foo"').sage(); s 'foo' sage: type(s) <type 'str'>