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 # needs sage.rings.real_mpfr 1.234000000000000000000000000000000000000000000000000000000000000000000000000 sage: a.parent() # needs sage.rings.real_mpfr Real Field with 256 bits of precision sage: pari.set_real_precision(15) 70 sage: a = gen_to_sage(pari('1.234')); a # needs sage.rings.real_mpfr 1.23400000000000000 sage: a.parent() # needs sage.rings.real_mpfr 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 # needs sage.rings.number_field i + 3 sage: a.parent() # needs sage.rings.number_field 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 # needs sage.rings.number_field 1/2*i + 3/2 sage: a.parent() # needs sage.rings.number_field 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 # needs sage.rings.real_mpfr 1.00000000000000000 + 2.00000000000000000*I sage: a.parent() # needs sage.rings.real_mpfr 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 # needs sage.rings.real_mpfr 1.00000000000000000 + 1.00000000000000000*I sage: a.parent() # needs sage.rings.real_mpfr 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 # needs sage.rings.real_mpfr 1.00000000000000000 + 1.00000000000000000*I sage: a.parent() # needs sage.rings.real_mpfr 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: # needs sage.symbolic 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: # needs sage.rings.number_field sage.rings.real_mpfr 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: # needs sage.modules 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: # needs sage.rings.padics 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) <class 'str'>
- sage.libs.pari.convert_sage.new_gen_from_integer(self)#
- sage.libs.pari.convert_sage.new_gen_from_rational(self)#
- sage.libs.pari.convert_sage.pari_divisors_small(self)#
Return the list of divisors of this number using PARI
divisorsu
.See also
This method is better used through
sage.rings.integer.Integer.divisors()
.EXAMPLES:
sage: from sage.libs.pari.convert_sage import pari_divisors_small sage: pari_divisors_small(4) [1, 2, 4]
The integer must fit into an unsigned long:
sage: pari_divisors_small(-4) Traceback (most recent call last): ... AssertionError sage: pari_divisors_small(2**65) Traceback (most recent call last): ... AssertionError
- sage.libs.pari.convert_sage.pari_is_prime(p)#
Return whether
p
is a prime.The caller must ensure that
p.value
fits in a long.EXAMPLES:
sage: from sage.libs.pari.convert_sage import pari_is_prime sage: pari_is_prime(2) True sage: pari_is_prime(3) True sage: pari_is_prime(1) False sage: pari_is_prime(4) False
Its recommended to use
sage.rings.integer.Integer.is_prime()
, which checks overflow. The following is incorrect, because the number does not fit into a long:sage: pari_is_prime(2**64 + 2) True
- sage.libs.pari.convert_sage.pari_is_prime_power(q, get_data)#
Return whether
q
is a prime power.The caller must ensure that
q.value
fits in a long.OUTPUT:
If
get_data
return a tuple of the prime and the exponent. Otherwise return a boolean.EXAMPLES:
sage: from sage.libs.pari.convert_sage import pari_is_prime_power sage: pari_is_prime_power(2, False) True sage: pari_is_prime_power(2, True) (2, 1) sage: pari_is_prime_power(4, False) True sage: pari_is_prime_power(4, True) (2, 2) sage: pari_is_prime_power(6, False) False sage: pari_is_prime_power(6, True) (6, 0)
Its recommended to use
sage.rings.integer.Integer.is_prime_power()
, which checks overflow. The following is incorrect, because the number does not fit into a long:sage: pari_is_prime_power(2**64 + 2, False) True
- sage.libs.pari.convert_sage.pari_maxprime()#
Return to which limit PARI has computed the primes.
EXAMPLES:
sage: from sage.libs.pari.convert_sage import pari_maxprime sage: a = pari_maxprime() sage: res = prime_range(2, 2*a) sage: b = pari_maxprime() sage: b >= 2*a True
- sage.libs.pari.convert_sage.pari_prime_range(c_start, c_stop, py_ints=False)#
Return a list of all primes between
start
andstop - 1
, inclusive.See also
- sage.libs.pari.convert_sage.set_integer_from_gen(self, x)#
EXAMPLES:
sage: [Integer(pari(x)) for x in [1, 2^60, 2., GF(3)(1), GF(9,'a')(2)]] # needs sage.rings.finite_rings [1, 1152921504606846976, 2, 1, 2] sage: Integer(pari(2.1)) # indirect doctest Traceback (most recent call last): ... TypeError: Attempt to coerce non-integral real number to an Integer
- sage.libs.pari.convert_sage.set_rational_from_gen(self, x)#
EXAMPLES:
sage: [Rational(pari(x)) for x in [1, 1/2, 2^60, 2., GF(3)(1), GF(9,'a')(2)]] # needs sage.rings.finite_rings [1, 1/2, 1152921504606846976, 2, 1, 2] sage: Rational(pari(2.1)) # indirect doctest Traceback (most recent call last): ... TypeError: Attempt to coerce non-integral real number to an Integer