Fixed and Arbitrary Precision Numerical Fields - Sage

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Sage Reference Manual: Fixed and Arbitrary Precision Numerical Fields, Release 6.2rounding_mode()Return the rounding mode.EXAMPLES:sage: RR.rounding_mode()’RNDN’sage: RealField(20,rnd=’RNDZ’).rounding_mode()’RNDZ’sage: RealField(20,rnd=’RNDU’).rounding_mode()’RNDU’sage: RealField(20,rnd=’RNDD’).rounding_mode()’RNDD’scientific_notation(status=None)Set or return the scientific notation printing flag. If this flag is True then real numbers with this space asparent print using scientific notation.INPUT:•status – boolean optional flagEXAMPLES:sage: RR.scientific_notation()Falsesage: elt = RR(0.2512); elt0.251200000000000sage: RR.scientific_notation(True)sage: elt2.51200000000000e-1sage: RR.scientific_notation()Truesage: RR.scientific_notation(False)sage: elt0.251200000000000sage: R = RealField(20, sci_not=1)sage: R.scientific_notation()Truesage: R(0.2512)2.5120e-1to_prec(prec)Return the real field that is identical to self, except that it has the specified precision.EXAMPLES:sage: RR.to_prec(212)Real Field with 212 bits of precisionsage: R = RealField(30, rnd="RNDZ")sage: R.to_prec(300)Real Field with 300 bits of precision and rounding RNDZzeta(n=2)Return an n-th root of unity in the real field, if one exists, or raise a ValueError otherwise.EXAMPLES:sage: R = RealField()sage: R.zeta()-1.00000000000000sage: R.zeta(1)32 Chapter 2. Arbitrary Precision Real Numbers
Sage Reference Manual: Fixed and Arbitrary Precision Numerical Fields, Release 6.21.00000000000000sage: R.zeta(5)Traceback (most recent call last):...ValueError: No 5th root of unity in selfclass sage.rings.real_mpfr.RealLiteralBases: sage.rings.real_mpfr.RealNumberReal literals are created in preparsing and provide a way to allow casting into higher precision rings.baseliteralclass sage.rings.real_mpfr.RealNumberBases: sage.structure.element.RingElementA floating point approximation to a real number using any specified precision. Answers derived from calculationswith such approximations may differ from what they would be if those calculations were performed withtrue real numbers. This is due to the rounding errors inherent to finite precision calculations.The approximation is printed to slightly fewer digits than its internal precision, in order to avoid confusingroundoff issues that occur because numbers are stored internally in binary.agm(other)Return the arithmetic-geometric mean of self and other.The arithmetic-geometric mean is the common limit of the sequences u n and v n , where u 0 is self, v 0is other, u n+1 is the arithmetic mean of u n and v n , and v n+1 is the geometric mean of u n and v n . If anyoperand is negative, the return value is NaN.INPUT:•right – another real numberOUTPUT:•the AGM of self and otherEXAMPLES:sage: a = 1.5sage: b = 2.5sage: a.agm(b)1.96811775182478sage: RealField(200)(a).agm(b)1.9681177518247777389894630877503739489139488203685819712291sage: a.agm(100)28.1189391225320The AGM always lies between the geometric and arithmetic mean:sage: sqrt(a*b) < a.agm(b) < (a+b)/2TrueIt is, of course, symmetric:sage: b.agm(a)1.96811775182478and satisfies the relation AGM(ra, rb) = rAGM(a, b):33
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CHAPTERTHIRTEENINDICES AND TABLES
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PYTHON MODULE INDEXrsage.rings.comp
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Fixed and Arbitrary Precision Numerical Fields - Sage

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