Fixed and Arbitrary Precision Numerical Fields - Sage

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Sage Reference Manual: Fixed and Arbitrary Precision Numerical Fields, Release 6.2sage: RDF.zeta(5)Traceback (most recent call last):...ValueError: No 5th root of unity in selfclass sage.rings.real_double.ToRDFBases: sage.categories.morphism.MorphismFast morphism from anything with a __float__ method to an RDF element.EXAMPLES:sage: f = RDF.coerce_map_from(ZZ); fNative morphism:From: Integer RingTo: Real Double Fieldsage: f(4)4.0sage: f = RDF.coerce_map_from(QQ); fNative morphism:From: Rational FieldTo: Real Double Fieldsage: f(1/2)0.5sage: f = RDF.coerce_map_from(int); fNative morphism:From: Set of Python objects of type ’int’To: Real Double Fieldsage: f(3r)3.0sage: f = RDF.coerce_map_from(float); fNative morphism:From: Set of Python objects of type ’float’To: Real Double Fieldsage: f(3.5)3.5sage.rings.real_double.is_RealDoubleElement(x)Check if x is an element of the real double field.EXAMPLE:sage: from sage.rings.real_double import is_RealDoubleElementsage: is_RealDoubleElement(RDF(3))Truesage: is_RealDoubleElement(RIF(3))Falsesage.rings.real_double.is_RealDoubleField(x)Returns True if x is the field of real double precision numbers.EXAMPLES:sage: from sage.rings.real_double import is_RealDoubleFieldsage: is_RealDoubleField(RDF)Truesage: is_RealDoubleField(RealField(53))Falsesage.rings.real_double.pool_stats()Statistics for the real double pool.22 Chapter 1. Double Precision Real Numbers
Sage Reference Manual: Fixed and Arbitrary Precision Numerical Fields, Release 6.2EXAMPLES:We first pull all elements from the pool (making sure it is empty to illustrate how the pool works):sage: from sage.rings.real_double import time_alloc_list, pool_statssage: L = time_alloc_list(50)sage: pool_stats()Used pool 0 / 0 timesPool contains 0 / 50 itemsDuring the operation (in this example, addition), we end up with two temporary elements. After completion ofthe operation, they are added to the pool:sage: RDF(2.1) + RDF(2.2)4.3sage: pool_stats()Used pool 0 / 0 timesPool contains 2 / 50 itemsNext when we call time_alloc_list(), the “created” elements are actually pulled from the pool:sage: time_alloc_list(3)[2.2, 2.1, 0.0]Note that the number of objects left in the pool depends on the garbage collector:sage: pool_stats()Used pool 0 / 0 timesPool contains 1 / 50 itemssage.rings.real_double.time_alloc(n)Allocate n RealDoubleElement instances.EXAMPLES:Since this does not store anything in a python object, the created elements will not be sent to the garbagecollector. Therefore they remain in the pool:sage: from sage.rings.real_double import time_alloc, pool_statssage: pool_stats()Used pool 0 / 0 timesPool contains 7 / 50 itemssage: time_alloc(25)sage: pool_stats()Used pool 0 / 0 timesPool contains 7 / 50 itemssage.rings.real_double.time_alloc_list(n)Allocate a list of length n of RealDoubleElement instances.EXAMPLES:During the operation (in this example, addition), we end up with two temporary elements. After completion ofthe operation, they are added to the pool:sage: from sage.rings.real_double import time_alloc_listsage: RDF(2.1) + RDF(2.2)4.3Next when we call time_alloc_list(), the “created” elements are actually pulled from the pool:23
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CHAPTERFOURFIELD OF ARBITRARY PRECI
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CHAPTERFIVEFILE:SAGE/RINGS/REAL_INT
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CHAPTERSIXTHESE CLASSES ARE VERY LA
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CHAPTERSEVENDOUBLE PRECISION COMPLE
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CHAPTERTHIRTEENINDICES AND TABLES
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PYTHON MODULE INDEXrsage.rings.comp
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INDEXAabs() (sage.rings.complex_dou
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Fixed and Arbitrary Precision Numerical Fields - Sage

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