Module: sage.functions.functions
SAGE Functions Class
Author Log:
Module-level Functions
var, defn, repr, latex, doc) |
s) |
Class: Function
self, [conversions=]) |
Functions: integral,
str
self, [bits=None]) |
Return a string representation of self as a decimal number to at least the given bits of precision.
Special Functions: __abs__,
__call__,
__cmp__,
__float__,
__init__,
__pow__,
_add_,
_axiom_init_,
_div_,
_gap_init_,
_interface_init_,
_kash_init_,
_maple_init_,
_mathematica_init_,
_maxima_init_,
_mpfr_,
_mul_,
_octave_init_,
_pari_init_,
_singular_init_,
_sub_
self, right) |
sage: s = e + pi sage: bool(s == 0) False sage: t = e^2 +pi sage: bool(s == t) False sage: bool(s == s) True sage: bool(t == t) True sage: bool(s < t) True sage: bool(t < s) False
self) |
Default init string for interfaces.
self) |
sage: s = singular(e); s 2.71828182845905
Class: Function_arith
sage: s = (pi + pi) * e + e sage: s 2*e*pi + e sage: RR(s) 19.7977502738062 sage: maxima(s) 2*%e*%pi+%e
sage: t = e^2 + pi + 2/3; t pi + e^2 + 2/3 sage: RR(t) 11.1973154191871 sage: maxima(t) %pi+%e^2+2/3 sage: t^e (pi + e^2 + 2/3)^e sage: RR(t^e) 710.865247688858
self, x, y, op) |
Special Functions: __init__,
_axiom_,
_call_,
_gap_init_,
_gp_,
_kash_,
_latex_,
_maple_,
_mathematica_,
_maxima_,
_maxima_init_,
_mpfr_,
_octave_,
_pari_,
_real_rqdf_,
_repr_,
_singular_init_
self) |
sage: gap(e + pi) pi + e
self, gp) |
sage: gp(e + pi) 5.859874482048838473822930855 # 32-bit 5.8598744820488384738229308546321653819 # 64-bit
self, kash) |
sage: kash(e + pi) # optional 5.85987448204883847382293085463
self) |
sage: latex(log2 * e + pi^2/2) {e \log \left( 2 \right)} + \frac{{\pi}^{2} }{2} sage: latex(NaN^3 + 1/golden_ratio) {\text{NaN}}^{3} + \frac{2}{\sqrt{ 5 } + 1} sage: latex(log2 + euler_gamma + catalan + khinchin + twinprime + merten + brun) \text{twinprime} + \text{merten} + \text{khinchin} + \gamma + \text{catalan} + \text{brun} + \log \left( 2 \right)
self, maple) |
sage: maple(e + pi) # optional exp(1)+Pi
self, mathematica) |
sage: mathematica(e + pi) # optional E + Pi
self, maxima) |
sage: maxima(e + pi) %pi+%e
self, R) |
sage: RealField(100)(e + pi) 5.8598744820488384738229308546
self, octave) |
sage: octave(e + pi) # optional 5.85987
self) |
sage: pari(e + pi) 5.859874482048838473822930855 # 32-bit 5.8598744820488384738229308546321653819 # 64-bit
self) |
sage: log2 * e + pi^2/2 e*log(2) + pi^2/2
self) |
sage: singular(e + pi) pi + e
Class: Function_at
self, f, x) |
Special Functions: __init__,
_maxima_init_,
_mpfr_,
_real_rqdf_,
_repr_
Class: Function_composition
self, f, g) |
Special Functions: __init__,
_axiom_,
_call_,
_latex_,
_mathematica_,
_maxima_,
_mpfr_,
_repr_
Class: Function_constant
self, x) |
Special Functions: __init__,
_call_,
_latex_,
_repr_
Class: Function_cos
sage: z = 1+2*I sage: theta = arg(z) sage: cos(theta)*abs(z) # slightly random output on cygwin 1.00000000000000 sage: cos(3.141592) -0.999999999999786
self) |
Functions: integral
Special Functions: __init__,
_call_,
_latex_,
_mpfr_,
_repr_
Class: Function_exp
self) |
Functions: integral
Special Functions: __init__,
_call_,
_latex_,
_mpfr_,
_repr_
Class: Function_gamma
self) |
Functions: integral
Special Functions: __init__,
_call_,
_latex_,
_mpfr_,
_repr_
Class: Function_gen
sage: a = pi/2 + e sage: a pi/2 + e sage: maxima(a) %pi/2+%e sage: RR(a) 4.28907815525394 sage: RealField(200)(a) 4.2890781552539418545916091629924139398558317933875124854544
sage: b = e + 5/7 sage: maxima(b) %e+5/7 sage: RR(b) 3.43256754274476
self, x) |
Functions: obj,
str
Special Functions: __init__,
_axiom_,
_gap_,
_gp_,
_kash_,
_latex_,
_maple_,
_mathematica_,
_maxima_,
_mpfr_,
_octave_,
_pari_,
_real_rqdf_,
_repr_,
_singular_
Class: Function_maxima
self, var, defn, repr, latex) |
Functions: integral
Special Functions: __init__,
_call_,
_latex_,
_mpfr_,
_repr_,
_x
Class: Function_polynomial
self, f) |
Special Functions: __init__,
_call_,
_latex_,
_repr_
Class: Function_sin
self) |
Functions: integral
Special Functions: __init__,
_call_,
_latex_,
_mpfr_,
_repr_
Class: Function_var
self, name) |
Special Functions: __init__,
_integral,
_latex_,
_mpfr_,
_repr_,
_subs
self, v) |
v dictionary function_var:object
Class: FunctionRing_class
self) |
Functions: characteristic,
default_precision,
set_precision
self) |
Get the precision of the default real field used for coercing functions.
self, prec) |
Change the precision of the default real field used for coercing functions.
sage: old_prec = FunctionRing.set_precision(200) sage: pi.str() '3.1415926535897932384626433832795028841971693993751058209749' sage: gap(pi) 3.1415926535897932384626433832795028841971693993751058209749 sage: _ = FunctionRing.set_precision(old_prec) sage: pi.str() '3.14159265358979'
Note that there seems to be no real numbers in GAP, which is why that coercion returns a GAP string.
The precision is only used when there is no way to describe the function to higher precision (or exactly) to the interface:
sage: maxima(pi) %pi
If we coerce into a GP/PARI session, then the resulting number will have precision the precision of that session irregardless of the default precision of FunctionRing. Note that GP/PARI precision is set in decimal digits, whereas in SAGE precisions are always in binary.
sage: gp = Gp() # new session so as not to affect overwrite global gp session sage: gp(pi) 3.141592653589793238462643383 # 32-bit 3.1415926535897932384626433832795028842 # 64-bit sage: gp.eval('\p 100') ' realprecision = 105 significant digits (100 digits displayed)' # 32-bit ' realprecision = 115 significant digits (100 digits displayed)' # 64-bit sage: gp(pi) 3.1415926535897932384626433832795028841971693993751058209749445923078164062 86208998628034825342117068 sage: _ = FunctionRing.set_precision(5) # has no affect on gp(pi) sage: gp(pi) 3.1415926535897932384626433832795028841971693993751058209749445923078164062 86208998628034825342117068 sage: _ = FunctionRing.set_precision(old_prec)
Special Functions: __call__,
__init__,
_coerce_impl,
_latex_,
_repr_
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