21819: Rewrite error functions and documentation

sagemath · Apr 11, 2017 · b56829c · b56829c
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Showing 8 changed files with 545 additions and 262 deletions.
diff --git a/src/doc/en/reference/functions/index.rst b/src/doc/en/reference/functions/index.rst
@@ -8,6 +8,7 @@ Functions
    sage/functions/trig
    sage/functions/hyperbolic
    sage/functions/transcendental
+   sage/functions/error
    sage/functions/piecewise
    sage/functions/spike_function
    sage/functions/orthogonal_polys

diff --git a/src/doc/en/reference/references/index.rst b/src/doc/en/reference/references/index.rst
@@ -539,6 +539,10 @@ REFERENCES:
                  Functions, in NIST Digital Library of Mathematical
                  Functions. http://dlmf.nist.gov/10
 
+.. [DLMF-Error] \N. M. Temme: 7. Error Functions, Dawson’s and Fresnel
+                 Integrals, in NIST Digital Library of Mathematical
+                 Functions. http://dlmf.nist.gov/7
+
 .. [DLMF-Struve] \R. B. Paris: 11. Struve and Related Functions, in
                  NIST Digital Library of Mathematical
                  Functions. http://dlmf.nist.gov/11
@@ -1630,6 +1634,8 @@ REFERENCES:
 
 .. [WP-Bessel] :wikipedia:`Bessel_function`
 
+.. [WP-Error] :wikipedia:`Error_function`
+
 .. [WP-Struve] :wikipedia:`Struve_function`
 
 .. _ref-X:

diff --git a/src/sage/functions/all.py b/src/sage/functions/all.py
@@ -4,6 +4,8 @@
 
 lazy_import('sage.functions.piecewise_old', 'Piecewise')   # deprecated
 lazy_import('sage.functions.piecewise', 'piecewise')
+lazy_import('sage.functions.error', ['erf', 'erfi', 'erfc',
+                                     'erfinv', 'error_fcn'])
 
 from .trig import ( sin, cos, sec, csc, cot, tan,
                    asin, acos, atan,
@@ -21,7 +23,7 @@
 
 
 from .other import ( ceil, floor, gamma, psi, factorial, beta, binomial,
-                    abs_symbolic, erf, sqrt, log_gamma,
+                    abs_symbolic, sqrt, log_gamma,
                     gamma_inc, incomplete_gamma, gamma_inc_lower,
                     arg, real_part, real, frac,
                     imag_part, imag, imaginary, conjugate)
@@ -37,8 +39,7 @@
                                    spherical_bessel_J, spherical_bessel_Y,
                                    spherical_hankel1, spherical_hankel2)
 
-from .special import (spherical_harmonic,
-                     error_fcn, elliptic_e,
+from .special import (spherical_harmonic, elliptic_e,
                      elliptic_f, elliptic_ec, elliptic_eu,
                      elliptic_kc, elliptic_pi, elliptic_j)
 
@@ -84,3 +85,4 @@
                           exponential_integral_1, Ei, exp_integral_ei)
 
 from .hypergeometric import hypergeometric, hypergeometric_M, hypergeometric_U
+