MAINT: limit the number of decimals in Polynomial representation (#21654)

* limit the number of decimals in Polynomial representation

* tests pass

* parenthesize exponential notation in polynomials

* fixed a long line warning

* added polynomial printoptions tests

* polynomial printoptions typo fixed

* made switch to exp notation in polynomial display more natural

* added a test on switching polynomials to exp notation

* fixed linter errors/warnings

* support for nanstr and infstr printoptions in polynomials

* 10^8 threshold for switching to exp notation when displaying polynomials

* merged in PR #21696 fixing issue #21695

* made linter happy

* made some docstring tests pass

* fixed the docs

Co-authored-by: Lev Maximov <lev.maximov@gmail.com>

1 files changed, 40 insertions, 1 deletions

diff --git a/numpy/polynomial/polyutils.py b/numpy/polynomial/polyutils.py
index a2bc75a4d..482913892 100644
--- a/numpy/polynomial/polyutils.py
+++ b/numpy/polynomial/polyutils.py
@@ -32,9 +32,13 @@ import warnings
 
 import numpy as np
 
+from numpy.core.multiarray import dragon4_positional, dragon4_scientific
+from numpy.core.umath import absolute
+
 __all__ = [
     'RankWarning', 'as_series', 'trimseq',
-    'trimcoef', 'getdomain', 'mapdomain', 'mapparms']
+    'trimcoef', 'getdomain', 'mapdomain', 'mapparms',
+    'format_float']
 
 #
 # Warnings and Exceptions
@@ -748,3 +752,38 @@ def _deprecate_as_int(x, desc):
                 return ix
 
         raise TypeError(f"{desc} must be an integer") from e
+
+
+def format_float(x, parens=False):
+    if not np.issubdtype(type(x), np.floating):
+        return str(x)
+
+    opts = np.get_printoptions()
+
+    if np.isnan(x):
+        return opts['nanstr']
+    elif np.isinf(x):
+        return opts['infstr']
+
+    exp_format = False
+    if x != 0:
+        a = absolute(x)
+        if a >= 1.e8 or a < 10**min(0, -(opts['precision']-1)//2):
+            exp_format = True
+
+    trim, unique = '0', True
+    if opts['floatmode'] == 'fixed':
+        trim, unique = 'k', False
+
+    if exp_format:
+        s = dragon4_scientific(x, precision=opts['precision'],
+                               unique=unique, trim=trim, 
+                               sign=opts['sign'] == '+')
+        if parens:
+            s = '(' + s + ')'
+    else:
+        s = dragon4_positional(x, precision=opts['precision'],
+                               fractional=True,
+                               unique=unique, trim=trim,
+                               sign=opts['sign'] == '+')
+    return s