include signals documentation; remove duplicate docstrings

mpmath · Nov 7, 2022 · b7c15d6 · b7c15d6
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diff --git a/docs/functions/index.rst b/docs/functions/index.rst
@@ -10,6 +10,7 @@ Mpmath implements the standard functions from Python's ``math`` and ``cmath`` mo
    powers
    trigonometric
    hyperbolic
+   signals
    gamma
    expintegrals
    bessel

diff --git a/mpmath/function_docs.py b/mpmath/function_docs.py
@@ -10069,7 +10069,7 @@
 Computes the square wave function using the definition:
 
 .. math::
-    x(t) = A(-1)^{\left\lfloor{\frac{2t}{P}}\right\rfloor}
+    x(t) = A(-1)^{\left\lfloor{2t / P}\right\rfloor}
 
 where `P` is the period of the wave and `A` is the amplitude.
 
@@ -10095,9 +10095,9 @@
 Computes the triangle wave function using the definition:
 
 .. math::
-    x(t) = 2A\left(\frac{1}{2}-\left|1-2frac\left(\frac{x}{P}+\frac{1}{4}\right)\right|\right)
+    x(t) = 2A\left(\frac{1}{2}-\left|1-2 \operatorname{frac}\left(\frac{x}{P}+\frac{1}{4}\right)\right|\right)
 
-where :math:`frac\left(\frac{t}{T}\right) = \frac{t}{T}-\left\lfloor{\frac{t}{T}}\right\rfloor`
+where :math:`\operatorname{frac}\left(\frac{t}{T}\right) = \frac{t}{T}-\left\lfloor{\frac{t}{T}}\right\rfloor`
 , `P` is the period of the wave, and `A` is the amplitude.
 
 **Examples**
@@ -10124,10 +10124,10 @@
 Computes the sawtooth wave function using the definition:
 
 .. math::
-    x(t) = Afrac\left(\frac{t}{T}\right)
+    x(t) = A\operatorname{frac}\left(\frac{t}{T}\right)
 
-where :math:`frac\left(\frac{t}{T}\right) = \frac{t}{T}-\left\lfloor{\frac{t}{T}}\right\rfloor`
-, `P` is the period of the wave, and `A` is the amplitude.
+where :math:`\operatorname{frac}\left(\frac{t}{T}\right) = \frac{t}{T}-\left\lfloor{\frac{t}{T}}\right\rfloor`,
+`P` is the period of the wave, and `A` is the amplitude.
 
 **Examples**
 

diff --git a/mpmath/functions/signals.py b/mpmath/functions/signals.py
@@ -2,161 +2,31 @@
 
 @defun_wrapped
 def squarew(ctx, t, amplitude=1, period=1):
-    r"""
-    Computes the square wave function using the definition:
-
-    .. math::
-        x(t) = A(-1)^{\left\lfloor{\frac{2t}{P}}\right\rfloor}
-
-    where `P` is the period of the wave and `A` is the amplitude.
-
-    **Examples**
-
-    Square wave with period = 2, amplitude = 1 ::
-
-        >>> from mpmath import *
-        >>> mp.dps = 25; mp.pretty = True
-        >>> squarew(0,1,2)
-        1.0
-        >>> squarew(0.5,1,2)
-        1.0
-        >>> squarew(1,1,2)
-        -1.0
-        >>> squarew(1.5,1,2)
-        -1.0
-        >>> squarew(2,1,2)
-        1.0
-    """
     P = period
     A = amplitude
     return A*((-1)**ctx.floor(2*t/P))
 
 @defun_wrapped
 def trianglew(ctx, t, amplitude=1, period=1):
-    r"""
-    Computes the triangle wave function using the definition:
-
-    .. math::
-        x(t) = 2A\left(\frac{1}{2}-\left|1-2frac\left(\frac{x}{P}+\frac{1}{4}\right)\right|\right)
-
-    where :math:`frac\left(\frac{t}{T}\right) = \frac{t}{T}-\left\lfloor{\frac{t}{T}}\right\rfloor`
-    , `P` is the period of the wave, and `A` is the amplitude.
-
-    **Examples**
-
-    Triangle wave with period = 2, amplitude = 1 ::
-
-        >>> from mpmath import *
-        >>> mp.dps = 25; mp.pretty = True
-        >>> trianglew(0,1,2)
-        0.0
-        >>> trianglew(0.25,1,2)
-        0.5
-        >>> trianglew(0.5,1,2)
-        1.0
-        >>> trianglew(1,1,2)
-        0.0
-        >>> trianglew(1.5,1,2)
-        -1.0
-        >>> trianglew(2,1,2)
-        0.0
-    """
     A = amplitude
     P = period
 
     return 2*A*(0.5 - ctx.fabs(1 - 2*ctx.frac(t/P + 0.25)))
 
 @defun_wrapped
 def sawtoothw(ctx, t, amplitude=1, period=1):
-    r"""
-    Computes the sawtooth wave function using the definition:
-
-    .. math::
-        x(t) = Afrac\left(\frac{t}{T}\right)
-
-    where :math:`frac\left(\frac{t}{T}\right) = \frac{t}{T}-\left\lfloor{\frac{t}{T}}\right\rfloor`
-    , `P` is the period of the wave, and `A` is the amplitude.
-
-    **Examples**
-
-    Sawtooth wave with period = 2, amplitude = 1 ::
-
-        >>> from mpmath import *
-        >>> mp.dps = 25; mp.pretty = True
-        >>> sawtoothw(0,1,2)
-        0.0
-        >>> sawtoothw(0.5,1,2)
-        0.25
-        >>> sawtoothw(1,1,2)
-        0.5
-        >>> sawtoothw(1.5,1,2)
-        0.75
-        >>> sawtoothw(2,1,2)
-        0.0
-    """
     A = amplitude
     P = period
     return A*ctx.frac(t/P)
 
 @defun_wrapped
 def unit_triangle(t, amplitude=1):
-    r"""
-    Computes the unit triangle using the definition:
-
-    .. math::
-        x(t) = A(-\left| t \right| + 1)
-
-    where `A` is the amplitude.
-
-    **Examples**
-
-    Unit triangle with amplitude = 1 ::
-
-        >>> from mpmath import *
-        >>> mp.dps = 25; mp.pretty = True
-        >>> unit_triangle(-1,1)
-        0
-        >>> unit_triangle(-0.5,1)
-        0.5
-        >>> unit_triangle(0,1)
-        1
-        >>> unit_triangle(0.5,1)
-        0.5
-        >>> unit_triangle(1,1)
-        0
-    """
     A = amplitude
     if t <= -1 or t >= 1:
         return ctx.zero
     return A*(-abs(t) + 1)
 
 @defun_wrapped
 def sigmoid(ctx, t, amplitude=1):
-    r"""
-    Computes the sigmoid function using the definition:
-
-    .. math::
-        x(t) = \frac{A}{1 + e^{-t}}
-
-    where `A` is the amplitude.
-
-    **Examples**
-
-    Sigmoid function with amplitude = 1 ::
-
-        >>> from mpmath import *
-        >>> mp.dps = 25; mp.pretty = True
-        >>> sigmoid(-1,1)
-        0.2689414213699951207488408
-        >>> sigmoid(-0.5,1)
-        0.3775406687981454353610994
-        >>> sigmoid(0,1)
-        0.5
-        >>> sigmoid(0.5,1)
-        0.6224593312018545646389006
-        >>> sigmoid(1,1)
-        0.7310585786300048792511592
-
-    """
     A = amplitude
     return A / (1 + ctx.exp(-t))