Clean up arithmetic examples

docs/basic-usage/array-arithmetic.rst

@@ -12,8 +12,8 @@ In the sections below, the finite field :math:`\mathrm{GF}(3^5)` and arrays :mat
     x = GF([184, 25, 157, 31]); x
     y = GF([179, 9, 139, 27]); y
 
-Ufuncs
-------
+Standard arithmetic
+-------------------
 
 `NumPy ufuncs <https://numpy.org/devdocs/reference/ufuncs.html>`_ are universal functions that operate on scalars. Unary ufuncs operate on
 a single scalar and binary ufuncs operate on two scalars. NumPy extends the scalar operation of ufuncs to operate on arrays in various ways.
@@ -23,123 +23,140 @@ Expand any section for more details.
 
 .. details:: Addition: `x + y == np.add(x, y)`
     :class: example
-    :open:
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        x
+        y
         x + y
         np.add(x, y)
 
 .. details:: Additive inverse: `-x == np.negative(x)`
     :class: example
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        x
         -x
         np.negative(x)
 
     Any array added to its additive inverse results in zero.
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        x
         x + np.negative(x)
 
 .. details:: Subtraction: `x - y == np.subtract(x, y)`
     :class: example
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        x
+        y
         x - y
         np.subtract(x, y)
 
 .. details:: Multiplication: `x * y == np.multiply(x, y)`
     :class: example
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        x
+        y
         x * y
         np.multiply(x, y)
 
-.. details:: Scalar multiplication: `x * z == np.multiply(x, z)`
+.. details:: Scalar multiplication: `x * 4 == np.multiply(x, 4)`
     :class: example
 
     Scalar multiplication is essentially *repeated addition*. It is the "multiplication" of finite field elements
     and integers. The integer value indicates how many additions of the field element to sum.
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        x
         x * 4
         np.multiply(x, 4)
         x + x + x + x
 
     In finite fields :math:`\mathrm{GF}(p^m)`, the characteristic :math:`p` is the smallest value when multiplied by
     any non-zero field element that results in 0.
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
         p = GF.characteristic; p
         x * p
 
 .. details:: Multiplicative inverse: `y ** -1 == np.reciprocal(y)`
     :class: example
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        y
         y ** -1
         GF(1) / y
         np.reciprocal(y)
 
     Any array multiplied by its multiplicative inverse results in one.
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
         y * np.reciprocal(y)
 
 .. details:: Division: `x / y == x // y == np.divide(x, y)`
     :class: example
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        x
+        y
         x / y
         x // y
         np.divide(x, y)
 
 .. details:: Remainder: `x % y == np.remainder(x, y)`
     :class: example
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        x
+        y
         x % y
         np.remainder(x, y)
 
 .. details:: Divmod: `divmod(x, y) == np.divmod(x, y)`
     :class: example
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        x
+        y
         x // y, x % y
         divmod(x, y)
         np.divmod(x, y)
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
         q, r = divmod(x, y)
         q*y + r == x
 
-.. details:: Exponentiation: `x ** z == np.power(x, z)`
+.. details:: Exponentiation: `x ** 3 == np.power(x, 3)`
     :class: example
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        x
         x ** 3
         np.power(x, 3)
         x * x * x
 
 .. details:: Square root: `np.sqrt(x)`
     :class: example
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        x
         x.is_square()
         z = np.sqrt(x); z
         z ** 2 == x
@@ -151,17 +168,19 @@ Expand any section for more details.
 
     Compute the logarithm base :math:`\alpha`, the primitive element of the field.
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        y
         z = np.log(y); z
         alpha = GF.primitive_element; alpha
         alpha ** z == y
 
     Compute the logarithm base :math:`\beta`, a different primitive element of the field. See :func:`FieldArray.log` for more
     details.
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        y
         beta = GF.primitive_elements[-1]; beta
         z = y.log(beta); z
         beta ** z == y
@@ -176,16 +195,16 @@ Expand any section for more details.
 
 .. details:: `reduce()`
     :class: example
-    :open:
 
     The :obj:`~numpy.ufunc.reduce` methods reduce the input array's dimension by one, applying the ufunc across one axis.
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        x
         np.add.reduce(x)
         x[0] + x[1] + x[2] + x[3]
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
         np.multiply.reduce(x)
         x[0] * x[1] * x[2] * x[3]
@@ -195,12 +214,13 @@ Expand any section for more details.
 
     The :obj:`~numpy.ufunc.accumulate` methods accumulate the result of the ufunc across a specified axis.
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        x
         np.add.accumulate(x)
         GF([x[0], x[0] + x[1], x[0] + x[1] + x[2], x[0] + x[1] + x[2] + x[3]])
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
         np.multiply.accumulate(x)
         GF([x[0], x[0] * x[1], x[0] * x[1] * x[2], x[0] * x[1] * x[2] * x[3]])
@@ -211,12 +231,13 @@ Expand any section for more details.
     The :obj:`~numpy.ufunc.reduceat` methods reduces the input array's dimension by one, applying the ufunc across one axis
     in-between certain indices.
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        x
         np.add.reduceat(x, [0, 3])
         GF([x[0] + x[1] + x[2], x[3]])
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
         np.multiply.reduceat(x, [0, 3])
         GF([x[0] * x[1] * x[2], x[3]])
@@ -226,11 +247,13 @@ Expand any section for more details.
 
     The :obj:`~numpy.ufunc.outer` methods applies the ufunc to each pair of inputs.
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        x
+        y
         np.add.outer(x, y)
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
         np.multiply.outer(x, y)
 
@@ -239,8 +262,9 @@ Expand any section for more details.
 
     The :obj:`~numpy.ufunc.at` methods performs the ufunc in-place at the specified indices.
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        x
         z = x.copy()
         # Negate indices 0 and 1 in-place
         np.negative.at(x, [0, 1]); x
@@ -253,10 +277,11 @@ Advanced arithmetic
 
 .. details:: Convolution: `np.convolve(x, y)`
     :class: example
-    :open:
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
+        x
+        y
         np.convolve(x, y)
 
 .. details:: FFT: `np.fft.fft(x)`
@@ -265,13 +290,13 @@ Advanced arithmetic
     The Discrete Fourier Transform (DFT) of size :math:`n` over the finite field :math:`\mathrm{GF}(p^m)` exists when there
     exists a primitive :math:`n`-th root of unity. This occurs when :math:`n\ |\ p^m - 1`.
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
         GF = galois.GF(7**5)
         n = 6
         # n divides p^m - 1
         (GF.order - 1) % n
-        x = GF.Random(n); x
+        x = GF.Random(n, seed=1); x
         X = np.fft.fft(x); X
         np.fft.ifft(X)
 
@@ -283,13 +308,13 @@ Advanced arithmetic
     The inverse Discrete Fourier Transform (DFT) of size :math:`n` over the finite field :math:`\mathrm{GF}(p^m)` exists when there
     exists a primitive :math:`n`-th root of unity. This occurs when :math:`n\ |\ p^m - 1`.
 
-    .. ipython:: python
+    .. ipython-with-reprs:: int,poly,power
 
         GF = galois.GF(7**5)
         n = 6
         # n divides p^m - 1
         (GF.order - 1) % n
-        x = GF.Random(n); x
+        x = GF.Random(n, seed=1); x
         X = np.fft.fft(x); X
         np.fft.ifft(X)
 
@@ -305,7 +330,6 @@ Expand any section for more details.
 
 .. details:: Dot product: `np.dot(a, b)`
     :class: example
-    :open:
 
     .. ipython:: python
 
@@ -355,7 +379,7 @@ Expand any section for more details.
         A @ B
         np.matmul(A, B)
 
-.. details:: Matrix exponentiation: `np.linalg.matrix_power(A, z)`
+.. details:: Matrix exponentiation: `np.linalg.matrix_power(A, 3)`
     :class: example
 
     .. ipython:: python
@@ -374,7 +398,7 @@ Expand any section for more details.
         A = GF([[23, 11, 3, 3], [13, 6, 16, 4], [12, 10, 5, 3], [17, 23, 15, 28]]); A
         np.linalg.det(A)
 
-.. details:: Matrix rank: `np.linalg.matrix_rank(A, z)`
+.. details:: Matrix rank: `np.linalg.matrix_rank(A)`
     :class: example
 
     .. ipython:: python
@@ -423,7 +447,6 @@ not included in NumPy.
 
 .. details:: Row space: `A.row_space()`
     :class: example
-    :open:
 
     .. ipython:: python