%display latex

load("../specifier.py")

S = Specification([],[[2,3,1,4],[3,2,4,1],[2,1,4,5,3],[4,5,2,1,3]])

S

$$\newcommand{\Bold}[1]{\mathbf{#1}}\begin{array} \mathcal T_{0}= &\{ \bullet \} \uplus \oplus[\mathcal T_{1},\mathcal T_{2}]\uplus \oplus[\mathcal T_{1},\mathcal T_{3}]\uplus \oplus[\mathcal T_{4},\mathcal T_{2}]\uplus \ominus[\mathcal T_{1},\mathcal T_{5}]\uplus \ominus[\mathcal T_{1},\mathcal T_{6}]\uplus \ominus[\mathcal T_{7},\mathcal T_{5}]\\ \mathcal T_{1}= &\{ \bullet \} \\ \mathcal T_{2}= &\{ \bullet \} \uplus \oplus[\mathcal T_{8},\mathcal T_{2}]\uplus \ominus[\mathcal T_{1},\mathcal T_{2}]\\ \mathcal T_{3}= &\oplus[\mathcal T_{1},\mathcal T_{3}]\uplus \ominus[\mathcal T_{1},\mathcal T_{9}]\uplus \ominus[\mathcal T_{1},\mathcal T_{10}]\uplus \ominus[\mathcal T_{7},\mathcal T_{9}]\uplus \ominus[\mathcal T_{7},\mathcal T_{11}]\\ \mathcal T_{4}= &\ominus[\mathcal T_{1},\mathcal T_{2}]\\ \mathcal T_{5}= &\{ \bullet \} \uplus \oplus[\mathcal T_{1},\mathcal T_{5}]\uplus \ominus[\mathcal T_{12},\mathcal T_{5}]\\ \mathcal T_{6}= &\oplus[\mathcal T_{1},\mathcal T_{13}]\uplus \oplus[\mathcal T_{1},\mathcal T_{10}]\uplus \oplus[\mathcal T_{4},\mathcal T_{13}]\uplus \oplus[\mathcal T_{4},\mathcal T_{11}]\uplus \ominus[\mathcal T_{1},\mathcal T_{6}]\\ \mathcal T_{7}= &\oplus[\mathcal T_{1},\mathcal T_{5}]\\ \mathcal T_{8}= &\{ \bullet \} \uplus \ominus[\mathcal T_{1},\mathcal T_{2}]\\ \mathcal T_{9}= &\oplus[\mathcal T_{1},\mathcal T_{9}]\uplus \ominus[\mathcal T_{7},\mathcal T_{9}]\uplus \ominus[\mathcal T_{1},\mathcal T_{9}]\uplus \ominus[\mathcal T_{7},\mathcal T_{11}]\\ \mathcal T_{10}= &\oplus[\mathcal T_{1},\mathcal T_{10}]\uplus \ominus[\mathcal T_{1},\mathcal T_{10}]\\ \mathcal T_{11}= &\{ \bullet \} \uplus \oplus[\mathcal T_{1},\mathcal T_{11}]\uplus \ominus[\mathcal T_{1},\mathcal T_{11}]\\ \mathcal T_{12}= &\{ \bullet \} \uplus \oplus[\mathcal T_{1},\mathcal T_{5}]\\ \mathcal T_{13}= &\oplus[\mathcal T_{4},\mathcal T_{13}]\uplus \oplus[\mathcal T_{1},\mathcal T_{13}]\uplus \oplus[\mathcal T_{4},\mathcal T_{11}]\uplus \ominus[\mathcal T_{1},\mathcal T_{13}]\end{array}$$

S.solve()

$$\newcommand{\Bold}[1]{\mathbf{#1}}\left[-\frac{6 \, z^{7} + z^{6} {\left(19 \, \sqrt{-4 \, z + 1} - 123\right)} - 2 \, z^{5} {\left(66 \, \sqrt{-4 \, z + 1} - 221\right)} + 7 \, z^{4} {\left(39 \, \sqrt{-4 \, z + 1} - 89\right)} - 2 \, z^{3} {\left(124 \, \sqrt{-4 \, z + 1} - 215\right)} + z^{2} {\left(111 \, \sqrt{-4 \, z + 1} - 155\right)} - 4 \, z {\left(6 \, \sqrt{-4 \, z + 1} - 7\right)} + 2 \, \sqrt{-4 \, z + 1} - 2}{4 \, z^{7} + 2 \, z^{6} {\left(5 \, \sqrt{-4 \, z + 1} - 26\right)} - 5 \, z^{5} {\left(9 \, \sqrt{-4 \, z + 1} - 25\right)} + 2 \, z^{4} {\left(31 \, \sqrt{-4 \, z + 1} - 60\right)} - z^{3} {\left(37 \, \sqrt{-4 \, z + 1} - 55\right)} + 2 \, z^{2} {\left(5 \, \sqrt{-4 \, z + 1} - 6\right)} - z {\left(\sqrt{-4 \, z + 1} - 1\right)}}, z, -\frac{2 \, z^{2} + 2 \, z {\left(\sqrt{-4 \, z + 1} - 2\right)} - \sqrt{-4 \, z + 1} + 1}{2 \, z^{2} + z {\left(\sqrt{-4 \, z + 1} - 1\right)}}, -\frac{2 \, z^{3} + 3 \, z^{2} {\left(\sqrt{-4 \, z + 1} - 3\right)} - 2 \, z {\left(2 \, \sqrt{-4 \, z + 1} - 3\right)} + \sqrt{-4 \, z + 1} - 1}{4 \, z^{3} + 2 \, z^{2} {\left(\sqrt{-4 \, z + 1} - 2\right)} - z {\left(\sqrt{-4 \, z + 1} - 1\right)}}, -\frac{2 \, z^{3} + 3 \, z^{2} {\left(\sqrt{-4 \, z + 1} - 3\right)} - 2 \, z {\left(2 \, \sqrt{-4 \, z + 1} - 3\right)} + \sqrt{-4 \, z + 1} - 1}{2 \, z^{2} + 2 \, z {\left(\sqrt{-4 \, z + 1} - 2\right)} - \sqrt{-4 \, z + 1} + 1}, -\frac{2 \, z^{2} + 2 \, z {\left(\sqrt{-4 \, z + 1} - 2\right)} - \sqrt{-4 \, z + 1} + 1}{2 \, z^{2} + z {\left(\sqrt{-4 \, z + 1} - 1\right)}}, -\frac{2 \, z^{3} + 3 \, z^{2} {\left(\sqrt{-4 \, z + 1} - 3\right)} - 2 \, z {\left(2 \, \sqrt{-4 \, z + 1} - 3\right)} + \sqrt{-4 \, z + 1} - 1}{4 \, z^{3} + 2 \, z^{2} {\left(\sqrt{-4 \, z + 1} - 2\right)} - z {\left(\sqrt{-4 \, z + 1} - 1\right)}}, -\frac{2 \, z^{2} + 2 \, z {\left(\sqrt{-4 \, z + 1} - 2\right)} - \sqrt{-4 \, z + 1} + 1}{2 \, z + \sqrt{-4 \, z + 1} - 1}, -\frac{z^{2} {\left(\sqrt{-4 \, z + 1} - 5\right)} - z {\left(3 \, \sqrt{-4 \, z + 1} - 5\right)} + \sqrt{-4 \, z + 1} - 1}{2 \, z^{2} + 2 \, z {\left(\sqrt{-4 \, z + 1} - 2\right)} - \sqrt{-4 \, z + 1} + 1}, -\frac{2 \, z^{2} + {\left(2 \, z - 1\right)} \sqrt{-4 \, z + 1} - 4 \, z + 1}{2 \, {\left(2 \, z^{2} - z\right)}}, 0, -\frac{z}{2 \, z - 1}, -\frac{z^{3} {\left(\sqrt{-4 \, z + 1} - 7\right)} - 2 \, z^{2} {\left(3 \, \sqrt{-4 \, z + 1} - 7\right)} + z {\left(5 \, \sqrt{-4 \, z + 1} - 7\right)} - \sqrt{-4 \, z + 1} + 1}{2 \, z^{3} + 3 \, z^{2} {\left(\sqrt{-4 \, z + 1} - 3\right)} - 2 \, z {\left(2 \, \sqrt{-4 \, z + 1} - 3\right)} + \sqrt{-4 \, z + 1} - 1}, -\frac{2 \, z^{2} + {\left(2 \, z - 1\right)} \sqrt{-4 \, z + 1} - 4 \, z + 1}{2 \, {\left(2 \, z^{2} - z\right)}}\right]$$

C = S.sampler(1/4, formal=True)

perm = [C.run(10) for _ in range(10)] 

list_plot(perm[0],aspect_ratio = 1,dpi = 50)

list_plot(perm[1],aspect_ratio = 1,dpi = 50)

list_plot(perm[2],aspect_ratio = 1,dpi = 50)

list_plot(perm[3],aspect_ratio = 1,dpi = 50)

list_plot(perm[4],aspect_ratio = 1,dpi = 50)

list_plot(perm[5],aspect_ratio = 1,dpi = 50)

list_plot(perm[6],aspect_ratio = 1,dpi = 50)

list_plot(perm[7],aspect_ratio = 1,dpi = 50)

list_plot(perm[8],aspect_ratio = 1,dpi = 50)

list_plot(perm[9],aspect_ratio = 1,dpi = 50)