Updated tutorial to include the rational toy example

Author: Antonio-JP

Tutorial.html

@@ -13120,7 +13120,7 @@ <h2 id="Basic-usage">Basic usage<a class="anchor-link" href="#Basic-usage">&#182
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 <div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="k">import</span> <span class="n">vring</span><span class="p">,</span> <span class="n">QQ</span>
-<span class="kn">from</span> <span class="nn">clue</span> <span class="k">import</span> <span class="n">FODESystem</span>
+<span class="kn">from</span> <span class="nn">clue</span> <span class="k">import</span> <span class="n">FODESystem</span><span class="p">,</span> <span class="n">SparsePolynomial</span><span class="p">,</span> <span class="n">RationalFunction</span>
 </pre></div>
 
     </div>
@@ -13235,6 +13235,76 @@ <h2 id="Basic-usage">Basic usage<a class="anchor-link" href="#Basic-usage">&#182
 
 </div>
 </div>
+</div>
+<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
+</div><div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>This software also allows systems with rational functions:</p>
+
+</div>
+</div>
+</div>
+<div class="cell border-box-sizing code_cell rendered">
+<div class="input">
+<div class="prompt input_prompt">In&nbsp;[5]:</div>
+<div class="inner_cell">
+    <div class="input_area">
+<div class=" highlight hl-ipython3"><pre><span></span><span class="n">varnames</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;x&#39;</span><span class="p">,</span><span class="s1">&#39;y&#39;</span><span class="p">]</span>
+<span class="n">rational_ode</span> <span class="o">=</span> <span class="n">FODESystem</span><span class="p">([</span>
+    <span class="n">RationalFunction</span><span class="o">.</span><span class="n">from_string</span><span class="p">(</span><span class="s2">&quot;y/(x-y)&quot;</span><span class="p">,</span> <span class="n">varnames</span><span class="p">),</span>
+    <span class="n">RationalFunction</span><span class="o">.</span><span class="n">from_string</span><span class="p">(</span><span class="s2">&quot;x/(x-y)&quot;</span><span class="p">,</span> <span class="n">varnames</span><span class="p">)</span>
+<span class="p">],</span> <span class="n">variables</span> <span class="o">=</span> <span class="n">varnames</span><span class="p">)</span>
+</pre></div>
+
+    </div>
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell rendered">
+<div class="input">
+<div class="prompt input_prompt">In&nbsp;[6]:</div>
+<div class="inner_cell">
+    <div class="input_area">
+<div class=" highlight hl-ipython3"><pre><span></span><span class="n">rational_ode</span><span class="o">.</span><span class="n">lumping</span><span class="p">([</span><span class="n">SparsePolynomial</span><span class="o">.</span><span class="n">from_string</span><span class="p">(</span><span class="s2">&quot;x-y&quot;</span><span class="p">,</span> <span class="n">varnames</span><span class="p">)]);</span>
+</pre></div>
+
+    </div>
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output">
+
+
+<div class="output_area">
+
+    <div class="prompt"></div>
+
+
+<div class="output_subarea output_stream output_stderr output_text">
+<pre>2021-11-26 14:14:43 WARNING  Method [polynomial] selected but input is not SparsePolynomial. Trying random...
+</pre>
+</div>
+</div>
+
+<div class="output_area">
+
+    <div class="prompt"></div>
+
+
+<div class="output_subarea output_stream output_stdout output_text">
+<pre>New variables:
+y0 = x + -y
+Lumped system:
+y0&#39; = (-1)/(1)
+</pre>
+</div>
+</div>
+
+</div>
+</div>
+
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@@ -13261,7 +13331,7 @@ <h3 id="Reading-models-from-*.ode-files">Reading models from *.ode files<a class
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-<div class="prompt input_prompt">In&nbsp;[5]:</div>
+<div class="prompt input_prompt">In&nbsp;[7]:</div>
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     <div class="input_area">
 <div class=" highlight hl-ipython3"><pre><span></span><span class="n">system</span> <span class="o">=</span> <span class="n">FODESystem</span><span class="p">(</span><span class="n">file</span><span class="o">=</span><span class="s2">&quot;Tutorial_files/model_example.ode&quot;</span><span class="p">)</span>
@@ -13278,7 +13348,7 @@ <h3 id="Reading-models-from-*.ode-files">Reading models from *.ode files<a class
 
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-    <div class="prompt output_prompt">Out[5]:</div>
+    <div class="prompt output_prompt">Out[7]:</div>
 
 
 
@@ -13303,7 +13373,7 @@ <h3 id="Reading-models-from-*.ode-files">Reading models from *.ode files<a class
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-<div class="prompt input_prompt">In&nbsp;[6]:</div>
+<div class="prompt input_prompt">In&nbsp;[8]:</div>
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 <div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">clue.rational_function</span> <span class="k">import</span> <span class="n">SparsePolynomial</span>
@@ -13369,7 +13439,7 @@ <h3 id="Rational-numbers">Rational numbers<a class="anchor-link" href="#Rational
 </div>
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-<div class="prompt input_prompt">In&nbsp;[7]:</div>
+<div class="prompt input_prompt">In&nbsp;[9]:</div>
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 <div class=" highlight hl-ipython3"><pre><span></span><span class="n">R</span> <span class="o">=</span> <span class="n">vring</span><span class="p">([</span><span class="s2">&quot;x1&quot;</span><span class="p">,</span> <span class="s2">&quot;x2&quot;</span><span class="p">],</span> <span class="n">QQ</span><span class="p">)</span>
@@ -13438,7 +13508,7 @@ <h3 id="Unknown-scalar-parameters">Unknown scalar parameters<a class="anchor-lin
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-<div class="prompt input_prompt">In&nbsp;[8]:</div>
+<div class="prompt input_prompt">In&nbsp;[10]:</div>
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 <div class=" highlight hl-ipython3"><pre><span></span><span class="n">R</span> <span class="o">=</span> <span class="n">vring</span><span class="p">([</span><span class="s2">&quot;x1&quot;</span><span class="p">,</span> <span class="s2">&quot;x2&quot;</span><span class="p">,</span> <span class="s2">&quot;a&quot;</span><span class="p">,</span> <span class="s2">&quot;b&quot;</span><span class="p">],</span> <span class="n">QQ</span><span class="p">)</span>
@@ -13502,7 +13572,7 @@ <h3 id="Unknown-scalar-parameters">Unknown scalar parameters<a class="anchor-lin
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-<div class="prompt input_prompt">In&nbsp;[9]:</div>
+<div class="prompt input_prompt">In&nbsp;[11]:</div>
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 <div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># defining the coefficient field</span>
@@ -13555,7 +13625,7 @@ <h3 id="Unknown-scalar-parameters">Unknown scalar parameters<a class="anchor-lin
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 <div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># defining the coefficient field</span>
@@ -13623,7 +13693,7 @@ <h3 id="Irrational-coefficients">Irrational coefficients<a class="anchor-link" h
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-<div class="prompt input_prompt">In&nbsp;[11]:</div>
+<div class="prompt input_prompt">In&nbsp;[13]:</div>
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 <div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="k">import</span> <span class="n">sqrt</span>

Tutorial.ipynb

@@ -47,7 +47,7 @@
    "outputs": [],
    "source": [
     "from sympy import vring, QQ\n",
-    "from clue import FODESystem"
+    "from clue import FODESystem, SparsePolynomial, RationalFunction"
    ]
   },
   {
@@ -130,6 +130,53 @@
     "*Remark:* to supress the output, use `print_reduction=False` keyword argument. If you would like to print the original system, use `print_system=True`. Check the documentation of the method `lumping` for further information."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This software also allows systems with rational functions:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "varnames = ['x','y']\n",
+    "rational_ode = FODESystem([\n",
+    "    RationalFunction.from_string(\"y/(x-y)\", varnames),\n",
+    "    RationalFunction.from_string(\"x/(x-y)\", varnames)\n",
+    "], variables = varnames)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "2021-11-26 14:14:43 WARNING  Method [polynomial] selected but input is not SparsePolynomial. Trying random...\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "New variables:\n",
+      "y0 = x + -y\n",
+      "Lumped system:\n",
+      "y0' = (-1)/(1)\n"
+     ]
+    }
+   ],
+   "source": [
+    "rational_ode.lumping([SparsePolynomial.from_string(\"x-y\", varnames)]);"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -155,7 +202,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
@@ -164,7 +211,7 @@
        "['Ap', 'ApB', 'Au', 'AuB', 'B', 'r1', 'r2']"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 7,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -183,7 +230,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
@@ -237,7 +284,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
@@ -298,7 +345,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
@@ -345,7 +392,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
@@ -383,7 +430,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
@@ -440,7 +487,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {