diff --git a/src/axiomatic/axtract.py b/src/axiomatic/axtract.py
index 9dda406..4c16fec 100644
--- a/src/axiomatic/axtract.py
+++ b/src/axiomatic/axtract.py
@@ -1,6 +1,9 @@
 import ipywidgets as widgets  # type: ignore
-from IPython.display import display  # type: ignore
+from IPython.display import display, Math, HTML  # type: ignore
 from dataclasses import dataclass, field
+import hypernetx as hnx # type: ignore
+import matplotlib.pyplot as plt
+import re
 
 OPTION_LIST = {
     "Select a template": [],
@@ -18,7 +21,7 @@
         "Pixel size (multispectral)",
         "Swath width",
     ],
-        "PAYLOAD": [
+    "PAYLOAD": [
         "Resolution (panchromatic)",
         "Ground sampling distance (panchromatic)",
         "Resolution (multispectral)",
@@ -117,7 +120,6 @@ def requirements_from_table(results, variable_dict):
         name = key
         numerical_value = value["Value"]
         unit = value["Units"]
-        tolerance = value["Tolerance"]
 
         requirements.append(
             Requirement(
@@ -125,7 +127,7 @@ def requirements_from_table(results, variable_dict):
                 latex_symbol=latex_symbol,
                 value=numerical_value,
                 units=unit,
-                tolerance=tolerance,
+                tolerance=0.0,
             )
         )
 
@@ -178,9 +180,15 @@ def display_table(change):
 
         if selected_option in preset_options_dict:
             rows = preset_options_dict[selected_option]
-            max_name_length = max(len(name) for name in rows)
-            # Update the name_label_width based on the longest row name
-            name_label_width[0] = f"{max_name_length + 2}ch"
+
+            if selected_option != "Select a template":
+                max_name_length = max(len(name) for name in rows)
+                # Update the name_label_width based on the longest row name
+                name_label_width[0] = f"{max_name_length + 2}ch"
+            else:
+                max_name_length = 40
+                # Update the name_label_width based on the longest row name
+                name_label_width[0] = f"{max_name_length + 2}ch"
 
             # Add Headers
             header_labels = [
@@ -194,16 +202,6 @@ def display_table(change):
                     layout=widgets.Layout(width="150px"),
                     style={'font_weight': 'bold'}
                 ),
-                widgets.Label(
-                    value="Tolerance",
-                    layout=widgets.Layout(width="150px"),
-                    style={'font_weight': 'bold'}
-                ),
-                widgets.Label(
-                    value="Accuracy",
-                    layout=widgets.Layout(width="150px"),
-                    style={'font_weight': 'bold'}
-                ),
                 widgets.Label(
                     value="Units",
                     layout=widgets.Layout(width="150px"),
@@ -216,7 +214,6 @@ def display_table(change):
             header.layout = widgets.Layout(
                 border='1px solid black',
                 padding='5px',
-                background_color='#f0f0f0'
             )
 
             # Add the header to the rows_output VBox
@@ -244,19 +241,12 @@ def display_table(change):
 
                 # Create input widgets
                 value_text = widgets.FloatText(
-                    placeholder="Value",
                     value=default_value,
                     layout=widgets.Layout(width="150px"),
                 )
-                tolerance_text = widgets.FloatText(
-                    placeholder="Tolerance", layout=widgets.Layout(width="150px")
-                )
-                accuracy_text = widgets.FloatText(
-                    placeholder="Accuracy", layout=widgets.Layout(width="150px")
-                )
                 units_text = widgets.Text(
-                    placeholder="Units", layout=widgets.Layout(width="150px"),
-                    value = default_unit
+                    layout=widgets.Layout(width="150px"),
+                    value=default_unit
                 )
 
                 # Combine widgets into a horizontal box
@@ -264,8 +254,6 @@ def display_table(change):
                     [
                         name_label,
                         value_text,
-                        tolerance_text,
-                        accuracy_text,
                         units_text,
                     ]
                 )
@@ -291,16 +279,12 @@ def submit_values(_):
             if key.startswith("req_"):
                 updated_values[variable] = {
                     "Value": widget.children[1].value,
-                    "Tolerance": widget.children[2].value,
-                    "Accuracy": widget.children[3].value,
-                    "Units": widget.children[4].value,
+                    "Units": widget.children[2].value,
                 }
             else:
                 updated_values[key] = {
                     "Value": widget.children[1].value,
-                    "Tolerance": widget.children[2].value,
-                    "Accuracy": widget.children[3].value,
-                    "Units": widget.children[4].value,
+                    "Units": widget.children[2].value,
                 }
 
         result["values"] = updated_values
@@ -327,18 +311,13 @@ def add_req(_):
             placeholder="Value",
             layout=widgets.Layout(width="150px"),
         )
-        tolerance_text = widgets.FloatText(
-            placeholder="Tolerance", layout=widgets.Layout(width="150px")
-        )
-        accuracy_text = widgets.FloatText(
-            placeholder="Accuracy", layout=widgets.Layout(width="150px")
-        )
+
         units_text = widgets.Text(
             placeholder="Units", layout=widgets.Layout(width="150px")
         )
 
         new_row = widgets.HBox(
-            [variable_dropdown, value_text, tolerance_text, accuracy_text, units_text]
+            [variable_dropdown, value_text, units_text]
         )
 
         rows_output.children += (new_row,)
@@ -354,3 +333,162 @@ def add_req(_):
     display(buttons_box)
 
     return result
+
+
+def display_formatted_answers(equations_dict):
+    """
+    Display LaTeX formatted equations and numerical results from a nested 
+    dictionary structure in Jupyter Notebook.
+
+    Parameters:
+    equations_dict (dict): The dictionary containing the equations.
+    """
+    results = equations_dict.get('results', {})
+    print("We identified the following equations that are relevant to your requirements:")
+
+    for key, value in results.items():
+        latex_equation = value.get('latex_equation')
+        lhs = value.get('lhs')
+        rhs = value.get('rhs')
+        match = value.get('match')
+        if latex_equation:
+            display(Math(latex_equation))
+            print(f"For provided values:\nleft hand side = {lhs}\nright hand side = {rhs}")
+            if match:
+                print("Provided requirements fulfill this mathematical relation")
+        else:
+            print(f"No LaTeX equation found for {key}")
+
+
+def display_results(equations_dict):
+
+    results = equations_dict.get('results', {})
+    not_match_counter = 0
+
+    for key, value in results.items():
+        match = value.get('match')
+        latex_equation = value.get('latex_equation')
+        lhs = value.get('lhs')
+        rhs = value.get('rhs')
+        if not match:
+            not_match_counter += 1
+            display(HTML(
+                '<p style="color:red; '
+                'font-weight:bold; '
+                'font-family:\'Times New Roman\'; '
+                'font-size:16px;">'
+                'Provided requirements DO NOT fulfill the following mathematical relation:'
+                '</p>'
+                ))           
+            display(Math(latex_equation))
+            print(f"For provided values:\nleft hand side = {lhs}\nright hand side = {rhs}")
+    if not_match_counter == 0:
+        display(HTML(
+            '<p style="color:green; '
+            'font-weight:bold; '
+            'font-family:\'Times New Roman\'; '
+            'font-size:16px;">'
+            'Requirements you provided do not cause any conflicts'
+            '</p>'
+        ))
+
+
+def _get_latex_string_format(input_string):
+    """
+    Properly formats LaTeX strings for matplotlib when text.usetex is False.
+    No escaping needed since mathtext handles backslashes properly.
+    """
+    return f"${input_string}$"  # No backslash escaping required
+
+
+def _get_requirements_set(requirements):
+    variable_set = set()
+    for req in requirements:
+        variable_set.add(req['latex_symbol'])
+
+    return variable_set
+
+
+def _find_vars_in_eq(equation, variable_set):
+    patterns = [re.escape(var) for var in variable_set]
+    combined_pattern = r'|'.join(patterns)
+    matches = re.findall(combined_pattern, equation)
+    return {fr"${match}$" for match in matches}
+
+
+def _add_used_vars_to_results(api_results, api_requirements):
+    requirements = _get_requirements_set(api_requirements)
+
+    for key, value in api_results['results'].items():
+        latex_equation = value.get('latex_equation')
+        # print(latex_equation)
+        if latex_equation:
+            used_vars = _find_vars_in_eq(latex_equation, requirements)
+            api_results['results'][key]['used_vars'] = used_vars
+
+    return api_results
+
+
+def get_eq_hypergraph(api_results, api_requirements):
+    # Disable external LaTeX rendering, using matplotlib's mathtext instead
+    plt.rcParams['text.usetex'] = False
+    plt.rcParams['mathtext.fontset'] = 'stix'
+    plt.rcParams['font.family'] = 'serif'
+
+    api_results = _add_used_vars_to_results(api_results, api_requirements)
+
+    # Prepare the data for HyperNetX visualization
+    hyperedges = {}
+    for eq, details in api_results["results"].items():
+        hyperedges[_get_latex_string_format(
+            details["latex_equation"])] = details["used_vars"]
+
+    # Create the hypergraph using HyperNetX
+    H = hnx.Hypergraph(hyperedges)
+
+    # Plot the hypergraph with enhanced clarity
+    plt.figure(figsize=(16, 12))
+
+    # Draw the hypergraph with node and edge labels
+    hnx.draw(
+        H, 
+        with_edge_labels=True, 
+        edge_labels_on_edge=False,
+        node_labels_kwargs={'fontsize': 14}, 
+        edge_labels_kwargs={'fontsize': 14},
+        layout_kwargs={'seed': 42, 'scale': 2.5}  
+    )
+
+    node_labels = list(H.nodes)
+    symbol_explanations = _get_node_names_for_node_lables(node_labels, api_requirements)
+
+    # Adding the symbol explanations as a legend
+    explanation_text = "\n".join([f"${symbol}$: {desc}" for symbol, desc in symbol_explanations])
+    plt.annotate(
+        explanation_text, 
+        xy=(1.05, 0.5), 
+        xycoords='axes fraction', 
+        fontsize=14, 
+        verticalalignment='center'
+    )
+
+    plt.title(r"Enhanced Hypergraph of Equations and Variables", fontsize=20)
+    plt.show()
+
+
+def _get_node_names_for_node_lables(node_labels, api_requirements):
+
+    # Create the output list
+    node_names = []
+
+    # Iterate through each symbol in S
+    for symbol in node_labels:
+        # Search for the matching requirement
+        symbol = symbol.replace("$", "")
+        for req in api_requirements:
+            if req['latex_symbol'] == symbol:
+                # Add the matching tuple to SS
+                node_names.append((req["latex_symbol"], req["requirement_name"]))
+                break  # Stop searching once a match is found
+
+    return node_names