Update app.py

app.py

@@ -52,7 +52,7 @@ def newton_interpolation_steps_latex(x, y, x_interp):
     steps_latex = []
 
     # Initial step in LaTeX
-    steps_latex.append(f"Initial value: $P(x) = f[x_0] = {y_interp:.4f}$")
+    steps_latex.append(r"Initial value: $P(x) = f[x_0] = {:.4f}$".format(y_interp))
 
     for i in range(1, n):
         term = 1.0
@@ -61,31 +61,31 @@ def newton_interpolation_steps_latex(x, y, x_interp):
         current_term_value = dd_table[0][i] * term
 
         # Construct divided difference notation in LaTeX: f[x_0, ..., x_i]
-        dd_notation_latex = f"f[x_0"
+        dd_notation_latex = r"f[x_0"
         for k in range(1, i + 1):
-            dd_notation_latex += f", x_{k}"
-        dd_notation_latex += "]"
+            dd_notation_latex += r", x_{" + str(k) + r"}"
+        dd_notation_latex += r"]"
 
         # Construct polynomial term in LaTeX: (x - x_0)(x - x_1)...(x - x_{i-1})
         polynomial_term_latex = ""
         for j in range(i):
-            polynomial_term_latex += f"(x - {x[j]})"
+            polynomial_term_latex += r"(x - " + str(x[j]) + r")"
         if not polynomial_term_latex:
-            polynomial_term_latex = "1" # For i=0 case which is handled outside loop, but for consistency
+            polynomial_term_latex = "1"
 
         # Step description in LaTeX
-        step_latex_description = f"Add term {i}: ${dd_notation_latex} \\times {polynomial_term_latex.replace('x', str(x_interp))} = {dd_table[0][i]:.4f} \\times "
+        step_latex_description = r"Add term {}: ${} \times {} = {:.4f} \times $".format(i, dd_notation_latex, polynomial_term_latex.replace('x', str(x_interp)), dd_table[0][i])
         if i > 0:
-            term_values_latex = " \\times ".join([f"({x_interp} - {x[j]})" for j in range(i)])
+            term_values_latex = r" $\times$ ".join([r"({:.1f} - {})".format(x_interp, val) for val in x[:i]]) # more robust float formatting
             step_latex_description += term_values_latex
         else:
-            step_latex_description = f"Initial value: $f[x_0] = {dd_table[0][0]:.4f}$" # Should not happen in loop, but for clarity
+            step_latex_description = r"Initial value: $f[x_0] = {:.4f}$".format(dd_table[0][0]) # Should not happen in loop, but for clarity
 
-        step_latex_description += f" = {current_term_value:.4f}$"
+        step_latex_description += r" = {:.4f}$".format(current_term_value)
         steps_latex.append(step_latex_description)
 
-        steps_latex.append(f"Current $P(x) = {y_interp:.4f}$")
-        y_interp += current_term_value
+        steps_latex.append(r"Current $P(x) = {:.4f}$".format(y_interp + current_term_value)) # Corrected accumulation here
+        y_interp += current_term_value # Accumulate interpolation value here
 
     return y_interp, dd_table_df, steps_latex
 
@@ -93,9 +93,9 @@ def newton_interpolation_steps_latex(x, y, x_interp):
 st.title("Newton's Divided Difference Interpolation")
 st.write("Enter the x and y values as comma-separated lists, and the x value you want to interpolate.")
 
-x_values_input = st.text_area("Enter x values (comma-separated):", "0, 1, 2")
-y_values_input = st.text_area("Enter y values (comma-separated):", "1, 3, 2")
-x_interpolate = st.number_input("Enter x value to interpolate:", value=1.5)
+x_values_input = st.text_area("Enter x values (comma-separated):", "2000, 2005, 2010, 2015")
+y_values_input = st.text_area("Enter y values (comma-separated):", "1000, 1040, 1032, 1025")
+x_interpolate = st.number_input("Enter x value to interpolate:", value=2001.0)
 
 if st.button("Calculate Interpolated Value with Steps (LaTeX)"):
     try: