fix(bignum): MonomialEval drops highest-degree coefficient and panics on constants

MonomialEval started Horner evaluation from poly[len-2] instead of the
highest-degree coefficient poly[len-1], so it silently ignored the top
coefficient (1 + 2x at x=3 gave 1 instead of 7) and indexed poly[-1] on a
constant polynomial, panicking. Start from poly[n] and iterate from n-1,
matching the documented y = sum x^i * poly[i].

Closes #579

utils/bignum/eval.go

@@ -7,8 +7,8 @@ import (
 // MonomialEval evaluates y = sum x^i * poly[i].
 func MonomialEval(x *big.Float, poly []*big.Float) (y *big.Float) {
 	n := len(poly) - 1
-	y = new(big.Float).Set(poly[n-1])
-	for i := n - 2; i >= 0; i-- {
+	y = new(big.Float).Set(poly[n])
+	for i := n - 1; i >= 0; i-- {
 		y.Mul(y, x)
 		y.Add(y, poly[i])
 	}

utils/bignum/eval_test.go

@@ -0,0 +1,24 @@
+package bignum
+
+import (
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/require"
+)
+
+func TestMonomialEval(t *testing.T) {
+	newFloat := func(f float64) *big.Float { return new(big.Float).SetPrec(53).SetFloat64(f) }
+
+	// 1 + 2x at x = 3 = 7: the highest-degree coefficient must not be dropped.
+	got := MonomialEval(newFloat(3), []*big.Float{newFloat(1), newFloat(2)})
+	require.Zerof(t, got.Cmp(newFloat(7)), "1 + 2x at x=3: got %v, want 7", got)
+
+	// 1 + 2x + 3x^2 at x = 2 = 17.
+	got = MonomialEval(newFloat(2), []*big.Float{newFloat(1), newFloat(2), newFloat(3)})
+	require.Zerof(t, got.Cmp(newFloat(17)), "1 + 2x + 3x^2 at x=2: got %v, want 17", got)
+
+	// A constant polynomial must return the constant without panicking.
+	got = MonomialEval(newFloat(9), []*big.Float{newFloat(5)})
+	require.Zerof(t, got.Cmp(newFloat(5)), "constant poly: got %v, want 5", got)
+}